The mathematical /
experimental theory and
practice of ship-building
improvement: Hooke,
Newton, Petty, and Du Son
M.H.J. Ultee
3549739
Thesis History and Philosophy of Science
Utrecht University
Supervisor: H.F. Cohen
29-8-2015
Index
Introduction............................................................................................................................................. 2
1.
Robert Hooke and the advantage of straight sails over bunting ones ............................................ 6
Robert Hooke ...................................................................................................................................... 7
The Cutlerian Lectures......................................................................................................................... 8
Effects of the lecture ......................................................................................................................... 14
Lampas............................................................................................................................................... 18
The intended audience ...................................................................................................................... 22
Conclusion ......................................................................................................................................... 24
2.
The Miraculous Ship of Rotterdam ............................................................................................... 26
Terror Terroris ................................................................................................................................... 27
Nicolas van Son, Mathesios sr de Lisson or Jean Du Son ................................................................... 29
International attention ...................................................................................................................... 31
The Lightning of the Sea .................................................................................................................... 32
A public attraction ............................................................................................................................. 35
Tomorrow Never Comes ................................................................................................................... 36
Watch making on a grand scale ........................................................................................................ 38
Everything is in the eye of the beholder ........................................................................................... 39
3.
A practical Newton ........................................................................................................................ 47
Newton’s references on shipbuilding................................................................................................ 49
The use of Newton’s remarks by historians ...................................................................................... 56
Conclusion ......................................................................................................................................... 66
4.
Petty’s Double Bottom .................................................................................................................. 71
The Invention..................................................................................................................................... 72
The Invention II.................................................................................................................................. 78
The Experiment ................................................................................................................................. 84
An Intermezzo ................................................................................................................................... 86
The St Michael the Archangel ............................................................................................................ 88
Conclusion ......................................................................................................................................... 92
Conclusion ............................................................................................................................................. 93
Bibliography........................................................................................................................................... 97
Primary Sources................................................................................................................................. 97
Secondary Sources ............................................................................................................................ 98
Appendix A .......................................................................................................................................... 101
1
Introduction
Francis Bacon gave two reasons for the study of nature in his New Atlantis: ‘[the reason] for
the finding out of the true nature of all things [is that] God might have more glory in the
workmanship of them, and men the more fruit in the use of them’.1 One of these reasons may
seem remarkable to our modern eye, and one would have been remarkable in the seventeenth
century. Few twenty-first century academic researchers fill in: ‘to further the glory of God’
under the heading valorisation when applying for a grant. In our modern times we do not see
the furthering of God’s glory as a task for either the sciences or the humanities. In the
seventeenth century, the remarkable part of the opening sentence was: ‘and man the more fruit
in the use of them’. In their view, investigations into nature were meant to discover the
intricacies of God’s creation. Moreover, few people in the seventeenth century could imagine
how investigations into nature could contribute to the easing of everyday life. The idea that
science and technology were two sides of the same coin was, contrary to modern times, not
prevalent at all. As a consequence the belief in science as a means for progress, which was
created through the use of theory in applications, was not present at the time. We now owe
much to science, from smartphones, TV’s and cars to microwaves, artificial light, and the
easily available paper on which these letters are printed. According to a standard historical
narrative, Bacon used applicability as a prominent point to distinguish his new philosophy
from scholastic natural philosophy and this emphasis on applicability was invoked later by
natural philosophers seeking to justify their research. The results of these natural
philosophical enquiries were immediately applied to everyday practice to the greater honour
and glory of what would become science. The notion that this interplay between science and
technology powered a flywheel of progress is so powerful because it seems so obvious to us:
we see, for example nineteenth century fundamental research on electromagnetism as the
basis for our modern use of electricity, and we look to new fundamental research to enrich our
lives even further.
In the seventeenth century such earlier examples of successful applications of science
were not yet in existence and, as a consequence, investigations into nature were not yet seen
as beneficial for mankind. This lack of existing examples to support the claim that science and
technology could be combined, undermines the classical historical narrative. The acceptance
of investigations into nature as beneficial for mankind had no reputation yet on which it could
fall back, which means that only the direct application of scientific theories could start this
1
Francis Bacon New Atlantis: A work unfinished (London 1627) 20
2
flywheel of progress. That there was not yet a tradition of science-based technology makes the
idea that this developed quite rapidly in the seventeenth century testable; the more practical
applications we can find that were derived from abstract theory, the more we will have to
accept that the march to hegemony of what we now call science was powered by direct
application of new scientific theories into practice. If, on the other hand, there is no crossfertilisation between theory and practice then it becomes interesting to see why natural
philosophers were prevented from achieving their goal. The reasons why natural philosophers
could not successfully apply their work can yield insight into the difficulties that had to be
conquered before the now all pervasive science-based-technology could come into existence.
Research into this topic has to be limited strictly. The investigation of all claims for
useful research would simply be too large a task. There are multiple ways in which the
boundaries of this research can be established. One method is to first try and identify the
greatest practical problems of the era and look to the theory-based solutions given to these
problems. Another method is to look at the greatest improvements in the everyday practice
introduced in the seventeenth century and investigate where they originated from. For this
investigation I have chosen a different method: selecting an area of seventeenth century
society and looking for a diverse range of scientific improvements proposed to improve the
everyday practice in this area. The area of society chosen in this research is an important
aspect of seventeenth century life: shipping. Maritime affairs became very important in northwest Europe during the second half of the seventeenth century. New European nations, most
notably the English and the Dutch, entered the overseas trade, laying the foundations of vast
maritime empires. An important part of these new naval empires were staple markets.
Amsterdam and, somewhat later, London would become trade hubs in which products from
over the world would be bought and sold. Competition in maritime trade led to conflict which
was largely fought out on the North Sea. This meant that any improvement in ships could lead
to advantages on the competition, both commercially and militarily.
One field of study for the improvement of maritime affairs is well-known, the search
for a reliable method to find one’s place at sea. A study of attempts to solve this problem has
been done by Karel Davids, who investigated the different solutions in the Dutch Republic
between 1585, the point in time when finding longitude at sea became a pressing navigational
concern as ships sailed an increasing percentage of their journey without any land in sight,
and 1815, when Harrison’s chronometer was used frequently in everyday shipping, solving
the problem of finding the longitude. The demarcation of this time period was also chosen
3
because it started at the de facto separation of the Northern and Southern Netherlands around
1585 and it ended with their reunification after the Congress of Vienna in 1815. The
advantage of Davids’ method is that he traces the development of one problem through a
prolonged period all the while placing the problem in the development of the field of
navigation itself. Through this he is able to compare solutions given by science with other
proposed solutions. There are also drawbacks to Davids’ method. He picked a problem which
was solved in the end, making that solution a touchstone for all earlier used improvements.
Additionally, by starting out from practice, Davids’ research method excludes those solutions
that were proposed but were never applied at all and developments are placed solely in the
context of the inquired field itself. Davids’ treatment of navigation in the period we are
investigating – done in his chapter on the period between 1650 and 1740 – shows that
although the period saw the introduction of some new ways to calculate the course that had
been sailed – for example using ‘het verbeterd bestek’2 – and some new methods tried to
measure the longitude of the ship’s position – for example the instruments of Vermase and
Van der Mast3 – there was no long-term successful results and thus no merger between theory
and practice.
Davids’ book is a good example of a description of attempts to merge science and
technology to solve one practical problem. A different method is used in H.F. Cohen’s How
Modern Science Came Into The World. Cohen takes a smaller time period and searches for
attempts to merge science and technology in different fields in that period. So instead of
Davids’ search in one field in an extended period of time Cohen searches in relatively small
time period in an extended number of fields. Cohen only looks at the seventeenth century, but
regards cases as varied as Stevin’s fortress building, musical tempering, Huygens’ gunpowder
engine and the improvement of scientific instruments.4 Cohen’s work gives a much richer
view of the attempt to improve practice by theorists, and by the diversity of the cases he
investigates he negates any criticisms that he cherry-picked his cases to give a picture
unrepresentative for the period he investigates. The drawback of Cohen’s work is that he puts
the different attempts exclusively in the context of seventeenth century society and is – by the
2
C.A. Davids Zeewezen en Wetenschap: De wetenschap en de ontwikkeling van de navigatietechniek in
Nederland tussen 1585 en 1815 (Amsterdam 1986) 165
3
Davids Zeewezen en Wetenschap 137-141
4
H.F. Cohen How modern science came into the world; four civilizations, one seventeenth-century breakthrough
(Chicago 2010) for Stevin’s fortress building see: 319; for Vincenzo Galilei’s organ tuning see: 311; for Huygens’
gunpowder engine see: 476 and for the improvement of scientific instruments see 474
4
nature of the diversity of his cases – not able to put them in the context of the fields
themselves.
The current investigation tries to combine the approaches of Davids and Cohen; it
focuses more on one area of society than Cohen’s work, giving the ability to construct a more
close-knit picture of the search in a specific part of society, while also being able to look
closer at social influences of a specific period than Davids’ work. The results of this research
can be compared to both Cohen’s results, to see if they fit in a wider trend of seventeenth
century attempts to combine science and technology as well as to Davids’ results, to see how
they compare to other improvements within shipbuilding. To build a case of diverse attempts
to improve ships or parts of shipping, the following four cases shall be treated: Robert
Hooke’s idea to use straight sails over bunting ones; Isaac Newton’s concern with the ideal
form for ships; William Petty’s fourfold effort to build double-bottomed or twin-hulled ships,
and a miraculous ship built in Rotterdam. These cases are of two sorts, the former two are
attempts to apply mathematics to improve the everyday practice of shipping and the latter two
are attempts to revolutionize the design of ships by experimental means.
The division between mathematical attempts to improve practice and experimental
ways to improve practice is a classical one. The separation is a consequence of the deep
chasms that historically have lain between experimental ways to seek knowledge,
mathematical ways to seek knowledge and philosophical ways to seek knowledge. Although
the seventeenth century is famous for the bridging of these chasms in what later would be
known as the Scientific Revolution, in the minds of theorists of that era these two methods
were still mostly separated. With this investigation we can also look whether one kind of
attempt – either mathematical or experimental – was more successful than the other, and
whether they were both unsuccessful if they struggled with the same problem.
Before we move on to the first case study, I would like to take a moment to thank
Floris Cohen, my very erudite and motivating supervisor who has shown that he is always
willing to go beyond the call of duty to aid in this research. Further I would like to thank C.
Schilt for his help on the Newton manuscript and M.F.J. Vermeulen who explained to me all
mathematics which I did not understand. As a last point I would like to thank all friends and
family and especially Eva Brokx, my girlfriend, who all had to endure my ramblings on
science, technology and naval affairs.
5
1. Robert Hooke and the advantage of straight sails over bunting
ones
There is no seventeenth century natural philosopher on which opinions diverge as
strongly as on Robert Hooke. Hooke is used by historians as an example par excellence of the
typical seventeenth century natural philosopher who could provide attentive listeners with a
plausible hypothesis, but who always stayed vague enough to be able to claim the theory as
their own whenever a dry calculator mathematically underpinned it, or to disavow ever
coming up with the theory when such a drudge proved it to be untenable.5 Another group of
historical authors describe Hooke as ‘the most important scientific figure of the period
following the Restoration’, ‘recognised by his contemporaries as their greatest
experimentalist’6 and as ‘a polymath who has never achieved the recognition he deserves’. 7 In
this view Hooke is wrongfully used in the history of science ‘to aggrandize Newton or Boyle
at [his] expense’,8 as the light by which Newton’s star shines the more brightly in comparison.
Most studies which involve Hooke focus either on Hooke’s accomplishments relative
to the accomplishments of his contempories or take him as a poster child for a certain era of
English scientific thinking. This study, in contrast, wants to view Hooke in what he attempted
to do and what he was known for at a later stage, as one author describes it: ‘More than any
other scientist of his day Hooke turned his skills to practical ends, directing the rebuilding of
the centre of one of Europe’s greatest cities, designing and constructing colleges, hospitals,
churches, suburban mansions and West End town houses, and discovering and publicizing a
range of important craft skills in pottery, glassware, metalwork and textiles. The mighty
Monument, still standing straight on its clay and gravel foundations after over three hundred
years, was not the work of a laboratory-bound eccentric.’9 This study wants to look at Hooke
as a bridge between the abstract world of theory and everyday practice, or to place it squarely
in the scope of this study: has Robert Hooke contributed something substantial to the practice
of sailing? Before we can look at this question a brief introduction of Hooke is in order.
5
H.F. Cohen Isaac Newton en het ware weten (Amsterdam 2010) 9
Margaret ‘Espinasse Robert Hooke (London 1956) 2
7
Jim Bennet et al. London’s Leonardo: The life and work of Robert Hooke (Oxford 2003) xi
8
Mordechai Feingold, ‘Robert Hooke: Gentleman of Science’ in: Michael Cooper and Michael Hunter (ed.)
Robert Hooke: Tercentennial Studies (Aldershot 2006) 203-217, 203
9
Stephen Inwood The Man Who Knew Too Much (London 2002) 441
6
6
Robert Hooke
Robert Hooke was born in Freshwater on the island of Wight on the 28th of July 1635
according to the Gregorian calendar.10 At the age of thirteen Hooke lost his father and the
same year he left his parental home to move to London. In London he enrolled in the
prestigious Westminster School, headed by Dr Richard Busby. At the Westminster School
Hooke’s fellow pupils included John Dryden, who would become a successful playwright,
and poet; John Locke, a budding philosopher; and Robert South: a future theological critic of
the new sciences. After his graduation from the Westminster School in 1652, Hooke moved to
Oxford where he continued his education as a chorister and a servitor at Christ Church. The
Oxford at which Hooke arrived was a rejuvenated one, it had benefitted greatly from the
ousting of royalist professors by Cromwell in 1648. The seats left vacant by the ousting were
filled by enthusiastic men of a more suitable political inclination. One of these new
professors, John Wilkins, formed a philosophical group around himself of which Hooke
became a member. Through this philosophical gathering Hooke was introduced to the wealthy
seventh son of the first earl of Cork, Robert Boyle. Boyle employed Hooke to work in the
former’s new laboratory, where the aim was to combine two experiments that were
challenging the Aristotelian concept of the absolute lightness of the air.
Void in the void
Boyle wanted to combine experiments of Torricelli and von Guericke into what would
become known as the void in the void experiment (the Torricellian void in the void of von
Guericke). With this experiment Boyle wanted to find out what would happen to the height of
the mercury in a tube when all the air was evacuated from the container the contraption was
in. There were a number of practical problems that Boyle had to overcome, first of all the
machine of von Guericke had to be made suitable for his experiment. Another problem was
that the machine had to be airtight; any leakage of air into the machine would distort the
outcome of the experiment. Quite a lot of alterations were made to von Guericke’s air-pump
before it was in accordance with Boyle’s wishes. In Boyle’s design the number of operators of
the machine was reduced from two to one; and von Guericke’s two famous hemispheres were
replaced by a glass container so people could see what happened to the Torricellian space
10
While the Gregorian calendar had been introduced in 1582, its origin as a papal invention made many
Protestants reluctant to adopt it. The most important Dutch regions adopted the new calendar early on, the
English only switched in 1752. In the intermediate period dual dating was common, the English calendar being
ten days behind the Dutch. All days are according to the Gregorian calendar unless otherwise specified.
Furthermore the English New Year started on March 25th, so February 1st 1653 in England was equal to
February 11th 1654 on the continent.
7
inside it. This glass container had a lid through which the Torricellian experiment was
lowered in the container and through which it could be operated. This lid was an important
feature of the air-pump because it was one of the main points through which air could leak
into the container, distorting the outcome. Boyle ordered a modified air-pump from the
instrument maker Greatorex, who was unable to make the device Boyle required. The young
Hooke then received the task that Greatorex couldn’t complete. Hooke managed to build a
working pump, or in his own words he ‘contrived and perfected the air-pump for Mr Boyle’11,
stating that the version of Greatorex was: ‘too gross to perform any great matter.’
The experiment itself is later described by Boyle as the seventeenth in his book: New
experiments physico-mechanical, touching the spring of the air.12 According to his account
the experiment of Torricelli was performed after which it was lowered into the air-pump.
Every suck which evacuated air out of the glass container lowered the level of mercury; it
started from a height of 29 inches above the bowl and would not go lower than one inch
above the bowl, a position that was reached after approximately fifteen minutes of pumping. 13
With the void in the void experiment Hooke started to make a name for himself. This
reputation made it possible for him to sustain himself when he moved back to London after
his graduation from Oxford. Hooke sustained himself through his work as an experimenter
and through a number of other jobs. His most notable positions were as the first curator of
experiments for the Royal Society and as a city-surveyor and architect during the rebuilding
of London after the great fire of 1666. Hooke operated from London for the rest of his life,
living in a few apartments at Gresham College. He died there on the 3 rd of March 1702/3
following the Julian calendar – March 13th 1703 according to the Gregorian calendar – at the
age of 68.
The Cutlerian Lectures
One of the positions Hooke held, besides those of city surveyor and curator of
experiments for the Royal Society, was that of Cutlerian lecturer. These lectures were named
– unimaginatively – after their sponsor: John Cutler, a merchant and financier specializing in
lending money to impoverished landowners on the security of their estates. After Cutler heard
from Robert Hooke that Hooke had failed to obtain the position as Gresham Professor of
Geometry he offered to match the £50 annual salary for Hooke if he started a new
11
Robert Hooke Posthumous Works of Robert Hooke Richard Waller ed. (London 1705) iii
Robert Boyle New experiments physico-mechanical, touching the spring of the air (Oxford 1660) 106-129
13
Steven Shapin & Simon Schaffer Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life
(amended edition; Princeton 2011) 40-43
12
8
professorship at Gresham concerned with the history of trade. According to Hooke’s contract
with Cutler, the lectures were to be given once a week during vacation time, sixteen weeks a
year. These lectures have been gathered and published by Richard Waller in 1705, two years
after Hooke’s death, under the title Posthumous works of Robert Hooke. The work was
dedicated to the council and fellows of the Royal Society and explicitly to the then president
of the Royal Society: Sir Isaac Newton. The lectures had a wide variety of topics which
ranged from: ‘whether the sands of Arabia and Egypt are Sea-sand’ and ‘a ship found in a
lake in Italy’ to lectures about ‘the æther as the cause of gravitation’ and ‘the nature of light’.
One of the lectures in the book is called: ‘A Lecture of the preference of strait to Bunting
Sails’ and it was first given on March 16th 1690. This lecture is interesting because it pits the
theoretical wisdom gathered by Hooke against the received practical and age old wisdom of
seamen. If Hooke´s contribution was adapted by sailors, it would be a significant contribution
from theoretical knowledge to the everyday practice of sailing. Hooke knew very well that his
new design would provoke opposition from: ‘not only all the Architects or Ships Builders, but
the Crue of Navigators also’,14 and he attributed this opposition not to a lack of value in his
work but to the inherent conservatism of these craftsmen, who were not to be swayed to
change their point of view than at ‘gradatim’,15 by length of time and by dear bought
experience.
Before we can look at the arguments brought forward by Hooke in this lecture, a
remark has to be made about the terminology he used. Concepts that are clearly and narrowly
defined in our time, concepts such as gravity and weight, were not clearly defined in Hooke’s
time and as a consequence are used without much exactitude. Hooke’s ambiguous use of a
number of these terms give room to interpret his work in a variety of ways and the way
different concepts are viewed by a later author is, as we will see, an important basis for the
way Hooke is viewed. A good example for the confusion that can arise through Hooke’s
terminology is his use of the term weight. Not only does Hooke use weight to represent the
modern concept of mass – nowadays expressed in kg – or the modern concept of weight –
which is mass multiplied with the free-fall acceleration (g) and is in modern physics
expressed in Newton – there are also instances in which Hooke uses the term weight were we,
probably, would use the term torque – which is measured in the unit Nm. Because the
interpretation of these terms influence the way in Hooke is viewed, we will look at them, and
modern interpretations of them, with some more detail. To understand the problem more
14
15
Robert Hooke Posthumous Works 564
Ibidem 564
9
thoroughly it would be convenient to look at these terms in the way Hooke presented them,
this is why I will try not to create any false clarity by replacing Hooke’s terms with terms
which he probably meant. I will refrain from this both when quoting Hooke, and when trying
to explain his method, it is best that we let the ambiguity last until we have seen it in action.
In his lecture, Hooke argues that when sails are in an oblique position towards the
wind – all cases except headwind and tailwind – ships will sail faster with sails that stay
completely straight when the wind blows against them, then when they are allowed to billow,
a notion contrary to the everyday practice used since time immemorial. To convince his
audience of this new theory, Hooke ventures on a number of detours. He starts his lecture by
introducing two great and universal powers namely gravity – ‘a Theory which I had the
happiness first to invent’, a statement which appears uncensored in the book dedicated to
Newton16 – and light. After a brief discussion of the experiments done to search for these
powers Hooke introduces a third power: ‘a third Power of Nature arising from the motions of
the Air and Water, two fluid Mediums which encompass the Body of the Earth’. 17 Hooke
needed this, in our view ill-defined, power of wind and air because it encompasses all
‘powers’ which play a role in the mechanics concerning the movement or regulation of ships
and vessels. The inquiry into the power of air and water served a direct and practical goal
according to Hooke: it would be ‘of great use for Merchant Ships in those times of danger, to
know the best Methods and Means of making these Powers the most serviceable to them that
may be for flying [i.e. fleeing] from and escaping the pursuit of their Enemies.’18 Whether or
not this claim reflects a general concern of Hooke is beside the point here. It could be that he
only used this proposed practical application to link his subject to the history of trades, or it
could be a sincere concern, what we in any case should take away from this introduction is
that Hooke justified his research by invoking possible practical uses for his theory.
Hooke considered many aspects of the ship in order to increase its speed: the shape
and size of the vessel, with consideration for its use and design; the manner of rigging and
fitting it with masts, sails and other tackle, while considering the shapes and magnitudes of
each and the ways of applying and using them to the best advantage; the power of wind and
water on the sails, masts, rigging and hulk of the vessel and on the rudder, oars, leeboards,
keel, head and sides. To these influences of air and water, especially concerning the aspects
concerned with the propulsion of a vessel, Hooke devoted this lecture for he feels that ‘it must
16
Robert Hooke Posthumous Works 563
Ibidem 563
18
Ibidem 563
17
10
be determin’d what quantity of Sails this or that kind of Vessel will bear; and what the form
of the Sail is best to be, and how to be order’d or fitted to the Vessel; how much Ballast such
Vessels so built and rigged, will require, and what strength of Wind each kind of Vessel can
indure; what the strength of the Wind is with relation to its swifter motion or higher blowing;
what strength and length of Oares is necessary for induring the powers to be apply’d to them;
and what Powers, whether of Men, or other, can be apply’d; and what are the best and most
advantageous ways for such applications’.19 From this list of things to investigate Hooke
focuses himself in this lecture exclusively on ´the form of the Sail […] and how [it had to be]
fitted to the Vessel´.
The strength of the wind is perpendicular to the said sail
Hooke starts the main section of his lecture by stating that fluid bodies, when moved,
impress a motion to other bodies against which they are moved proportional to their ´Gravity
and Velocity´.20 He continues by claiming that air must be seen as a fluid body, or, to be more
precise, as a ponderous fluid body whose integrant parts have both bulk and weight. To
investigate sailing, Hooke looks at the ratio between the ´Gravity and Velocity´ of air and
water, which is one of 1 to 800 or 900 according to him, meaning that ‘28,3 times as much
Air in bulk mov´d against the Recipient Body as there is of the bulk of Water in the same
time, and that the Velocity be 28,3 swifter than that of the Water […] will produce an equality
of Motion´. By looking at the equilibrium between the water and the air Hooke presents this
problem of a ship moving through the water with help of the wind, as an old, abstract and
well-known problem in mechanics namely as a balance problem with solids formalised by
Archimedes of Syracuse as the law of the lever (287 BCE -212 BCE).
After presenting the problem as one about equality of motion Hooke transfers his
attention to collisions. After the casual remark that all ponderous fluids consist of small
particles – ‘For a fluid Medium, in motion, is to be consider’d as made up of an indefinite
number of small Cylinders, Prisms, Wires or Strings lying close together’ 21 – he argues that
‘the Body struck receiveth a motion Perpendicular to the Surface of it that is so struck’,22
while the striking body is redirected from the body struck at an angle equal to the angle of
incidence. Hooke built his theory on this argument so we will look at it detail. Why the body
19
Robert Hooke Posthumous Works 563-564
Ibidem564
21
Ibidem 565 NB although this remark is not crucial for Hooke’s argument, nor was it controversial for the time
(1690), it does signify the fundamental change in attitude towards the atom theory during the seventeenth
century.
22
Ibidem 565
20
11
struck obtains a motion that is perpendicular to its surface is explained by use of geometry.
Besides being an important part of the argument it also is the only extensive use of
mathematics by Hooke in this lecture, as well as the only figure (figure 1.1) used by him. It is
at this point in Hooke’s argument that theory appears on stage.
Figure 1.1 Hooke’s illustration of his proof that wind hitting sail at oblique angles creates a movement perpendicular to
the sail. This is an amended version of the figure published the posthumous work of Robert Hooke it is, contrary to the
original not to scale; source: Michael Cooper and Michael Hunter (ed.) Robert Hooke: Tercentennial Studies 103
The first axiom postulated by Hooke is that when a prism of air moves against a sail
whose surface stands perpendicular to that prism, all of its power is transferred to the sail.
When, however, a prism of wind collides with a sail whose surface is at an angle oblique to
the direction the prism is travelling in, not all its power is transferred to the sail. To compute
the power given by the wind to the sail when they are at an oblique angle Hooke only takes
that component of the length of the sail which is at right angles with the wind. This means that
Hooke regards the sail as only having the size that he would see when he looked at the sail
from the point the wind is blowing when he lost his depth perception. In figure 1.1 this means
that the sail between EF is projected as either a sail between PF, a sail between ER, a sail
between QL or a sail between KI. In the following paragraphs we will take an in-depth look
into the geometrical proof of Hooke, I advise those readers who are not the least interested in
geometry or think they will only get frustrated by it – although the geometry is not
12
particularly hard and requires attentive reading more than anything else – to move on to the
last paragraph of this section.
We will start with the case that the sail and the wind are perpendicular to each other –
all letters are represented in figure 1.1, only the letter M has fallen off but is supposed to be at
the intersection below B. We take a sail between AB and we let a prism of air be represented
by the rectangle ABCD moving from DC to AB with a given speed. Additionally, we suppose
the rectangle ABNO to ‘represent a Prism of Water, equal Base with the said Sail AB, and
that AN […] the length of the said Prism be
1
30
of the length AD’. If the speed of the wind
going from DC to AB is 30 times greater as the motion of water going from NO to AB the sail
will not move either way according to Hooke: ‘because the same power is imprest on the Sail,
whether the Cylinder of Water be mov’d against the Sail from NO to AB, or the Sail be
mov’d against the Water from AB to NO; if the said Cylinder of Air be made one degree
swifter, it must drive the same Sail from AB, to NO’.
In Hooke’s scenario the ship changes course at this point and the sail represented by
AB earlier is now represented by EF, with the wind still coming from DC. It is at this moment
clear that only the wind that blows between the lines HK and GI (only the prism EFGH) hits
the sail. The power of this wind on the sail EF in comparison with the wind on the sail AB is
equal to AB:KI, which is equal to the sine of the angle ∠PEF (the angle at point E made by
the lines PE and EF) which is
𝑃𝐹
𝐸𝐹
. From this Hooke concludes that the ratio between the
amount of wind hitting the sail at a perpendicular angle and the amount of wind hitting the
sail at an oblique angle is equal to the sine of the angle that the oblique sail has with the
incoming wind. Now we know, Hooke argues, that the power on EF is the same as the power
on FP, we can conclude on the basis of similarity that the power on EL is the same as the
power on FL (this can be seen because ∠PEF is equal to ∠EFL and both ∠FPE and ∠LEF are
right angles). Hooke argumentation ends by stating that when one imagines a cylinder of air
PFHG moving from HG to PF that similarity dictates that in the same time that PF is moved
to QL that FE is moved to LM (this seems to be because Hooke assumes that PF*FL is equal
to EF*EL which is geometrically correct: PF*FL=PF*EF*(the magnification ratio of the two
triangles ΔPEF and ΔEFL) which is the same as EF*EL because EF*EL=EF*PF*(the
magnification ratio of the two triangles ΔPEF and ΔEFL)). This confirms in Hooke’s eyes
what he wanted to show, that when wind blows obliquely on a sail the sail is moved
perpendicular to its surface.
13
Now that it is geometrical proven that the ‘strength or power of the Wind upon the
Oblique Sail is Perpendicular to the said Sail’,23 Hooke is ready to draw the conclusion of his
inquiry. He argues that when we accept that the wind moves a sail perpendicular to its surface
it is a logical conclusion that a strait sail is better than a bunting one. This is because with a
straight sail the perpendiculars of all parts of the sail, point in the same direction and so the
wind moves all these parts of the sail in the same direction. When you use a bunting sail not
all parts of the sail point in the same direction and because the wind always moves a part of a
sail perpendicular to its direction different parts want to go in different directions partially
counteracting each other. Furthermore when using a bunting sail the part that is the furthest
away from the direction from which the wind is coming will receive the most wind and thus
will pull the ship off course, a motion that is only partly counteracted by the part of the sail
which is closest to the wind, this part receives the smallest amount of wind but through its
inclination tries to pull the ship off course in the other way. The conclusion is simple
according to Hooke: the sail provides the most ‘power’24 when all parts of the sail work
together harmoniously and the only case when this happens is when the perpendicular of all
parts of the sail point in the same direction which is only when a sail is straight. This is why,
according to Hooke, sailors should use a straight sail and not a bunting one.
Effects of the lecture
History would teach that, as Hooke lamented at the beginning of this lecture, seaman would
not be convinced and would not put his idea into practice. The question here is in what way
Hooke’s argument lacked the power to convince the seamen and their superiors. To find an
answer we should look at the contents of the lecture itself and the audience intended.
The lecture itself
The lecture, held at Gresham’s College, works from the abstract towards the more
specific. It starts, as we have seen, with vague and universal powers and zooms in towards the
specific case of effect of wind on a sail. To come to this conclusion Hooke not only uses
rhetorical arguments but also gives a substantial geometrical account. The geometrical
argument is at the heart of Hooke’s reasoning, with the knowledge in hand that the ‘power’ of
the wind always works perpendicular to the sail Hooke swiftly concludes that wind power is
used with maximum effect when all of the sail is pointing in the same direction. There are,
however, a number of issues with the geometrical proof Hooke delivers. First of all the whole
23
Robert Hooke Posthumous Works 566
Ibidem 567
24
14
proof of Hooke hinges on the assumption that in the same time a sail at PF would travel along
the line FL that a sail at EF would travel along the line EL (see figure 1.1). Although there is
sound geometrical proof to support this claim, it remains unclear if to approach the problem
geometrically is a useful way of viewing it, let alone if this makes the result applicable to
practice.
Hooke complicated his proof further by his unclear references to his object of study.
Although this is not uncommon for seventeenth century natural philosophers, the vagueness
on what precisely his object of study was complicated matters for Hooke, because where he
started out talking about ships and vessels, he later, at the crucial moment, spoke about sails.
While this might look like I’m straining at gnats, there is a big difference. If Hooke meant the
whole ship when he used the term sails then he has to take into account which part of the ship
causes the ship to go towards a certain direction, in other words he also has to account for the
hull, the rudder and the effects of the water upon them.
When Hooke, on the other hand, only meant the sail itself by using the term sail then
he only argues that the angle between the surface of the sail and the incoming wind
determines which way the sail will move. Although this last interpretation seems
unproblematic, it is not. In the case that he only intended the sail itself, Hooke would be
investigating the irrelevant case of a sail unattached to a vessel and a thought experiment will
show further problems. Picture yourself in a boat on a river, with the boat using straight sails.
Each sail is attached to a frame, made of light material which keeps the sail perfectly straight
while not being too heavy to drag the sail down. The wind is coming from an oblique angle to
the way you are going. Now, all of a sudden you hear the snapping of ropes. All ropes holding
one of the frames with a sail in place have broken at precisely the same time and the frame
with the straight sail in it is free to go wherever it wants to go. If Hooke was talking only
about the sail in his lecture then the frame would keep moving in the direction it was already
positioned in, regardless of the direction of the wind. For, in this case, it is the sail that
harnesses a part of the power of the wind and redirects it to move in the direction
perpendicular to the surface of the sail, while the wind is unable to change the orientation of
the sail. This will lead to the strange situation that the sail with its frame will be doomed to
keep travelling on the same straight line on the globe, for the sail will always redirect the
incoming force of the wind towards a line perpendicular to its surface. Not only reasoning
along the lines of this thought experiment could convince Hooke’s listeners that there was
something wrong with his argument, but also the fact that Hooke did not account for the drift
15
of the ship, a phenomenon already well known in 158525 – the phenomenon that the ship
could be blown of course by side wind – and in fact implicitly denied its existence was a
source for scepticism.
S.H. Joseph has correctly noted, in his treatment of this lecture, that Hooke considers
the case where ‘the sail’ is set at an arbitrary angle to the ship’s course, but that he does not
give an analysis of it. This is, according to Joseph a show of caution on Hooke’s account.26
This abstinence of Hooke is a pity; the case in which the sail is set at an arbitrary angle to the
way the ship was sailing would have been very insightful for Hooke’s use of the term sail. In
the case that Hooke’s analysis showed that there would not be a difference in the direction
‘the sails’ would be pushed by the wind and the path the vessel was travelling, then Hooke
meant the whole ship when he mentioned ‘the sail’ in his account. The power of the wind has
to contribute to the ship’s direction or else the ship would change course; this is problematic
however for the idea that the power of the wind will always be perpendicular to the sail, the
sail being at an oblique angle to the way. When the sails were pushed in a different direction
than the ship they were on, we would have known that he had regarded only the sail in his
geometrical proof.
The problem with the interpretation of what Hooke meant, when he used the term sail,
is clarifying for the way different interpretations shape the way in which Hooke is seen by
modern historians. Richard Westfall writes in a 1983 article rather dismissingly about
Hooke’s lecture. Westfall takes issue at the sentence in which Hooke states that when a
column of air, with a volume of 30 and a speed of 30, moves against a sail, while a prism of
water, with a volume of 1 and a speed of 1, moves against the sail from the other side, that
then the sail will be in equilibrium due to the fact that the ‘gravity’ of the water is as to the
‘gravity’ of the air as 1 to 900. From this sentence Westfall concludes that if both wind and
water push against the sail at the same time ‘the ship must sail right side up and upside down
at the same time’ which he finds to be ‘a difficult posture in the best circumstances, and one
perilously close to the vulgar notion of shipwreck’.27 After this dismissal Westfall ignores
Hooke’s geometrical proof that wind works perpendicular to the sail of the vessel, he takes it
as an axiom from which he explains the rest of Hooke’s reasoning. Westfall attributes the, in
his vision, poor quality of the lecture to the fact that Hooke ‘was an old man in decline when
25
Davids Zeewezen en Wetenschap 60-61
S.H. Joseph ‘Assessment of the Scientific Value of Hooke’s Work’ in: Michael Cooper and Michael Hunter
(ed.) Robert Hooke: Tercentennial Studies (Aldershot 2006) 89-108, 104
27
Richard S. Westfall, ‘Robert Hooke, Mechanical Technology, and Scientific Investigation’, in: John G. Burke
(ed.), The Uses of Science in the Age of Newton (Berkeley 1983) 85-110, 98
26
16
he produced it’ and finishes his analysis with the bane of Hooke’s legacy: a comparison with
Newton stating that ‘the propositions on the resistance of fluids, the most analogous parts of
Newton’s Principia, were also its weakest sections’.
Although Westfall’s analysis shows an identification of where a major problem lies in
Hooke’s argumentation – to wit his problem of clearly defining his object of study – the
concise way in which Westfall’s analysis is written down gives the feeling that he dismissed
Hooke’s line of reasoning too quickly. Westfall takes a single term, ‘sail’ to dismiss Hooke’s
lecture, while this term can, without heavy intellectual strain, be seen to mean the vessel as a
whole in this context. It is therefore not Westfall’s conclusion that ‘[s]cience did not then
have in its power the tools to answer correctly the question Hooke posed’ with which I
disagree – on the contrary – but what I object to is that this conclusion is hardly supported by
Westfall in this article because he dismisses Hooke’s reasoning on a technicality.
A different opinion on Hooke’s lecture can be found in an article by the earlier
mentioned S.H. Joseph. Joseph focuses on both the theoretical value of Hooke’s lecture and
on the problems of translating it into practice. Joseph’s article particularly praises Hooke’s
idea that the balance between the power of the wind and the resistance of the water
determines the speed of the ship, and he praises those parts of Hooke’s lecture where he gives
answers which are used to this day, most notably: ‘this assumption is still made in fluid
mechanics in the present day; indeed, the calculation of drag on a bluff body is now done
using the same formula together with an empirical drag coefficient’28 and later ‘his conclusion
that a straight sail performs better is one shared by yachtspeople today’. 29 This focus on what
we still retain from Hooke’s lecture is anachronistic. Although it is laudable that the way
Hooke calculated drag resembles the method still in use today, it does not mean that the
outcome of the two calculations – those of Hooke and modern physicists respectively – are
similar. It would be a fallacy to assume that they are both based on the same theoretical
foundations, because modern calculations must be placed in a context which includes
Newton’s Principia and both of Einstein’s relativity theories. Another historiographical sin is
that Joseph should know that it should not matter what the opinion of yachtspeople is on
straight sails, for the same reason we do not credit Jean Baptist Lamarck with the discovery of
evolution, it is filtering historical texts through our modern knowledge and regarding only the
filtrate, regardless of the way it was obtained. That Aristarchus believed that the earth
revolved around the sun does not mean that he had the same arguments as Copernicus and
28
29
Joseph ‘Assessment of the Scientific Value of Hooke’s Work’ 102-103
Ibidem 104
17
Galileo later had. To present anonymous modern day experts to agree with Hooke is
describing a history of winners and losers without any regard for the historical context in
which Hooke presented his arguments.
To be sure, this principle works both ways, the analysis of Hooke’s lecture in this
chapter is therefore not meant to show why modern readers should disregard it – to do that it
should have sufficed to show that vector addition dictates that you should add all
perpendiculars of all infinitesimally small parts of the bellying sail, which would give you a
force comparable to that of a straight sail while negating the sideward movement – but that it
was a lecture which can be dismissed using seventeenth century knowledge, knowledge which
was available for listeners at Hooke’s lecture.
Lampas
Hooke’s lecture on the advantageous of straight sails was not his only work on which
modern authors hold fundamentally different views. Another work on which opinions differ
concerns itself with producing steady flames, or rather, with devising a lamp which would
burn steadily. The work, published in 1677, bore the title: Lampas: or a description of some
Mechanical Improvements of Lamps30 and it is not only interesting because it is a good
illustration on the division of opinions on Hooke; it has
an important topic as well. The steady burning of a
P
A
D
flame was not only helpful for lighting rooms it was
important for a variety of chemical experiments. Only
with a well regulated flame, i.e. a steady and continuous H
heat source, could heating processes be well regulated.
Z
O
This new lamp was intended to be an early modern
equivalent of a Bunsen burner. This makes the
contrivance of such a lamp not only important for
B
C
R
further investigations into chemical reactions, it also
puts this lamp squarely in the category of instruments
used to further investigations into nature. This category
also includes the telescope, the microscope, and the airpump, instruments through the use of which Hooke
received most of his fame. Moreover, scientific
Figure 1.2 Hooke’s lamp Source: ‘The Cutler
lectures of Robert Hooke’ 208
30
Robert Hooke ‘The Cutler lectures of Robert Hooke’ R.T. Gunther (ed.) Early Science in Oxford vol. VIII (Oxford
1930) 155-208
18
Figure 1.3 Hooke’s lamp Source: ‘The Cutler
lectures of Robert Hooke’ 208
instruments form the one category from the seventeenth century in which there are examples
that theory has demonstrably improved practice. That it were scientific instruments that were
improved by science-based technology is not remarkable, only in this category were the
craftsmen making and operating these instruments the same people as the theorists devising
improvements for them.
The device envisioned by Hooke was intended to be a hollow spherical container
divided in equal halves by a diaphragm which could pivot around an axis through its centre
(the axis is drawn perpendicular to the paper in figure 1.2 and is indicated by the letter O) the
bottom half would be filled with oil and the top half would be a counterweight (in figure 1.2
the oil is the dark substance between O,B and Z in the figure and lower left half is the
counterweight, everything below the line that goes from A to B). In modern terms the idea
behind the lamp was that when oil was used by the flame the amount of oil would lessen, this
meant that the liquid would push less on the counterpoise (the left side), which made the
centre of gravity of the counterpoise descent, and as a consequence of that rotated the
counterweight around the axis and raising the oil. Simply put the counterweight raised the
liquid and kept the top layer of oil at the same point, providing a constant amount of fuel for
the flame to use.
This lecture of Hooke has, not unlike his lecture on straight over bunting sails, been
interpreted differently by different modern authors. Westfall starts his analysis with the
comment that Hooke had his concepts mixed up: ‘[he] consistently used the word weight
where the word (or the concept) moment was needed’ to which he somewhat later adds that
Hooke again ‘used the word weight, this time in place of specific gravity (or its equivalent)’.31
But as Westfall insightfully continues this should not be held against Hooke for ‘[t]he science
of mechanics was still sorting out the elements of circular motion. Newton, who did much to
clarify them, made at least one egregious blunder in a similar problem in the first edition of
the Principia’.32 Westfall becomes more critical in his commentary after this point, especially
on the way Hooke intended to make his counterpoise workable in practice. The problem with
the use of the counterpoise by Hooke is that in order for the system to work, the counterpoise
should have a volumetric mass density – the mass per unit of volume (kg/L) – that is half that
of the oil. It would be very difficult for Hooke to find a counterpoise that had exactly half the
density of the oil – Westfall is ‘inclined to say impossible in that age’33 – and it would mean
31
Westfall, ‘Robert Hooke, Mechanical Technology, and Scientific Investigation’, 96-97
Ibidem 96
33
Ibidem, 97
32
19
that at every refilling the new oil would have to have exactly the same density as the previous
batch or, alternatively, that at every refilling a new counterpoise had to be made. Hooke
anticipated this remark and tries to circumvent this problem by stating that the counterpoise
could be replaced by a hollow float with weight suspended from the line that bisects it.
According to Westfall this replacement ‘[o]bviously […] would not have worked’34 because
‘[a] counterpoise made in this manner would have been in the equilibrium Hooke desired only
in two positions –when the lamp was completely full before it was lit, and when it was
completely empty after the flame had gone out’.35 For Westfall this problem makes the
scientific analysis in Hooke’s lecture ‘an illusion covering a misconception that flowed from
the current level of the science of mechanics.’36
Joseph has, similar to their respective views on Hooke’s work on straight sails, a view
quite different than Westfall’s on Lampas or rather: Joseph spends a majority of his
discussion of Lampas disavowing the earlier treated comments of Westfall. Joseph’s first
remark is that Hooke ‘uses the verb “counterpoise” consistently throughout to describe the
action of a turning moment, and “weight” to describe the weight of an equal volume, that is
density’.37 Joseph continues with attacking Westfall’s comments on Hooke’s plan to use a
hollow float with a weight in it as a counterpoise. He argues that so long the total mass is the
same and the centre of gravity of the hollow float and the weight in it coincide with that of the
earlier proposed counterpoise – which had half the density of the oil – the counterpoise
system would still work. As a last point he quotes Hooke in the explanation of his system ‘Let
there be a counterpoise … fixed somewhere in the line PO, so that the said upper [solid]
Hemisphere shall have half the gravity of the under [liquid filled] Hemisphere upon the
Center of motion O’.38 Joseph accuses Westfall of ignoring the phrase ‘upon the Center of
motion’ and concludes that ‘Hooke not only understands moments about a centre but employs
the concept of centre of gravity, which appear to be beyond Westfall’s knowledge of
mechanics.’39
The opinions of Westfall and Joseph are so far apart that it is not difficult to give a
more nuanced view by looking at their arguments. Westfall claims that Hooke used the term
weight for either the concept moment or the concept specific gravity and Joseph claims that
34
Westfall, ‘Robert Hooke, Mechanical Technology, and Scientific Investigation’, 97
Ibidem97
36
Ibidem 97
37
Joseph ‘Assessment of the Scientific Value of Hooke’s Work’ 99
38
Ibidem 99; taken from: Robert Hooke ‘The Cutler lectures of Robert Hooke’ 166
39
Ibidem 99
35
20
Hooke consistently uses the term weight for the concept density, while he also consistently
uses the verb counterpoise. It is true that Hooke used the verb counterpoise consistently and
that he used weight where he meant density or specific gravity – specific gravity is after all
nothing else then an expression of the density of a substance relative to the density of a
reference substance – but the question remains if that means something. There were no clear
and well established definitions of physical properties when Hooke wrote this lecture: not for
density, not for weight and not in the least for moment – which is closely related to the
notoriously vague seventeenth century concept of force, a concept so vague that it is known in
history of science as the force knot40 – these concepts only became clearly defined with the
help of Newton’s Principia. So although it is laudable that Hooke used terms consistently,
modern historians cannot deduce much from that fact and especially not if Hooke was
knowledgeable about modern concepts, for example moments about a centre, for we do not
know what Hooke meant by those terms. Even when those concepts are concerned which
seem to have clear modern equivalents such as in the case of the replacement of the term
weight with the term density, we cannot know if Hooke had a concept of weight which
resembles, or even comes close to, our notion of density, not in the least because, as one
historian has put it, Hooke had ‘that very special ability to miss his own point’.41 The remark
of Joseph on Hooke’s use of the term centre of gravity is an enlightening example. In modern
physics the term centre of gravity denotes that point which is the weighted average for the
position of all mass points which make up a body. If, in modern physics, we look at the effect
that the force of gravity has on an object, we may imagine, for the large majority of cases, that
all the mass of that object is concentrated in the centre of gravity without having to fear that
the calculation would be any different than if we calculated the effect of the force of gravity
on every individual atom and added up all those individual effects. This, or any similar idea,
can impossibly be distilled from the lecture of Hooke because gravity was only vaguely
understood in the pre-Principia time this lecture was given in. There are also other clues that
make it unlikely that Hooke actively used the concept centre of gravity. We find these clues
by looking at the moments in his lecture when Hooke used centre of gravity, and especially
when he didn’t use it. Hooke used centre of gravity once, to describe why the heavier oil
would remain in its place in the case that the lower half of his sphere was filled with oil and
40
See: Richard S. Westfall Force in Newton’s Physics. The Science of Dynamics in the Seventeenth Century
(London 1971); for problems with definitions of force in the Principia see: E.J. Dijksterhuis De Mechanisering
van het Wereldbeeld (7th print: Amsterdam 1996) 515
41
Cohen Newton en het ware weten (Amsterdam 2010) 123
21
the lighter counterpoise filled the upper half of his spherical lamp.42 After Hooke’s
description of that situation he lights his imaginary lamp and describes three more situations,
the first when the flame has burnt up a quarter of the hemisphere of oil, the second is when
there remains a quarter sphere of oil and the last when there is only an quarter of the original
oil left – to wit an eight of a sphere of oil. In these last three cases, which are less obvious
than the first one, the centre of gravity is not used anymore, neither explicitly nor implicitly.
Hooke uses the same type of geometrical arguments as in his lecture on straight sails (see
figure 1.2): ‘the Wedge COR of the Liquor doth counterpoise the Wedge ROB [of the liquor]
on the other side the Perpendicular, and that the Wedge POD of the upper Hemisphere doth
counterpoise the Wedge POA [of the upper hemisphere] on the other side of the
Perpendicular, so that neither of these have any prepollency to move the Globe out of this
Posture. Next, it is plain that the Wedge BOZ of the Liquor will be counterpoised by Wedge
AOC, which is double the bigness of BOZ’.43 This kind of reasoning – cancelling out
counteracting parts of the same body – becomes superfluous when one introduces the concept
of centre of gravity. This does not mean that Hooke is totally lost on the subject of motion
around a centre. When we look at the point where Hooke uses the concept centre of gravity,
we see that it is to state that the liquid does not move because its centre of gravity is in a line
exactly below the centre. It sound plausible, and it gives the idea that Hooke, in typical
fashion, has heard something about it, but he does not know the rights of it.
The assumed lack of knowledge about the centre of gravity does not in any way mean
that the lamp devised by Hooke did not work as Westfall states, the idea does work – as can
be seen in the analysis of this idea, with the help of modern mathematics, in appendix A,
which uses the centre of gravity for simplification – the only thing that should be seen is that
Hooke is using a form of mathematics introduced by Galileo, essentially the same as the
mathematics used in ancient Greece, notably the law of the lever, with that difference that
there is an attempt to apply it to practice.
The intended audience
The second part of the answer to the question why Hooke’s idea of straight sails was
never implemented is to be found through an inquiry into the audience for the lecture. This
audience should be divided into two categories. On the one hand there are those people who
attended Hooke’s lectures and on the other there are those who could actually apply the
42
43
Robert Hooke ‘The Cutler lectures of Robert Hooke’ 166
Ibidem 167
22
knowledge dispensed by Hooke. A large part of the first group was comprised of members of
the Royal Society. The Cutlerian lectures were, after all, held at their meetings and they were,
to be honest, just regular lectures to the Royal Society, only at special times, and sponsored by
the financier Cutler – who at first required them to concern the history of trades but Hooke’s
topics became increasingly diverse as Cutler’s payments became increasingly irregular.
Hooke’s audience at these lectures hardly occupied themselves with sailing as can been seen
from the fellows of the Royal Society in the first forty years of its existence. Of the 479
English and Scottish fellows: ‘16% were courtiers, politicians, or diplomats; 16% were
medical practitioners; 15% were gentlemen of independent means; 14% were members of the
aristocracy; 12% were scholars or writers; 8% were divines; 7% were merchants or
tradesmen; 4% were lawyers; 4% were civil servants or members of the armed forces; and 3%
are unclassifiable’.44 From this we can conclude that in the most generous estimate 14% were
active in sailing (this would be the case if all merchants and tradesmen, all civil servants and
members of the armed forces and all deemed unclassifiable were involved with the practical
matters of shipping). It is far more likely however that not 10% of all members had any ties to
shipping and the actual number of captains, navigators, shipwrights and seamen at Hooke’s
lecture would be very close to zero.
The second group of the intended audience were those people who could apply
Hooke’s idea on the proper way of sailing into everyday practice. These were the earlier
mentioned captains, navigators, shipwrights and the rest of the crew working on ships. It is
unlikely that many of them went to the meetings of the Royal Society and it would be equally
unlikely that many of them were convinced by Hooke’s argument if he had brought them up
in a discussion with them. They might not have criticised Hooke for the vague use of the word
sail but they would have had some fundamental objections to the notion that Hooke found a
legitimate foundation for his idea in geometry. When you realize that most of the inhabitants
of seventeenth century England were unable to read or write and that the practical
mathematics used by navigators was crude, it should not be any surprise that the geometrical
arguments of Hooke, which led to a conclusion diametrically opposed to an old and well
established practice, were not accepted. It seems that in the end there remained no other
option for the gifted mathematician who used the geometrical argument than to return scorned
and embittered to his lodgings at Gresham’s College.
44
Michael Hunter The Royal Society and its Fellows 1660-1700. The Morphology of an Early Scientific
Institution. (Oxford 1994) 27
23
Conclusion
Hooke has remained a controversial figure throughout the history of science. The
answer to why this is has a multitude of aspects; but one aspect is Hooke’s aspiration to be a
virtuoso. This aspiration resulted in Hooke contributing to many a field and him being
involved in innumerable projects. This versatility of Hooke was part of his work as curator of
experiments at the Royal Society, but its downside was that Hooke almost never followed his
own line of reasoning through to a fundamental level – leaving in the middle whether this is
because he did not have the time, did not feel the need or did not have the skill to write a
fundamental work, his Micrographia being the obvious exception that proves the rule – and
therefore never received the fame of Newton or Galileo. His work on sailing was no exception
to this; it did not use the newest developed mathematical tools, most prominently differential
calculus; Hooke did not take the time to cater it to an audience which could do something
with it and he did not take the time to present the experimental proof of his theory he
promised in his lecture to the Royal Society.
These difficulties in the judgement of Hooke have found their echo in the treatment of
Hooke by modern authors, regardless of if one is trying to aggrandize Hooke’s
contemporaries at his cost or if another is trying to rehabilitate Hooke’s reputation by being
overly apologetic. The difficulties arising from the lack of consensus that surrounds the
person of Robert Hooke resulted in the situation that the question if Hooke succeeded in the
goals he had set for himself has not been answered satisfactorily.
In the case of his attempt to replace bunting sails by straight sails as the standard in
sailing, the answer has to be that Hooke was not able to achieve his own goal, which was to
implement this new way of sailing. More important than that he did not succeed in achieving
his goal is why he did not succeed. As Westfall pointed out – and many a science student will
have experienced – aerodynamics and hydrostatics, the fields to which we in retrospect can
state that this problem belongs to, are notoriously difficult subjects and have a wide range of
variables which are not able to be accounted for in a, relatively, simple geometrical proof. The
method used by Hooke prevented him from reaching the mathematical exactitude that was
needed to give a clear and definitive answer to the questions if straight sails are to be
preferred over bunting sails or not. Another problem for Hooke is how he reached the
audience he intended. From the fact that Hooke chose to give this lecture to the Royal
Society, we can be reasonably sure that his audience was not comprised of people actively
involved with the day to day practice of sailing, let alone sailors or navigators. This argument
24
is nuanced by pointing to Hooke’s proclamation that he had had frequent discussions on the
topic with sailors, naval captains, navigators and shipwrights. But seeing that Hooke
presented only one argument in his lecture, a geometrical one, the question if he also had
different types of arguments urges itself upon us and through the lack of alternative lines of
argumentation we can only assume that he only used his geometrical proof to convince sailors
of his idea. It is not hard to imagine how a frustrated Hooke would have exclaimed in an
encounter with a sailor: ‘but look at my geometrical proof, it shows clearly that straight sails
will give more speed than bunting ones!’ at which a unimpressed sailors would only reply: ‘I
only see some lines and a circle. This is not much proof, certainly not enough to change
practice as my father has done it, and my father’s father, and his father’s before him’. Hooke
needed to come up with other types of arguments than his geometrical one to sway the sailing
practitioners, and we do not know of any that he possessed. We therefore have to conclude
that in this instance theory-based practice did not materialise and that Hooke did not advanced
the art of sailing.
25
2. The Miraculous Ship of Rotterdam
There were not only attempts to improve practice by applying mathematics to it; there
were also not only attempts to improve practice which were forgotten soon after they were
introduced and there were even some attempts to improve practice in cases where the general
public perceived a pertinent problem. In contrast to Hooke, who came up with his sailing
method quietly in his apartments at Gresham College, the vessel we will be investigating in
this chapter was the answer to an English blockade of the Dutch coast during the first AngloDutch war and the imminent threat of defeat in that war.
In retrospect, it may not seem remarkable that the English and the Dutch built up some
animosity towards each other. Since Dutch independence in 1648, they fought each other in
four wars – six when you include the wars between the British and the French empire, in
which the Dutch Republic was either a French client state or a part of the French empire – and
this animosity spilled over into the respective languages. In the Dutch language, rachitis is
known as the English disease, objects made of English silver only have a small outer shell of
silver and using an English screwdriver is hammering in a screw; in the English language the
word ‘Dutch’ usually has a negative connotation, with examples as varied as Dutch courage
(bravery obtained by drinking alcohol), a Dutch nightingale (a frog), a Dutch defence (weak
defence), to do a Dutch act (to desert, but also to commit suicide), a Dutch double shuffle (to
cheat at a card game) and Dutch generosity (avarice). This animosity was not preordained or
even likely, the English and the Dutch Republic were very much alike, 45 both were seafaring
countries and centres of maritime trade; in both the ruling class was protestant and both were
republics in a part of the world where most nations were moving more and more towards
absolutism. The Dutch gained their independence in 1648 with the peace of Westphalia. The
English became a republic a year later, after the beheading of Charles I. This similarity did
not lead to companionship but to rivalry, the English and the Dutch became fierce mercantile
competitors, which in the end led to the earlier introduced Anglo-Dutch wars, which in fact
were a number of maritime trade conflicts.
The first Anglo-Dutch war started on the 10th of July 1652 – which was the 30th of
June in England where the Julian calendar was still used – although hostilities had begun
earlier that year off the coast of Dover.46 The Dutch entered the maritime war with great
confidence prompted by their superior numbers, mustering 115 warships against 85 English
ships and on top of that they were led by three admirals with more experience and more
45
D. H. Pennington Europe in the Seventeenth Century (2nd edition: London 1989) 476
46
Maarten Prak The Dutch Republic in the Seventeenth Century (Cambridge 2005) 47
26
international fame than their English adversaries.47 However, the Dutch quickly lost their
confidence, when the English fleet proved to have superior firepower at their disposal. The
largest ship of the Dutch only carried 59 guns into battle, being by far the most heavily armed
Dutch ship. The English Sovereign, on the other hand, had a hundred guns and she was
supported by another eighteen ships with over 40 cannons.48 This difference in firepower was
put to good use during naval engagements and the Dutch fleet was forced to retreat with
heavy casualties time and again. The decisive battles of the war, the battles at Gabbard and
Scheveningen, also resulted in English victories. The battle at Gabbard was fought on June
12th 1653, and the difference in firepower was so favourable for the English that the Dutch
were utterly defeated within one day. The Dutch admiral Tromp blamed the loss on the Dutch
lack of fire power: ‘there were more than fifty ships in the English fleet which were bigger,
better built, and better gunned [than my ship]’49.
After this humiliating defeat the Dutch sought refuge in their harbours and the English
took control of the North Sea, a dominance they exploited immediately by imposing a sea
blockade on the Dutch. The defeat and the subsequent blockade were disastrous blows to the
Dutch war effort, the Dutch morale and most of all to the Dutch economy, which largely
depended on maritime trade. The situation was so dire that on the 30th of July the StatesGeneral ordered Admiral Tromp to put to sea again as soon as the wind and the weather
permitted to break the English blockade in order to prevent the total collapse of the Dutch
economy. The wind was favourable on August 10th and Tromp immediately set out. This
desperate attempt to break the blockade led to the battle of Scheveningen and it ended in
another decisive defeat for the Dutch. The English had forced the Dutch back into their
homeports by nightfall after losing eleven ships and some 4000 men, including Maarten
Harpertszoon Tromp.50
Terror Terroris
It was during these desperate times of blockade and crisis that a French inventor came
to the Netherlands with the promise of building a ship (figure 2.1) that could ‘go out in the
morning from Rotterdam, and make to be at Dieppe in France by dinner time, and return back
again that night to Rotterdam´.51 The ship was known under a number of names but it was
47
C.R. Boxer The Anglo-Dutch Wars of the 17th Century:1652-1674 (London 1974) 4
Boxer The Anglo-Dutch Wars 4-7
49
As told in: Ibidem 15
50
Ibidem 15
51
A collection of the State Papers of John Thurloe, 1638-1660 I, 1638-1653 Thomas Burch (ed.) 521; most of the
notes found in the State Papers can, in an almost literal translation, be found in: Lieuwe van Aitzema Saken van
48
27
most often called: ‘het Wonderlijke schip’ (the miraculous ship); ‘Blixem van de See’
(Lightning of the Sea) or ‘Terror Terroris’ (terror of terrors). 52 The inventor claimed that his
ship was going to be able to reach a speed of ‘15 miles in an hour, or 180 miles in twenty four
Figure 2.1 Depiction of the Miraculous ship of Rotterdam in a pamphlet written by its inventor. Source: Leiden University
Special Collections
hours, 1260 miles a week, and 5040 miles in twenty eight days, which would be almost the
whole circumference of the world’;53 by comparison, most conventional ships sailed to the
East Indies in six to eight months. The inventor did not only promise that his new ship would
be very swift, it would also have the unprecedented benefit of going just as swift either with
or against the wind. The most important claim of the inventor was, however, that his ship was
to be an unparalleled weapon of war: ‘The strength of [the ship] will be of such force, that
[the inventor] doth undertake to make his way […] through the biggest and strongest ship of
the English […] and doth promise that he with his ship alone will destroy thirty of the English
Men of War.’54 These promises were like music to the ears of the demoralised Dutch, who
could hardly provide in their own livelihood due to the English blockade, especially because
staet en oorlogh In, ende omtrent de Vereenigde Nederlanden III, beginnende met het Jaer 1645, ende
eyndigende met het jaar 1656 (The Hague 1669) leading to the theory that Aitzema was a spy for the English
commonwealth
52
the names can be found in: Du Son Terror Terroris, werelts-wonder-schrick seldsame, noyt-gehoorde noch
bedachte vondt, mitsgaders grondige omstandelycke beschryvingh van seecker wonderbaerlyck, schrickelyck,
en onverwinnelyck vaer-tuygh, ghenaemt den Oorlog-blixem ter Zee (The Hague, 1654), fol. A2v (University
Library, Leiden) and in Perfecte Afbeeldinge: van ‘t Wonderlycke Schip, Gemaakt tot Rotterdam 1653
(Rotterdam 1653) P2350 (Maritime Museum, Rotterdam)
53
A collection of the State Papers of John Thurloe, 1638-1660 I ,521; there is an odd thing in this advertisement,
given that a ship could do 15 miles an hour, it would be able to do 180 miles in 12 hours and 360 miles in a day,
not the 180 it is advertised to do, the distances the ship was supposed to travel also take into account that the
ship would lie still for half a day. This can be a miscalculation but it can also be an insight into the workings of
the ship. Furthermore, it has to be taken into account that the round voyage Rotterdam- Dieppe is
approximately 380 nautical miles which would fit 15 miles an hour but not 180 miles in 24. All further claims
build upon the 180 mile a day speed.
54
A collection of the State Papers of John Thurloe, 1638-1660 I ,521
28
the inventor did not need any state support. He provided the large amount of money he poured
into the construction – allegedly twenty to thirty thousand guilders55 – himself. The way he
could pay for the project was subject of wild speculation. One theory was that he had an estate
of sixteen thousand guilders to spend per annum, while another theory said that he was an
engraver by trade and that a certain rich usurer in France supplied him with money.
Figure 2.2 The Lightning of the Sea imagined as being in action against hostile warships, the accompanying explanatory
text was written both in Dutch and French. Source: Municipal Archives Rotterdam
Nicolas van Son, Mathesios sr de Lisson or Jean Du Son
The inventor proposed a revolutionary new ship that would save the Dutch from defeat
in the war and would break the ongoing naval blockade, but who was this man who presented
himself as the saviour of this young nation? The identity of this inventor is not completely
clear, he is known under a variety of family names such as Du Son, Duson, D’esson, sr de
Lisson to Deson and van Son, but we will refer to him as Du Son from now on. What we do
know, is that he came from France, where he had gained some powerful support: ‘he comes
recommended hither by the lord ambassador Boreel, and he is known to be a subtle
mathematician, and forasmuch as concerneth the theory, he giveth good reason for the
55
A collection of the State Papers of John Thurloe, 1638-1660 I, 522
29
design.’56 The support of Boreel carried some weight; this former lawyer for the VOC became
the Republic’s ambassador to Louis XIV just before the arrival of Du Son in Rotterdam. It
was Boreel who, in a letter dated the 25th of February 1653, advised the States of Holland to
receive Du Son and listen to his proposals because the Frenchman would reveal ‘a great
service in the domain of Mathematics; nothing speculative but matters of great use in public
and private Navigation affairs.’57
Although Du Son might have had political and financial backing, he was considered
an odd figure with strange habits. He is described as eating ‘very little, especially that which
hath had wings; but he takes forty pipes of tobacco in a day.’ 58 Another remarkable aspect of
Du Son was his choice to build his ship in the Dutch Republic and not in France, his home
country. When he was asked why he did not built his vessel in France, he answered that ‘he
was afraid they would have secured him for his art’s sake, that so his art might have remained
in France alone’.59 It was thus the relative lack of censorship in the Dutch Republic and the
fear of incarceration in his home land that made Du Son come to the Dutch Republic.
The exorbitant promises of this mysterious man led to mixed reactions; the ship was
hailed and scorned at the same time. Some suggested that the inventor should take some
hellebores, to combat his insanity;60 others saw the construction of the ship as a divine
intervention to end the war between the Dutch and the English.61 A number of pamphlets
appeared in order to give those who were interested in the design a little more insight into the
workings of the ship. One of them, entitled True and Correct drawings of the wondrous
ship,62 did present the ship as divine providence. Furthermore it put the ship in a broader
context of technological progress, stating that ‘in a world which becomes more subtle every
day and in which many new and wonderful arts and practices are found [God] has awakened
the mind of Le Sr de Lisson which has designed a ship as presented here before.’63
56
A collection of the State Papers of John Thurloe, 1638-1660 I, 521
National Archives, The Hague, States of Holland, 1831, Boreel to the States of Holland and Western-Frisia.
Translation taken from: Marika Keblusek ‘Keeping it Secret: the Identity and Status of an Early-Modern
Inventor’ History of Science 43 (2005) 37-56, 38
58
A collection of the State Papers of John Thurloe, 1638-1660 I 522
59
Ibidem 522
60
Ibidem 521;
61
Ware en correcte afteekening naer ’t leven gedaen, van ’t wonderlijcke schip dat tot Rotterdam gemaeckt is /
Le vray Poutraict[!] de cette admirable navire ou machine faicte a Roterdam par le Sieur de Lisson grand
ingenieur de ce temps (Amsterdam, 1653): engraving with explanatory text in Dutch and French (Municipal
Archives, Rotterdam).
62
Ware en Corecte Afteekening naer T’Leeven gedaen
63
Ibidem
57
30
International attention
Du Son’s design did not only interest the public of the Dutch Republic; News of the
construction of the Terror Terroris was soon published in English periodicals. The periodical
Mercurius Politicus summed up six ‘wonders’ that the ship was supposed to accomplish.
These wonders were that the ship would have perpetual motion without sails, going as swift
as the moon, the swiftest birds, or at least 30 miles an hour; she would be able to change
direction very quickly and could reverse to use the stern of the ship as her prow and vice
versa; that she had the ability to make a hole as big as a table in the greatest man of war, being
able to sink 15 or 16 enemy ships in an hour this way; that she could sail to the East Indies in
8 or 9 weeks; that she could hunt so many whales in Greenland that a 100 good whaling
vessels could be loaded in 14 days; and that she could destroy any piers in the sea with great
ease.64 This list is remarkable due to the fact that besides all the possibilities for the ship in
wartime, it also contains various uses for the ship in a wide range of commercial and tactical
exploits during peacetime. Not only could the ship be used in the commercial whale hunt, but
it was also seen as being an excellent postal vessel between Europe and the East Indies,
swiftly delivering correspondence between the colonies and the motherland.
Besides the reports in the English periodicals there are more examples that the ship
received international attention, the explanatory pamphlet (of which figure 2.1 is a fragment)
was translated into German (figure 2.4) and into English (figure 2.3) and figure 2.2 is part of a
pamphlet which featured explanations of the workings of the ship in both Dutch and French.
The existence of an English and a German pamphlet shows that people all over Europe were
interested in the ship all over. The English interest can fairly easily be explained, given that
the ship was built by their enemy and that it was built with the intention not simply to be the
bane of the English fleet, but to destroy it completely in one afternoon.
The existence of a German version cannot be explained in the same way; the lands of
the Holy Roman Empire did not have such a direct involvement with the ship. The ship was
not an immediate threat to its seafaring member states and neither was the Dutch republic.
The German interest cannot have been instigated by political motives, so it has to be
awakened by the extraordinary design, the extraordinary claims or the new technology
implemented in the ship.
64
Mercurius Politicus 180, November 17th-24th ,2888-2889
31
Figure 2.3 The vessel as depicted on the English version of the explanatory pamphlet. The pamphlets for all three
languages (Dutch, German and English) had a flap which revealed the inner workings of the ship as depicted here.
Source: Rijksmuseum
The French situation is similar to the German one. It would be unlikely that the French
would soon be involved in a maritime war with the Dutch, first of all because the French navy
did not become a powerful force until later in the century, moreover because the emphasis of
the French military had always laid emphasize on the army and it would be much more simple
for them to start a land war with the Dutch Republic, as they would do some twenty years
later. Thus the interest of the French was also not of a military nature, leaving the
extraordinary design and the exorbitant promises as the most likely candidates that generated
the interest. In the specific case of the French there was another reason to show interest in the
construction of this ship which was the fact that Du Son was a Frenchman. Therefore,
patriotic motives must also be taken into account to provide
a
possible explanation of the
interest from France.
The Lightning of the Sea
Neither criticisms nor critiques could stop Du Son in his attempt to build his vessel
and thus the Lightning of the Sea was built in the city of Rotterdam at the shipyards on the
crossing of the Boompjes and the Leuvehaven, close to where the local Maritime Museum is
located nowadays. The exterior of the ship was in concordance with Du Son’s extraordinary
claims. Where conventional ships had multiple masts, multiple decks, multiple guns, and just
one keel, Du Son’s ship had none of that. It had no masts, no guns, just one deck, and two
keels, which came together in a point at the ends just like a snout, according to an eyewitness
report by Lieuwe van Aitzema.65 The Lightning of the Sea was 8 feet wide, 13½ feet high,
65
Aitzema Saken van staet en oorlogh III 837
32
almost half of it would be under water, and its middle beam, to be used as a battering ram,
measured 80 feet from end to end.66 The inside was divided into three compartments; two
cabins for crew and passengers which were separated by a compartment that housed the
propulsion mechanism.
Figure 2.4 Depiction of the ship from the German version of the pamphlet;
source: Rijksmuseum
Although Du Son kept the precise workings of the ship secret, we can reconstruct it
through the pieces of information we do have. First of all, we know the ship used a
paddlewheel to move (see figures 2, 3 and 5) and we know that the ship had to be steered by
using two rudders – one on the port side and one on the starboard side – which were placed at
the middle of the ship. Other information that can be obtained from the pamphlets is that the
ship was semi-submerged and that there was a hole in the roof of each passenger compartment
to let in fresh air. Du Son kept the system from which the paddle received its power a secret;
he argued that this was necessary to prevent the English from using the vessel if they captured
it, or alternatively to prevent them from constructing a Terror Terroris themselves. In spite of
this secrecy, the earlier cited Aitzema gave some hints on how the vessel was powered. He
stated that the ship had a ‘ressort’, which could, when it was fully wounded up, run for eight
hours. Another source suggests that the wheel would be set in motion by a system of
‘unknown screws and wheels’.67 These sources make it appear that the ship must have been
intended to have a mechanism in which potential energy was stored which could be directed
towards the paddle, by a system of cogs and screws, quite similar to the way the then popular
pocket watches worked. Watches could be made since the early to mid-fifteenth century when
66
Ware en correcte afteekening near ‘t leven gedaen, van ’t wonderlijcke schip dat tot rotterdam gemaeckt is
Cort-verhael van het wonderherlijcke schip tot Rotterdam (Rotterdam, 1653), fol. A2r (Royal Library, The
Hague)
67
33
the power generated by the controlled unwinding of a coiled spring was discovered as a
motive force.68
Now that we have some knowledge of the workings of the ship, we can also see how
Du Son wanted to redeem some of his extraordinary promises. If the supposed mechanism of
transmission could be set in reverse, the ship would be able to change its course rapidly and
move as fast forward as it could move backwards, which are two of the promises Du Son
made; in that case the rudders would be able to affect the course of the ship as well, using the
same principle to stir a rowing boat, giving it the ability to cut very sharp corners. The semisubmergible design of the ship meant that the ship did not rise very far above the surface of
the sea which, in combination with the paddle as mode of propulsion, meant that the direction
and magnitude of the wind did not have much effect on the vessel.
For the construction of the ship, 22,000 pounds of iron were used;69 to compare, the
largest English vessels of the early eighteenth century used 100,000 kg of iron70, almost ten
times as much as Du Son’s vessel. On the contrary, the wale – an extra heavy and through its
great width outwardly projecting plank used on the side of the ship –was two to three times as
large and thick as it was on the largest ships of the VOC.71 This strong wale is a very
powerful indication that the designer expected the ship to be under a lot of stress, which in
itself is an indication that the inventor himself had a clear plan about the way his ship should
work and at least a basic knowledge of shipbuilding.
The extraordinary character of the Terror Terroris can best be understood when you
compare Du Son’s ship with other navy vessels of that period. An illustrative comparison can
be made with Tromp’s flagship, the Brederode. Tromp’s ship was 132 feet long, 32 feet wide
and had a draught of 13½ feet at its christening. The total construction cost was 42,000
guilders.72 During most of its existence it was the largest ship in the fleet of the Dutch
Republic.73 Built in 1642, the Brederode was during its lifespan only surpassed by the ship
Eendragt in 1655, three years before the Brederode’s final demise during the battle of the
Sound. The Brederode used the conventional type of propulsion, harnessing the power of the
wind, and she supported 54 cannons and a crew of 270 men. In comparison, the Terror
68
Anthony Turner, ‘Not to Hurt of Trade’: Guilds and Innovation in Horology and Precision Instrument Making’,
in: S.R. Epstein & M. Prak (ed.) Guilds, Innovation and the European Economy, 1400-1800 (Cambridge 2008)
264-287, 264
69
A collection of the State Papers of John Thurloe, 1638-1660 I, 521
70
F.L. Diekerhoff De Oorlogsvloot in de zeventiende eeuw (Bussum 1967) 32
71
Aitzema Saken van staet en oorlogh III 837
72
Christiaan Nooteboom De Brederode: het leven van een admiraalsschip (Rotterdam 1955) 5
73
Nooteboom De Brederode 1
34
Terroris was 24 feet less wide, she was 52 feet shorter and her draught was only half that of
the Brederode. Remarkable figures, the more because this difference includes the length of the
battering ram which added quite a few feet to the length of Du Son’s vessel.74
To sum up: the Lightning of the Sea was semi-submerged, the water coming to the
middle of her ram. She had a secret propulsion system, most likely resembling that of an early
modern pocket watch, driving a paddle which would be in the middle of the ship, submerged
to just under its axis, pushing the water away as a modern hydrocycle would. The ship had
two rudders which made it possible for her to turn rapidly. The large middle beam was used
as a ram to pierce enemy ships on their most vulnerable point, at sea level. The ram would be
the only weapon of the ship. On either side of the paddle compartment were huts where the
captain of the ship and a small crew could be housed. It was a truly remarkable design in a
time when ships followed the transformation from the Brederode to the Eendracht making
them larger, bulkier and especially able to carry more crew and more and heavier cannons.
A public attraction
Du Son’s remarkably shaped ship generated curiosity when it was announced, and this
curiosity was not satisfied by the pamphlets that were published. The construction of the ship
drew a hefty number of spectators to the dockyard where she was being built, from all
echelons of society. The most important person who came to visit the wharf must have been
count William.75 Although it is not specified which count William came to visit it, is most
likely that it was Count William Frederick of Nassau-Dietz, Stadtholder of Friesland,
Groningen and Drenthe, the most prominent military leader of the Dutch Republic at that
moment. Alternatively, it could have been Count William III of Orange, who would later
become King William III of England and Scotland, but he was only three years old at the time
of the construction of the miraculous ship. Other prominent figures who came to the dockyard
to watch the construction of the Lightning of the Sea were admiral Opdam, commander of the
Dutch Navy, and several members of the States General.
The general public also came in droves to the construction site, according to a letter of
intelligence sent to England ‘the multitude of spectators is so great, that the magistrates of
Rotterdam sent to this inventor, to ask him, whether the concourse of the people did not
hinder his work: he said no: every spectator gives a penny to the poor.’76 Given entrance fee
and the financial records of the only orphanage that existed at that time in the city of
74
Nooteboom De Brederode 8
I A collection of the State Papers of John Thurloe, 1638-1660 I, 572
76
Ibidem 522
75
35
Rotterdam,77 a relatively good estimate can be made of the number of visitors. In the
cashbook, comprised from papers in 1801, there is a note which reads: ‘in the year 1653
between 1300 and 1400 guilders have been received for visiting the miraculous ship, the
invention which caused a lot of rumours although the machine did not live up to its
expectations’.78 Given the five cent entry fee, this means a total of between 26,000 and 28,000
visitors.
Tomorrow Never Comes
When Aitzema visited the construction site of the Lightning of the Sea on October 14 th
1653, De Son allegedly told him that his ship was ready to be launched in eight to ten days.
Aitzema could not believe that such an extraordinary ship could be built so quickly and asked
Du Son if he was going to test the ship to be sure everything worked. Du Son answered that
he was so sure of his own art that he would only play a bit in the river and did not need any
trial runs.79 On the 14th of November, when count William paid the earlier mentioned visit,
the ship was still incomplete and the inventor complained of his workmen being slow and
tedious, he also claimed not to be a man who could endure to put out to sea in the winter, and
that the ship, when finished, would only be launched in the spring or summer.80 A letter of
intelligence dated 28th of November informed the English government that: ‘the invented ship
is now near ready […] the Frenchman the inventor thereof is sick of an ague at Rotterdam,
and till he be cured, he cannot go to sea, and it is to be feared, his ague will last long, and
without him this new device cannot go to sea’.81 So the ship was not launched on the 22nd or
the 24th of October and she was still not finished on the 28th of November. Furthermore, the
inventor was struck by a high fever, preventing him from taking the ship offshore. This meant
that the ship’s maiden voyage had to wait until next spring, for the inventor did not want to
sail in the cold. Still Count William is reported to have said, in the winter of 1653, that
although the prospects for the outcome of the war were not bright, everything would be all
77
Arie van der schoor In plaats van uw aardse ouders: geschiedenis van het Gereformeerd Burgerweeshuis te
Rotterdam (Rotterdam 1995) 29
78
Staat van de inkomsten van het Gereformeerd Burgerweeshuis van de vroegste tijden af tot 1796 toe
(Rotterdam city archive, Hoog Collection: 37-05_18)
79
Lieuwe van Aitzema Saken van staet en oorlogh In, ende omtrent de Vereenigde Nederlanden III, beginnende
met het Jaer 1645, ende eyndigende met het jaar 1656 (The Hague 1669) 837: ‘Ick seyde/ of hy niet eenighe
proeve soude doen: hy seyde / Ick gae so vast in mijn Const, dat ick geen proef doe: Ik sal wel in de Revier wat
gaan spelen, ander niet
80
A collection of the State Papers of John Thurloe, 1638-1660 I, 572
81
Ibidem 595
36
right, since Lord Opdam is admiral and Mr. Du Son is building his machine in Rotterdam,
thus showing his continuing support.82
The year 1654 would not be better for the Lightning of the Sea, nor for Du Son.
During that year the war, which from 1665 onwards would be known as the First AngloDutch war, came to a close when a peace treaty was negotiated at Westminster. Due to that
peace treaty, a peace unfavourable for the Dutch, the ship of Du Son would not see any
wartime action; it had missed its main goal, to be the turning point in the war against the
English. Although the ship missed its opportunity to be in the spotlight during the war, it
already had had its influence; the English were reportedly happy for making peace before Du
Son’s ship was finished.83 The construction of the ship continued after the peace agreement
was reached and on the second of July Du Son sent out the following announcement:
‘Tot op huyden is verscheydelijck ende onseker gesproken, aengaende
dit rare ende noyt gehoorde stuck wercks ofte wonderlijck Schip,
gefabriceert ende gebouwt door den Heer de Son. Ende also het selfde
door verscheyden verhinderingen tot noch toe niet in ’t water heeft
konnen gebracht worden; soo wort een yegelijck by desen geadviseert,
dat den dagh is vast ende seker gestelt, dat het voornoemde gebouw of
wonderlijkck Schip, op Maendagh den sesten July, 1654 sal in de
Maes gebracht worden. Alle curieuse Liefhebbers konnen haer tegen
den dagh voornoemt tot Rotterdam laten vinden, om het beloofde
effect daer van te sien. Segget voort.’84
Almost nine months after his original comment that the ship would be ready in a fortnight, Du
Son appeared to be ready to launch his ship into the waters of the Meuse River. For this
special occasion, the Lords van der Meyden, Veth, Wolfsen, and Ysbrants were dispatched to
Rotterdam by the States General to witness the maiden voyage of the ship, on Monday the
July 6th 1654. These high lords even sent an agent to talk to and encourage its inventor. On
82
A collection of the State Papers of John Thurloe, 1638-1660 I, 629
A collection of the State Papers of John Thurloe, 1638-1660 II, 1654 Thomas Burch (ed.) 394
84
Aitzema Saken van staet en oorlogh 935 translation: Until this day there has been different and uncertain
tongues on this strange and unheard work or Miraculous ship, made and build by the Lord de Son. And
although the vessel, through different hindrances, until now could not have been brought into the water, so
now it is proclaimed that the day has been appointed that the earlier mentioned building or Miraculous ship
will be brought in the Meuse River on Monday the sixth of July, 1654. All lovers of curiosities can bring
themselves on the earlier mentioned day to Rotterdam to see the promised effects spread the word
83
37
Sunday the 5th of July – a day before the prospected launch – Mr. Bonneau, a friend and
confidante of Du Son, informed the envoy of the high lords that the Terror Terroris would not
be able to go out to sea the next day for Mr. Du Son had not succeeded ‘in his search for iron
with certain qualities or certain temperament which he needed’,85 the launch was thus
cancelled again. After the workmen and the cold, it were technical difficulties hindering the
launch of the ‘miraculous’ ship.
This was not the last unpleasant announcement Bonneau had to make in Du Son’s
name. He achieved this dubious honour later when he had to announce that Du Son had gone
and that the money he himself had supplied the inventor with was gone, too.86 The ship, nearly
finished but without the possibility of any future use, lay in the docks as an attraction for a
couple of years and was eventually sold as firewood.87
Watch making on a grand scale
The reactions to this last failure to launch were very harsh. Du Son was portrayed as a
fraud and a charlatan, but was this justified? The published account of the conversation that
Aitzema had with Du Son, the one mentioned earlier in which Du Son allegedly claimed not to
need any tests before going out to sea, together with all the claims Du Son made for his ship,
clearly give the impression that the French inventor was not a modest man, which may have
supported the idea that Du Son was a fraud. Besides, there are clues that the miraculous ship
might not be the only ambitious war machine that Du Son tried to build.88 Already in the
1640’s there were mentions – notably in a letter from Marin Mersenne89 – of an inventor from
Rheims who was building a flying machine. This inventor claimed that by using his machine,
he could leave Paris, fly to Constantinople to have lunch and return the same night to have
dinner in Paris, a claim remarkably similar to the claims made by Du Son for his ship.90 To
utter the claim that Du Son was a fraud more understandable doesn’t make it more true, just as
85
‘Dat hy noch seker trempe of temprament van seker yser / dat hy van nooden haddde sochte’ in: Ibidem 935
Aitzema Saken van staet en oorlogh 935; Marika Keblusek, in her paper on Du Son’s life gives reasons to
doubt this sudden departure citing a court case of may 1655 where two metalworkers testified about a servant
Du Son; see: Marika Keblusek ‘Keeping it Secret: the Identity and Status of an Early-Modern Inventor’ History of
Science 43 (2005) n24 52
87
Keblusek ‘Keeping it Secret’ 42
88
Ibidem 43-44
89
Marin Mersenne Correspondance du P. Marin Mersenne religieux minime, P. Tannery & C. de Waard ed. XI
(Paris 1932-88) 435-6, Mersenne to Haak 13 december 1640: ‘on nous parle icy d’un homme de Rheims4 qui a
esté en vostre Angleterre, qui a une machine de 32 pieds en quarré, qu’il prétend faire voler en l’air partout où
il voudra, avec 8 ou 10 hommes, qui le pourant accompagnes ; le jour nous enseignera ce qui en est, ou ce que
en arrivera, je tien bien difficule, pour ne dire pas impossible de farie voler un legis, ou une machine garnie de
plusieurs poutres en autre chose(s) […] (4 il s’agit sans doute d’un certain Nicolas Deson)’
90
Keblusek ‘Keeping it Secret’ 43
86
38
the information that Du Son likely had tried and failed to build another experimental machine
does not point in the direction of Du Son being completely honest to his supporters, but it does
not make him an outright fraud either, especially when you take into account that Du Son
seems to have had a working plan from the start. In the beginning he was praised for his
mathematical skills. The ship design itself shows that Du Son must have had some clue of
what he was doing, since he planned to reinforce the ship at its weakest points. Besides, a
fraud would not have built the whole ship before abandoning the project at the very last
instance. It is far more likely that Du Son spoke the truth when he said that he could not
launch the ship because he was searching for iron with the right temperament, for, while iron
can be wound up to store enough energy to power a watch on a small scale, this technique
cannot be easily be transferred to a larger scale, the iron being too brittle to be wound up
enough to store all the potential energy needed to power a ship.91
We must conclude that Du Son does not seem to be a charlatan, or at least that he does
appear to have had a workable plan to build a workable ship. This does not mean that he was
sincere in every way, as his stalling tactics and excuses make clear, but it seems that he started
the program with a reasonable amount of sincerity. What the story also indicates is that Du
Son tried to use theory to improve practice; he took a relatively new concept, the powering of
watches by springs, and tried to adapt it so that at least some men may have the more Fruit in
their use of nature. Put differently, Du Son tried to use new technology to improve the fate of
the Dutch. Moreover, he did not only try to use new technology, he actually expected to find
new technology while building the ship, even if he only started to seek new materials when his
first idea of a direct translation from the propulsion system of a watch failed. It is unlikely that
Du Son thought he could use an enlarged clock mechanism without problems, given that he
had probably tried to use the same method to power his supposed flying machine, but even if it
would be his first encounter with such a problem and even if he only looked at it reluctantly
when his original plan laid in shambles, Du Son tried to improve his machine by using nature
and trying to obtain from nature a new sort of iron with a specific temperament to complete
his new technique and through that his new machine. He chose to search for new applicable
knowledge instead of relying on a tested method.
Everything is in the eye of the beholder
The story seems to end here. Du Son had fled, no one knew how to use his invention,
and his contraption, although built on experimental theories, had not helped to improve
91
Keblusek ‘Keeping it Secret’ 41
39
everyday practice. But the story goes on, for, while the ship did not make a lasting positive
impact on everyday shipping, it did make an impact. The criticisms on the failed vessel were
harsh and plentiful. This is remarkable in itself. In comparison: when Hooke’s new method of
sailing wasn’t adopted, just one living soul was disappointed or angry: Hooke himself. After
Du Son’s failure, he had to endure the scorn not only of a city, not only of a region, not even
of just one country, but it seems like the whole of Western Europe was laughing at him. Du
Son could have seen this scorn coming however, because with the prolongation of the
construction process the amount of scepticism about the project increased. Already on the 6 th
of December 1653, Du Son is reported to have complained that the people of Rotterdam did
not treat him with the appropriate respect and even insulted him calling him ‘the man of the
foolish ship’ and calling the ship itself ‘het malle schip’ or the ‘ship of fools’, a maltreatment
that Du Son wanted to stop and he threatened that he would abandon his project if it did not
stop. According to the report, these negative reactions were caused by impatience: ‘the truth is
that everyone is impatient and desires to see the effects and the actions of the machine’.92
Later the critiques became more derogatory: ‘it will turn out to be Parturiunt montes,
and what could one expect from someone who had said ten times that he would be ready, once
in a fortnight, on another occasion in ten days, on yet another in eight days and now it would
be more than a month?’; another person of class wondered ‘how can it be that such an
important College as that of the lofty members of the States General, prostitutes itself and let
itself be wronged by such a charlatan, all the while they keep encouraging him.’93
The opinion in England deteriorated just as quickly. The newspaper Mercurius
Politicus even reported in December 1653 that the inventor of the ship had out-stripped his
vessel in nimbleness and ran away.94 Although this report was a few months too early, the
lack of faith in the completion of the ship is clear. The majority of the English critiques on Du
Son were, however, written after the cancellation of the launch of his ship on July the 6 th.
Interesting is that two English periodicals reported the launch of the ship as being a success.
The A perfect account published a story dated July 8th stating that ‘The incomparable ship, so
92
A collection of the State Papers of John Thurloe, 1638-1660 I, 629 personal translation: ‘la verité est, que le
monde estant impatient & desireux de voir les effects & aĉtions de la machiene’
93
H.G. Jansen ‘Iets over het Malleschip’ in: G.A. Tindal & J. Swart (eds.) Verhandelingen en Berigten betrekkelijk
het Zeewezen en de Zeevaartkunde, III (Amsterdam 1842) 133-148, 144 my translation, my italics: ‘dat het
zoude zijn: Parturiunt montes, en wat waarheid was van hem te verwachten die nu tienmaal gezegd had dat
het gereeed zoude zijn, dan binnen veertien, dan binnen tien, dan binnen acht dagen, en nu zoude het nog wel
ééne maand aanlopen? Terwijl een degelijk man sprak: “ ‘t Is wonder so hoogen Vergadering al is die van haer
Hoogmogende, haer so prostitueert, ende doet besendinge aan een charlatan, om hem quanswijs ’t
encourageren’
94
Mercurius Politicus 183, 9th-16th December, 3137
40
much spoken of, being launched, the contriver thereof hath shewed some experiments of his
work, and extraordinary undertakings’.95 The story continued by restating the claims Du Son
had made the previous autumn. The Weekly intelligencer wrote an article quite similar to the
one of A perfect account, with the difference that after the declaration that the trial had
succeeded it directly moved on to making even stronger claims for the newly built ship. It
reported that engineers working within the ship could force the ship to dive down into the
deep, where she would sail invisibly for a whole league, and even further. The writer of the
article was also very astonished by the control the crew supposedly had of the vessel and by
the ability of the engineers to control the ship’s speed, accelerating and decelerating when
they felt like it.96 The interesting part of these false accounts is that they give the impression
that the belief in progress was continually resetting its beacons; when a new design, deemed
to be miraculous, had fulfilled its promise, rumours about it having even more, and even more
miraculous, attributes surfaced.
The Mercurius Politicus newspaper on the other hand reported in an article dated July
10th that the inventor had failed again to launch the Lightning of the Sea. In the article the
vessel is referred to as both ‘the miraculous ship’ and ‘the foolish ship’. By breaking his
promise he disappointed many ‘people of Quality that were come from severall parts to have
seen the Tryall therof’.97 The periodical further reports that with this new delay of the launch
the people were beginning to rally against Du Son, and see him as a cheat and a mountebank –
a swindler or a charlatan. Two weeks later another report appeared in the Mercurius Politicus,
it states that Du Son, after ‘having made a foole of himself and the Country’ was nowhere to
be heard of, or at least dared not to appear in public out of shame and out of fear of being
hooted at in the streets by local children.98
The Dutch too, gave full rein to their frustrations after the failed launch of July 6th, but
instead of the dry newspaper reports the English had written the Dutch put their discontent
with the whole affair in a number of satires. One example of these satires is: Het Malle
SCHIP van ROTTERDAM. Aen monsieur du Son, vinder ende autheur van’t Malle Schip.99
This poem is specifically interesting because it gives a number of very specific criticisms of
Du Son and his ship. The work has six stanzas and already in the first one the opinion of the
author becomes clear, it reads:
95
A Perfect account 183, 5th – 12th July, 1461
Weekly intelligencer 114, 4th – 11th July, 317
97
Mercurius Politicus 213, 6th – 13th July, 3615
98
Mercurius Politicus 215, 20th – 27th July, 3639
99
Het Malle Schip van Rotterdam. Aen monsieur du Son, vinder ende autheur van’t Malle Schip (1654)
96
41
‘Je bruickt noch Kloot, noch Loot, noch Schut, om hondert Scheepen
Te schieten in de gront, deur sonderlinge greepen.
Nochtans je schiet een gat, en maeckt de Schepen leck:
Waer me doch schietje dan, O lieve Son? Met Speck’100
This stanza really shows the distrust in the person Du Son. The writer uses Du Son’s most
prominent and one of his most extraordinary claims, that he would destroy a whole armada in
a single day, with outdated techniques, due to the miraculous workings of his new vessel. The
last line – ‘waer me schietje dan, O lieve Son? Met Speck’ – first of all contrasts with Du
Son’s lack of cannon use, but the line also has a second meaning which becomes clear when it
is taken into account that ‘to shoot with lard is’, in Dutch, an expression which means as
much as ‘to tell a tall story’ or ‘to boast’. The idea that Du Son was only boasting and that he
was a liar and a cheat is the main message of the satire, it is a reoccurring theme in most of
the stanzas:
‘Sons Schip kan sonder Mast en Seyl en Cabels varen,
ja sneller als een Vinck, deur ’t midden van de Baren.
‘tIs oock waer; dat een Vinck kan sonder Vleugels Vliegen,
En Son kan sonder Mont en sonder Tonge liegen.101 (strophe 2)
Or in another strophe:
Niemandt, segt Son, sal oyt, de gront van mijn Secreeten,
Niemandt sal oyt mijn konst, ter Werelt konnen weten:
Ick deel het niemant me: de reden dat gebiet;
O Son, je hebt gelijck: je wetet sellif niet’ 102
(strophe 4)
100
Het malle schip van Rotterdam; translation You use neither ball, nor lead, nor cannons to shoot a hundred
ships / into the ground through eccentric actions, / nonetheless you shoot the ships and make them leak, / with
what do you shoot, O dear Son? With lard’
101
Ibidem: ‘Son’s ship can sail without cable’s and masts, having two prows, / swifter than a finch,
straight through the billows / it is true that a finch without wings can fly / and that Son without
mouth or tongue can lie.’ Personal translation
102
Ibidem; No one, says de Son, will ever know my secrets / No one in the world will ever know my art / I won’t
tell anybody; reason thus commands me / Oh Son, you are so right: you were ignorant from the start’ traslation
taken from Keblusek ‘Keeping it Secret: the Identity and Status of an Early-Modern Inventor’ 43
42
Figure 2.5 Fragment of a depiction added to a satire, pay attention on the difference in naming, the large title at the bottom reads: ‘the foolish ship’
while the left-hand top corner reads: a perfect depiction of the miraculous ship or Sea monster made in Rotterdam’. Van Gijn collection Dordrecht
43
The satire ends unambiguously by calling Du Son the greatest fool:
Ghy wilt onsterffelijck naest by Erasmus leeven:
Ghy hebtet wel verdient: het moet u sijn gegeven:
Twee beelden van Metael sullen staen op de Maes:
Hy als de wijste Man, ghy als de grootste Dwaes 103
(strophe 6)
It becomes clear in these lines that Du Son is not only blamed for fraud and deception but also
for dishonesty and hauteur. It is his persistence to stand firm behind his extraordinary
promises that receives the biggest scorn from this author.
A different version of the satire, which is also interesting, appeared in Latin, it is entitled;
Epitheton seu, super navis, istius rarae Gallicae.104 In and of itself it is not very strange that
there are multiple satires about the failure of Du Son; as we have seen, the ship was visited by
a large number of people, it got international attention and the promises made by the inventor
made it an easy target to ridicule. The fact that there is a poem in Latin suggests, however,
that the writer, or writers, intended to reach a wide and diverse audience with these satires.
For while a satire in the vernacular would be expected, a satire in Latin is remarkable. The
vernacular version caters to the wide audience that was interested in the machine of
Rotterdam – remember that the people came en masse to the building site to take a look at the
way the ship was constructed – and while of course literacy levels were not high in the
seventeenth century, a satire in the vernacular could be recited to the illiterate. Besides, it
were the Dutch people who felt grieved because of the failure of Du Son’s promises to
materialize, they had been given false hopes, and they would have to endure the smashing of
that hope. Writing in the vernacular seems to be adequate for most goals when writing a satire
about Du Son’s ship: it was available to an audience that would be most likely interested, it
had a high likelihood to be spread because all layers of society could understand the satire,
and they were the most likely to relate to the grievances expressed by it. The possibility for
the easy availability of the poem in Dutch makes the appearance of a Latin satire all the more
103
Het malle schip van Rotterdam; You want to live immortal next to Erasmus / A right that you earned, I grant
you that /Two metal statues will stand on the River Meuse / He from the wisest school, you as the largest fool.
Personal translation
104
epitheton seu, super navis, istius rarae gallicae avis fabrica, nuper editae censurae Appendix (Rotterdam,
1654)
44
remarkable. It was not aimed at the masses, who were unlikely to read, speak or understand
Latin. It was therefore aimed at an elite group, which included people not necessarily fluent in
Dutch. This Latin poem suggests that there was an audience of international elites which was
interested in the demise of Du Son’s shipbuilding program, and, for this study more
important, that the failure of Du Son’s ship could have had a more widespread impact on the
belief in progress than just in the Netherlands.
Du Son really was the centre of ridicule, but why is this backlash important for the
investigation into the attempt to apply theory to everyday practice? It is important because the
foolish ship became a symbol for megalomania and naivity. This can be seen in a poem by
Constantijn Huygens, first published in the second edition of his Korenbloemen and called
‘Journael van de gedenckwaerdighe kijck-reis gedaen in ‘tjaer 1660’. In the poem the people
of Rotterdam are ridiculed trying to compete with the city of Amsterdam; this part of the
poem is set in a carriage in which a lady is shown the city:
‘Elck riep om ‘t seerst, Kijck hier, Mevrouw, Mevrouw kijck daer;
Kijck watte Straten, watte Winckels! all voll Waer:
Dat ’s eerst een Rotterdam: siet Havens, en siet Kaeyen,
En watter woelens is: wij sullen stracks eens draeyen
En siender noch vijf sess, al van den selven slagh:
Laet prachtigh Amsterdam all roemen wat het magh:
‘t En heeft er sulcke geen’. Kijck, hier is ‘t Schip gesoncken;
Daer lagh het Malle schip: ‘t Voorhout daer wij mé proncken’105
The last line specifically focuses on the ship we are investigating but the whole strophe
satirizes the pride the inhabitants of Rotterdam have in their city. It especially ridicules those
inhabitants who are trying to present their city as being better and having more exclusive
features than the metropolis of Amsterdam, in 1660 one of the most important cities in the
world. The poem gives the idea that a person is being pointed out the many magnificent
features of the city while riding through it, the guides expecting to infer a sense of
bewilderment into the main character at every turn. One of the sights that no visitor to the city
105
Constantijn Huygens Koren-bloemen Nederlandsche gedichten van Constantin Huygens I, (Amsterdam 1672)
552 ‘they all shouted for atention, look here, madam, look there / look at the streets, at the shops, all bulging
full of wares / only in Rotterdam, see those docks and those quays / and all what more, we shall return to them
later / and here are 5, no 6 of the same kind / let beautiful Amsterdam boast whatever it want / it has none of
those / look here is where the ship sunk / there lay the foolish ship; there the woodlands we boast about
45
could miss according to these city guides is the building site of the foolish ship. The foolish
ship is used in two ways in this poem, firstly to give a unique feature of Rotterdam, showing
that what the citizens rightly point out to be unique features of the city, are not features one
necessarily wants his city to be known for. Secondly the ship is used to portray the citizens of
Rotterdam as foolish since they appear to see the foolish ship as an addition to their city, as
one would expect them to. The ship is used to mock both the foolishness of the people of
Rotterdam and their misplaced pride.
The most important of the negative impression the ship made is that she was later
actively used as a deterrent for inventors who tried to introduce revolutionary new types of
ships: the Hollandsche Mercurius periodical writes in its August edition of 1663, a month
after William Petty won a race from Holyhead to Dublin with a new type of vessel: ‘While
[William Petty] was making [his new invention] he was ridiculed, like Noach when he was
building his ark, some said: “it will be the equal of the Foolish ship of Rotterdam.”’106
With Du Son’s abandonment of his own project he did not only fail to introduce a new
type of ship, and he not only failed to introduce a new kind of propulsion for ships, but he had
made a ship which became actively harmful for the idea that the study of nature could
improve practice. In the end we have to conclude that despite his best efforts Du Son was not
able to improve shipping with his Terror Terroris.
106
Thien boecken der Hollandsche Mercurius, off histoorisch-verhaal aller gedenckwaardighste
gheschiedenissen van de beginne des jaars 1650 tot den jaare 1660, in christenrijck voorgevallen. XIV Augustus
1663, 130-131 My Italics
46
3. A practical Newton
Isaac Newton was born in the burrow Woolsthorpe-by-Colsterworth in Lincolnshire
on Sunday January 4th 1643. Sir Isaac has made major contributions to mechanics, optics and
our understanding of the motion of the heavens in approximately 84 years that separated his
day of birth from the day he died. In the Principia, one of his most famous works, Newton
remarks that: ‘Quam quidem propositionem in construendis navibus non inutilem futuram
esse censeo’107 which translates to: ‘Indeed, I think this proposition will be of some use for
the construction of ships’ in Newton’s mother tongue.108
The Principia is composed of three books. The first book introduces the mathematical
description of movement in idealised conditions, the second book takes the description of
movement introduced in Book I and studies what happens to these rules in resisting media and
the third book is dedicated to the application of the first two books on the system of the world.
Because the contents of both the first and the third book have been hailed by historians as
revolutionary transformations of a conceptual level, the essential step that is the second book
has been removed from the limelight. The lesser status of book II is due to the fact that
although the book is an indispensable part of the Principia it is not perceived as such. The
shroud of superfluity that surrounds the Prinicipia’s second book is mainly due to our modern
projection of the success of Newton’s work back on the Principia. This later success shows
that the abstract mathematical descriptions of book I can successfully be applied to the system
of the world from the third book, but this was certainly not trivial in Newton’s days. This
application could only be made plausible by the intermediate step of describing movement in
resisting media. Furthermore, the modern projection of Book I on the world is a projection of
movement on a mostly empty space with the occasional particle in it, while most seventeenth
century theories of space and matter excluded the possibility of the existence of vacuums.
This means that Newton, contrary to modern physicists, looked at a world in which
everything always travelled through a deluge of particles. A third point of origin for this idea
of the superfluity comes from the author himself when he advised the readers of his work:
‘But since in books 1 and 2 a great number of propositions occur which might be too timeconsuming even for readers who are proficient in mathematics, I am unwilling to advise
anyone to study every one of these propositions. It will be sufficient to read with care the
107
Isaac Newton, Philosophiæ Naturalis principia Mathematica A. Koyré & I.B. Cohen (ed.) 1, (Cambridge 1972)
474
108
Isaac Newton The ‘Principia’: mathematical principles of natural philosophy: a new translation by I. Bernard
Cohen and Anne Whitman: preceded by A guide to Newton’s ‘Principia’ by I. Bernard Cohen I.B. Cohen & A.
Whitman ed. (Berkeley 1999) 730
47
Definitions, the Laws of Motion, and the first three sections of book 1, and then turn to this
book 3 on the system of the world’.109 In this quote the audience is asked not to read large
parts of the first book, and more important for this study, to skip the whole second book and
to take their contents as gospel. It is true that these points caused book II to be the least
studied volume, but it goes too far to go along with C. Truesdell who claims that: ‘[book II] is
the part of the Principia that historians and philosophers, apparently, tear out of their personal
copies’110
Although book II is the least studied part of the Principia, it is not completely
neglected. When the book is studied in the history of science, it is not the book as a whole that
is investigated but rather there are four parts of the book which are studied individually. These
four focal points are: the 11th lemma in which Newton sets his method of calculus to print for
the first time; the concluding scholium in which Newton proves that Descartes’ theory of
vortices lead to conclusions which are inconsistent with Kepler’s laws; Newton’s
determination of the speed of sound in which he makes a number of incorrect assumptions on
the expansion of air; and Newton’s search for the solid of least resistance. Right before the
paragraph on the solid of least resistance Newton makes the observation about shipbuilding
that was introduced in the first paragraph. This remark on the usefulness has been interpreted
a number of times as a token of Newton’s concern for practical problems and, alternatively, as
evidence that practical problems influenced which theoretical problems Newton studied.
Although this sentence draws the most attention in studies on Newton’s relation with
the practice of shipbuilding, it is not his only remark on the matter. In the first edition of the
Principia – the edition of 1687 – Newton gives an alternative method how the best shape of
the hulls of ships could be found. This method has taken out of the work for the first revision
and is not mentioned often in discussions about Newton’s relationship with practical
problems. A third source on Newton’s interest in shipbuilding is manuscript Newton wrote,
but did not publish. This source is consulted the least of all three sources but deals most
directly with the relation between Newton and shipbuilding.
109
Isaac Newton The ‘Principia’ Cohen & Whitman ed. 793
Clifford Truesdell, ‘Reactions of Late Baroque Mechanics to Success, Conjectures, Error, and Failure in
Newton’s Principia’ in: Robert Palter ed., The Annus Mirabilis of Sir Isaac Newton, 1666-1966, (London 1970)
192-232, 198
110
48
Newton’s references on shipbuilding
Proposition 34 book II
Newton’s observation that a part of his work could be ‘of some use for the
construction of ships’ is part of the scholium – an explanatory note – which directly follows
after proposition 34 of book II. The 34th proposition proposes – in the most rhetorical sense of
the word – that: ‘in a rare medium, consisting of particles that are equal and arranged freely at
equal distances from one another, let a sphere and a cylinder – described with equal diameters
– move with equal velocity along the direction of the axis of the cylinder; then the resistance
of the sphere will be half the resistance of the cylinder.’ 111 To support this proposition
Newton looked a situation in which both the cylinder and the sphere remain stationary but the
particles of which the medium consist move with a constant velocity towards the objects – he
argues that this case is the same as the case in which the cylinder and the sphere travel
through a stationary medium by referring to Galileo’s principle of the relativity of motion. In
this situation, where the particles that make up the medium are moving and the objects remain
stationary, Newton looks at that component of the force with which the particles hit the
objects which is in the direction the particle were moving in. Because this direction is parallel
to the axis of the cylinder, the component of the force with which the particles hit the
cylinder, to wit the force in the direction in which the particles were moving before they
collided, is equal to the total force the moving particles could exert. The case of the sphere is
different, only at the midpoint of the sphere is the direction in which the particles were
moving completely perpendicular to the area of the sphere, meaning that the particles only
there convey their full force on the sphere. The further you move to the extremities of the
sphere the smaller this component becomes, until at the very top and bottom the colliding
particles only brush the sphere and transfer no force upon it. Newton treats this motion
geometrically and shows that when you compare the average force on both the cylinder and
the sphere the force on the cylinder is twice as large as the force on the sphere.
After his treatment of the resistance on the sphere and the cylinder Newton uses the
ensuing scholium to generalise this theorem to include all shapes. In the first two paragraphs
of the scholium Newton looks at two distinct problems – one in each paragraph. In the first
paragraph he searches for the shape of a frustum that has the least resistance. Given is a
frustum (BGFC, see figure 3.1) with a given circular base CEBH, a centre O, radius OC and
height OD. The question that Newton wants to answer here is: what should the radius of the
111
Isaac Newton The ‘Principia’ Cohen & Whitman ed. 728
49
top plateau (FDG) of the frustum be for the frustum to be resisted the least when moving
along the axis OD in the direction of D? Newton states that the answer to this question is
found by bisecting OD in Q, drawing the line QC and then making a cone with the base
1
CEBH and a height OS in length equal to 𝑂𝑄 + 𝑄𝐶 – because 𝑂𝑄 = 2 𝑂𝐷 and because
𝑄𝐶 2 = 𝑂𝑄 2 + 𝑂𝐶 2 , 𝑂𝑄 and 𝑂𝐶 both being given, this solution is independent of OS and
thus independent of the question. We now have a
cone CSB which only has to be cut to size for the
height to become the given length OD and this
shape is the frustum which is resisted less than any
other frustum with base OC and height OD,
according to Newton.
In the second paragraph Newton looks at an
ellipsoid ADBE (of which figure 3.2 is a crosssection) and conclude that the result of the former
paragraph implies that if the frustum FGHI is added
to the ellipsoid ADBE – with GH being
Figure 3.1 Frustum as used by Newton source: Isaac
Newton The ‘Principia’ Cohen & Whitman ed. 730
perpendicular to the axis at point B and ∠𝐼𝐻𝐵 =
∠𝐹𝐺𝐵 = 135° – that this new shape, created by
the revolution of ADFGHIE around AB, will, as a consequence of the first paragraph of the
scholium, be resisted less than the ellipsoid ADBE when moving through the earlier
introduced rare medium. After this
conclusion Newton states that ‘this
proposition will be of use for the
construction of ships’.
In a third, and final, paragraph
of the scholium Newton searches for
the attachment to the ellipse ADBE
which, when the whole is rotated
around AB is resisted less than any
other ellipsoid. This problem has
become known as the search for the
‘solid of least resistance’. A search not
Figure 3.2 Cross-section of the ellipsoid when the depicted ellipse
(ADBE) is revolved around the axis AB. The first frustum is
constructed by drawing HG perpendicular on AB in such a way
that: ∠𝑰𝑯𝑩 = ∠𝑭𝑮𝑩 = 𝟏𝟑𝟓°. Source: Isaac Newton,
Philosophiæ Naturalis principia Mathematica (London 1687) 327
aided by Newton who, in a style
50
typical of his printed works, omitted all elaboration and gave as a solution that to the object
ADFGHIE112 a cone should be added with a base HG and a height BR which is defined as
GR4
𝐵𝑅 = 4HN×GB2
113.
The concise manner in which Newton wrote his work on movement through a rare
medium with particles that are equal and arranged freely at equal distances from one another,
meant that only a very exclusive group could follow Sir Isaac. This group had just one
member, and it was not Leibniz – who in the
margins of his own copy of the Principia wrote the
following ambivalent commentary ‘investigandum
est isoclinis facillimè progrediens’.114 The only one
who could follow Newton was Christiaan Huygens.
Although even he was not without error in his
replication of Newton’s work. This error of Huygens
is found in the formula for the resisting force he
deduced from figure 3.3. He writes this formula as
Figure 3.3 The figure used by Huygens to illustrate
the problem of the solid of least resistance. Be sure
to notice the difference between the vertices which
are indicated with capital letters and the line
segments which are indicated with lower-case
letters. Source: Christiaan Huygens Œuvres
complètes XXII Supplément à la correspondance.
Varia. Biographie. Catalogue de vente J.A. Vollgraff
ed. (Den Haag 1950)
𝑎4
𝑎4
𝑎2 +𝑥 2
+ 𝑎2 +𝑏2 while it should be of the form
2𝑎3 𝑦 115
.
𝑎2 +𝑏2
2𝑎3 𝑦
𝑎2 +𝑥 2
+
These formulas are only equal if 𝑦 = 𝑎,
which would mean that point C in figure 3.3 would
coincide with point D. Although Huygens could not
deduce the correct answer, this did not prevent him
from making an astute observation in the margins of his computation stating that the search
for the solid of least resistance did not meet a practical goal because it was impossible to
make a hull which looked like the investigated shapes.116 The fact that only Huygens
comprehended what Newton did in his investigation of the solid of least resistance does not
mean that the problem was never discussed. David Gregory, who was the Savilian professor
112
All letters refer to the letters in figure 3.2
MN
113
GR3
Originally the height of the cone was defined by the equation
=
GR
4BR×GB2
114
Isaac Newton, The Mathematical Papers of Isaac Newton VI, 1684-1691, D.T. Whiteside ed. (Cambridge
1974) 466; personal translation: What has to be researched is in what manner the lines with the same tangent
can be found the easiest.
115
Herman H. Goldstine A History of the Calculus of Variations from the 17th through the 19th Century (New York
1980) 29
116
Christiaan Huygens, Oeuvres complètes de Christiaan Huygens, XXII, Supplément à la correspondance, J.A.
Vollgraff ed. (The Hague 1950) 339 Nulla minime resistens in planis perpendicularibus datur quae, in prora,
curvae rotunditate finiatur.
51
of Astronomy at Oxford from 1691 to 1708, gave lectures on the problem in his first year as
professor with the help of extensive notes supplied by Newton without which Gregory also
could not understand Newton’s work.117
An experimental method
Proposition 34 of book II is not the only place in the Principia where Newton shows
interest in the practice of shipbuilding. Besides the investigated sentence on the applicability
of the mathematical investigation into the resistance of shapes, there is another reference to
shipbuilding in the second book of the Principia, although it only appeared in the first edition
of the work. In the scholium concluding section 7 of book II – this is the same section in
which the mathematical search for the solid of least resistance is featured, but it is a different
scholium – Newton presents a way to determine the resistance of shapes in water and
quicksilver. In the last lines of this scholium Newton again spots that the just presented
method is useful for shipbuilding: ‘by the same method by which we have found the
resistance of spherical bodies in water and in quick-silver, the resistance of bodies of other
figures or shapes can be found; and thus various shapes or figures of ships constructed in tiny
modes [can be] compared among themselves, so that there may be tested at small expense
which ones are most suitable for sailing’.118 The method Newton alluded to in this quote was
an experiment wherein he first suspended a sphere from a sufficiently secure hook using a
fine thread, after which he submerged the whole contraption in the chosen liquid and made
the sphere oscillate in it. The decrease of the lengths of each arc described by the suspended
ball was a measure for the resisting properties of the medium. In Newton’s view the ball could
easily be replaced by a different shape, the shape of a ship for example. What this intention to
experimentally determine the drag of ships shows is that Newton did not think that his
mathematical attempt to find the keel most suitable for sailing would suffice, else he would
not have included this method and would not have praised it for it needing but a small
expense.
The experimental search for the best shape of a ship was part of Newton’s work for a
quarter of a century. It was cut during the first revision of the book, in preparation of the
second edition which came out in 1713; the mathematical reference to ships on the other hand
117
Goldstine [,] A History of the Calculus of Variations [,] 8[.]
Isaac Newton, Principia Mathematica, I, Koyré & I.B. Cohen ed. 463 translation from: I.B. Cohen ‘Isaac
Newton, the calculus of variations, and the design of ships: An Example of Pure Mathematics in Newton’s
PRINCIPIA, allegedly developed for the Sake of Practical Applications’ in: R.S. Cohen, J.J. Stachel, and W.
Wartofsky (ed.) For Dirk Struik: Scientific, Historical and Political Essays in Honor of Dirk J. Struik (Dordrecht
1974) 169-183, 182
118
52
remained part of all editions published during Newton’s life. This difference in treatment
during the revisions of the book does not imply that Newton preferred the mathematical
method for finding the best shape for a ship when he wrote the first edition of the Principia.
Although the removal of the experimental method from the second edition seems to indicate
that Newton held this method in lower regard, it would be wrong to conclude this solely on
the basis of the first revision. A revision only reveals what an author thought to be important
at the time of that revision or what he thought to be wrong with the original publication at that
point, but not what he was influenced by during the composition of his original work. It is
during the original composition, when Newton came up with the theories for the first time,
that practical problems could have exerted their influence. That there is no connection
between the influence of a practical problem in the first edition of the Principia and its
disappearance from later editions can be made plausible by comparing the circumstances in
which the first and the second edition were written. The author of the first edition of the
Principia was a young, unknown and eccentric professor at Cambridge. The author of the
second edition, on the other hand, was president of the Royal Society, had written a second
revolutionary and epoch-making book which he called the Opticks, had had a long career at
the Royal Mint, had left his productive years decades behind him, had suffered from a deep
mental breakdown and had become the greatest authority on natural philosophy in Europe.
Newton had transformed from an outsider into the standard of all natural philosophers of his
age and this made his work relevant regardless of any possible practical applications they
might feature.
An additional factor is that Newton took the section in which both references to
shipbuilding appeared to be the hardest part in the work and he found it difficult to revise.119
That he nonetheless made profound changes in this section is clearly demonstrated by G.E.
Smith.120 The experimental search for the least resting hull was, as we have seen, placed at the
end of a long set of experiments designed to measure the resistance of objects travelling
through media. In preparation for the second edition this section changed profoundly, with
changes in a lot of measured values. Besides, the section was transferred from the end of
section seven to the end of section six. These changes are seen most clearly in the theoretical
expectations Newton had calculated for his experiments. For these expectations Newton
119
Richard S. Westfall Never at Rest: A biography of Isaac Newton (Cambridge 1983) 698-699
G.E. Smith ‘Fluid resistance: why did Newton change his mind?’, In: Richard H. Dalitz & Micheal Nauenberg
The Foundations of Newtonian Scholarship (Singapore 2000) 105-136,
120
53
discerned between two types of fluids, rarefied fluids and continuous fluids.121 Rarefied fluids
were described as consisting of particles which only had perfectly elastic collisions;
continuous fluids were all other fluids. In the first edition both types of fluids had a drag
coefficient of 𝐶𝐷 = 2,0 – the drag coefficient has been non-dimensionalised for reading
comfort by employing an anachronistic method where 𝐶𝐷 = 𝜌
𝐹𝑅𝐸𝑆𝐼𝑆𝑇
𝑓 𝐴𝑓𝑟𝑜𝑛𝑡 𝑣
2
wherein 𝐹𝑅𝐸𝑆𝐼𝑆𝑇 is the
force due to the fluid resistance; 𝜌𝑓 is the density of the medium; 𝐴𝑓𝑟𝑜𝑛𝑡 is the frontal area of
the object moving and 𝑣 is the relative velocity between the object and the medium.122 In the
first edition Newton predicted another force besides the resisting force. This force propelled
the object due to fluid particles rushing into the void left by the travelling object. This
additional force counteracted the force due to resistance and could become as large as ⅔ of
that force.
In the second edition the additional force working on the back of the object had
disappeared and the drag coefficient had differentiated its values for rarefied fluids (𝐶𝐷 = 2,0)
and for continuous fluids (𝐶𝐷 = 0,5). These changes were most likely an attempt to bring the
predicted values closer to the test results which gave a drag coefficient between 0,7 and 0,9 in
the first edition but had changed to a drag coefficient of roughly 0,5 in the second edition. It is
likely that these changed results and the uncertainty in the method they implicated led Newton
to understand that his assumption that resistance to motion in fluids varies simply as the
square of the sine of the angle of the slope was completely artificial.123 This could have been
an incentive for him to remove the experimental search for ship hulls from the Principia but
there is no hard evidence for this.
An unpublished manuscript
Not only in the Principia did Newton reveal his knowledge of shipbuilding. There also
exists a manuscript about shipbuilding written in Newton’s hand. This manuscript carries the
revealing title: ‘General proportions & observations for all the parts & Lines to be used in any
kind of ship or galley & how the proportions do depend on one another after a most excellent
manner observed by my own experience in my practice’.124 The text was part of Newton’s
private notes; it was listed on an index of records for the first time in 1888 and was not
published until 1984.
121
Newton also distinguished a third type but he did not try to give a theoretical expectation for this kind of
fluid see further: Smith ‘Fluid resistance: why did Newton change his mind?’ 128 n. 7
122
Smith ‘Fluid resistance: why did Newton change his mind?’ 105-106
123
Isaac Newton, The Mathematical Papers of Isaac Newton VI) 463 n23
124
Cambridge University Library manuscript Ms Add. 4005 53r
54
The text is a collection of instructions for building a ship with ideal proportions. The
text consists of a list of propositions which enable the reader to calculate the ideal size of a
component of the ship using the sizes already known, i.e. with the use of the length of the
ship, her breadth could be calculated and using a combination of her length and width her
ideal depth could be found. The manuscript is written in the handwriting of the mature
Newton which means this manuscript is written between 1670 and 1710.125 Although the
work is written in Newton’s hand it is unlikely that this manuscript is the reflection of an
independent thought of Newton. That this is unlikely becomes clear when you notice that
there are only a few corrections made in the text, while Newton normally crosses out many
words in a manuscript and adds almost as many back in afterwards.126 It is almost equally
unlikely that we are dealing here with a third, seventh, tenth or fifteenth draft of an original
manuscript of Newton, because we know of Newton that he never threw away any draft and
that there is no other version of this text in existence. This is also unlikely because Newton
had no purpose for a version of this manuscript without corrections, he could just as easily
have used the first version of this manuscript since it was only for personal use.
The corrections that are made in the work also indicate that we are not talking about an
original manuscript of Newton’s hand. As can be seen in figure 3.4 the first attempt to write
Figure 3.4 Newton’s copying error from his unpublished manuscripts source: Newton Papers MS. Add. 4005.12 54r
University of Cambridge
down proposition 23 is crossed out, because while it received the number 23, the sentence that
is written after the number is a literal copy of the first sentence of proposition 22. After this
crossed out proposition 23 a new proposition 23 is written down and this proposition 23
125
126
I am indebted to C. Schilt for dating this manuscript to this period
This keen observation also came from C. Schilt
55
concerns itself with a different topic – proposition 22 and the first attempt at proposition 23
concern themselves with the length of the sternpost while the second version of proposition
23 is about the place of the upper edge of the lower wale.
Another sign that indicates that this manuscript is copied by Newton from another
source can be found in an epilogue of the work which is concerned with masts. In this
epilogue a mention is made of the construction of ‘ye queens [ship] named the Beare’.127 A
ship that was constructed from 1599 onward, during the reign of Queen Elizabeth I,128 a time
before the birth of Isaac Newton, Sir Isaac’s father.129 Naval historians also identified parts of
the manuscript as almost identical to the disappeared ‘Scott manuscript’, a manuscript from
the early seventeenth century ascribed to both Captain George Waymouth and Philleas Pett.130
Although it is very unlikely that Newton was the original author of this text, it still is
relevant for the search into the possible connections between theory and practice in Newton’s
work. First of all the existence of a copy of the text in Newton’s hand tells us that Newton at
least had some interest in shipbuilding. Secondly the amount of jargon used in the text tells us
something about the familiarity that Newton must have had with nautical terms. For while it
might be expected to find jargon in an instruction manual for shipbuilders it tells us that the
author or the transcriber has to know this lingo before he could understand the text – and there
is no reason to assume that Newton did not want to understand this private record.
The use of Newton’s remarks by historians
As one of the tallest giants on whose shoulders his successors stood, Newton’s work is
often investigated to determine the relation between theory and practice in the early modern
period. The sentence in the scholium after proposition 34 of book II on the use of that part of
the Principia for shipbuilding is cited often to show that such a relationship did exist in
Newton’s work. This sentence is used in two ways to argue that there is a mutual influence of
theory and practice in the Principia. On the one hand some historians argue that the sentence
shows that the Principia was written in an attempt to solve practical issues, on the other hand,
other historians have traced the origin of the calculus of variations back to Newton’s problem
of the solid of least resistance, a problem introduced directly after the remark on shipbuilding.
Historians investigating the relation between Newton and shipbuilding fixated on this one
127
Ms Add. 4005 63r
Richard Barker ‘A manuscript on shipbuilding, circa 1600, copied by Newton’
Mariners mirror 80 (1994) 16
129
Westfall Never at Rest 44
130
J.F. Coates ‘The authorship of a manuscript on shipbuilding, C. 1600-1620’ Mariners mirror 67 (1981) 286
128
56
sentence of Newton and neglect the other two, earlier introduced, sources. These neglected
sources can help to put this one sentence into perspective which will give a more complete
picture of the relationship between theory and practice in all of Newton’s works.
The Hessen Thesis
The soviet physicist Boris Hessen has used Newton, and especially his Principia as a
prime example for the influence of practical problems on theoretical knowledge gathering. He
did this in his contribution for the Second International Congress of the History of Science
and Technology held in 1931. His contribution later appeared as an article entitled ‘The Social
and Economic Roots of Newton’s “Principia”.’131 In this article Hessen argues that ‘the
brilliant successes of natural science during the sixteenth and seventeenth centuries were
conditioned by the disintegration of the feudal economy, the development of merchant capital,
of international maritime relationships and of heavy (mining) industry’ 132 somewhat further in
the article he argues: ‘the above specified problems embrace almost the whole sphere of
physics. If we compare this basic series of themes with the physical problems which we found
[…] it becomes quite clear that these problems of physics were fundamentally determined by
these demands’.133 Hessen uses two crucial phrases in these passages, the term conditioned in
the first quote and the past participle determined in the second one. These words indicate that
Hessen thought that Newton was controlled by the socio-economic factors of his age and that
the author of the Principia had no influence on his own work. In other words, Hessen thought
Newton to be the plaything of his surroundings. He supports this claim in two ways. First of
all Hessen searches for references to practical problems in all works Newton left on paper –
he overlooked all the sources we are discussing here, a fact which cannot be completely held
against him since he was not a historian by training. Secondly he analyses both the Principia
and early modern technological problems, with the conclusion that the fields of study which
in the end provided the answers for these technological questions were the same fields which
were treated extensively in the Principia.
That Hessen has a structuralist view might not seem surprising at first, seeing that he
was appointed professor in physics at Moscow University just before the congress. 134 It
becomes even more unsurprising when it is taken into account that the Soviet delegation to
131
Boris Hessen ‘The Social and Economic Roots of Newton’s ‘Principia.’’ In: N. I. Bukharin (ed.) Science at the
Cross Roads (London 1931)
132
Hessen ‘The Social and Economic Roots of Newton’s ‘Principia. 155
133
Ibidem 166
134
L. Graham ‘The Socio-Political Roots of Boris Hessen: Soviet Marxism and the History of Science’, Social
Studies of Science 15 (1985) 705-722, 708
57
that Congress of the History of Science and Technology was led by Nikolai Bukharin – at the
moment already side-lined by Stalin politically but still held in high regard in the Western
world.135 The truth is, like so often, a wee bit more complicated though. More complicated
because it seems like it was not Hessen’s intention to show the socio-economic factors which
forced Newton to write the Principia but that he rather intended to prove his own orthodoxy.
This show of orthodoxy was necessary because Hessen, in his role as professor of physics,
was a supporter of both quantum mechanics, which was heavily attacked in the Soviet-Union
at the time and the equally controversial relativity theory of Einstein. The, for Hessen, most
dangerous attacks on these theories came from radical ideologues,136 who attacked the
perceived bourgeois roots of both theories. These attacks were dangerous for Hessen because
they labelled the theories he supported as suspicious and not simply as wrong. Relativity
theory caused the most problems because Einstein had explicitly acknowledged the influence
of philosopher Ernst Mach on the work while Lenin had denounced Mach’s ideas a confused
idealism. The situation became even more worrisome when Western philosophers interpreted
relativity theory and quantum mechanics as devastating for both nineteenth century
materialism and nineteenth century determinism, two major pillars of Marx’ analysis of the
world and as a consequence also major pillars of the Bolshevist analysis of the world.
Hessen argued against the rejection of these physical theories in the same vein as a
young Pisan astronomer had done 300 years prior when his Mother Church renounced
heliocentrism. They both argued that those who rejected new physical theories because of the
potentially dangerous philosophical, or theological, implications could not separate physics
from metaphysics. The fear of both Hessen and Galileo was that the ideologies they ascribed
to – respectively Bolshevism and Catholicism – took an unnecessary definitive stance on
physical theories, making them unnecessarily vulnerable in the process.
Hessen was attacked for his support of these physical theories during the frightening
build up to the Great Purge of the middle of the 1930’s and it was at this point in time that
Hessen was allowed to show off his orthodoxy by supporting Stalin’s idea that technology
was of crucial importance for the advancement of society. He had to do this by showing the
deep influences of technological problems on the writing of the Principia. Hessen did not
squander this opportunity and it is likely that this is the reason that the article is full of literal
quotations taken from Marx’ preface of his Zur Kritik der politischen Oekonomie.137 But as
135
H.F. Cohen The Scientific Revolution: A Historiographical Inquiry (Chicago 1994) 331
Graham ‘ The Socio-Political Roots of Boris Hessen’ 709-710
137
Cohen The Scientific Revolution 329
136
58
Graham points out, the article of Hessen is also a support of his own idea of a strict separation
between physics and metaphysics.138 Hessen does this by celebrating Newton’s
accomplishments while criticising the philosophical and theological conclusions Newton
draws from his own work. The implicit argument Hessen seems to want to make is: ‘we
accept Newton’s physical theories but reject his metaphysical conclusions, so why don’t we
do the same with modern theories? In spite of this elegant interwoven argumentation and in
spite of the explicit support of Stalin’s theory Hessen could not escape the clutches of the
NKVD and he died in one of their prison cells during the Great Purge.
It may seem unexpected to talk about such a peculiar work during this investigation
into the mutual influence of theory and practice in Newton’s works. However, Hessen’s work
has had a major impact on historians of science and the history of science in general. He
greatly contributed to the division of the field in an internal approach – historians who look at
the progress within science as an autonomous progression of the field itself, and thus
disagreed with Hessen’s article – and an external approach – historians who place the
development of science in a broader social context and agreed with more parts of Hessen’s
work. Historians of science that were influenced by Hessen were J.D Bernal, Joseph Needham
and Robert K. Merton, who would become an important figure in the American Sociology of
Science movement.139 Hessen most clearly influenced Merton’s dissertation which came out
under the title Science, Technology and Society in Seventeenth Century England, but even
when you take Hessen’s influence on this important work into account, it still is a work
published in 1931. Merton’s work also came out before 1940, and even when you also take
into account the text of the third historian featuring in this chapter, A.R. Hall, who, in 1963,
wrote a reply to Merton’s dissertation it does not become immediately apparent why these
works are still relevant enough today to be discussed here. These works are still relevant
because Merton’s work, and Hall’s reply have started a discussion which is still very much
alive within the modern history of science community140 and this makes Hessen’s work
interesting by proxy.
138
Graham ‘ The Socio-Political Roots of Boris Hessen’ 716
Cohen The Scientific Revolution 334
140
See: The mindful hand Inquiry and invention from the late Renaissance to early industrialisation Lisa Roberts
et al ed. (Amsterdam 2007); Puritanism and the rise of modern science: the Merton thesis I.B. Cohen ed. (New
Brunswick 1990)
139
59
Merton Thesis
Robert K. Merton was thus inspired by Hessen and he borrowed parts of his
dissertation from a rushed translation of Hessen’s original paper141 – Merton, for instance,
wrote on a certain Herique which is just an unfortunate transliteration of the Cyrillic name
Герике, Russian for Otto von Guericke.142 According to its author, Science, Technology and
Society in Seventeenth century England concerns itself with the sociological factors
underlying the blossoming of science in seventeenth century England. Hessen’s showpiece,
the influence of socio-economic factors on the progress of science, also returns in Merton’s
work.
There is, however, a fundamental difference between the ideas of Merton and Hessen.
Hessen’s work is a traditional, deterministic, structuralist version of history which takes after
the work of Marx. According to Marx, and as consequence according to Hessen, individuals
are puppets of the socio-economic circumstances of their time period, and Newton was no
exception to this. Merton does not share this view. He remains much more nuanced in his
book — a feat not always noticed by historians. The first part of Merton’s book is about the
role Puritanism played in the rise of knowledge gathering in seventeenth century England.
This part of Merton’s thesis has later been interpreted as an attempt to causally link the rise of
Puritanism and the Scientific Revolution in Europe.143 That this was not Merton’s goal can be
demonstrated in two steps. First of all the concept of the Scientific Revolution had not yet
developed into the universal reference point that it is today.144 Secondly, it was never
Merton’s goal to explain the rise of science in the whole of Europe, on the contrary, he
actively refrains from doing that.145 Moreover Merton did not attempt to causally connect the
rise of Puritanism and the rise of science, or in his own words: ‘[It is also possible] that other
circumstances may equally conduce to the espousal of science and that these factors may be
sufficiently effective to overcome the antagonism involved in the [non puritan] existing
religious system’.146 This quote clearly shows that Merton concerns himself with facilitating
factors, unlike Hessen, who talks about determining factors.
141
Cohen The Scientific Revolution 331
My thanks goes out to H.F. Cohen who seems to have been the only historian who ever stopped to think
about who Herique could be
143
Cohen The Scientific Revolution 318
144
Ibidem 318
145
Ibidem 317; Robert K. Merton Science, Technology and Society in Seventeenth Century England (1938; 2nd
1978 New Jersey) XXXI
146
Merton Science, Technology and Society in Seventeenth Century England 136
142
60
The second part of Merton’s book is about the influence of socio-economic factors on
the rise of science. Here too Merton outstrips Hessen in both nuance and ambivalence. Merton
admits on some points in his work: ‘in the last analysis it is impossible to determine even
approximately the degree to which practical concerns focussed the scientific attention upon
certain problems’,147 while he becomes much more definitive when he looks at individual
cases.148 For example, Merton refuses to regard the founding of the East India Company and
the publication of William Gilbert’s De Magnete in the same year as a coincidence.149 Most of
the other analyses Merton makes are concerned either with mining or transportation. For
mining he looks at the drainage of deep mineshafts with pumps, the supply of fresh air to the
miners, improvements in metallurgy and the surfacing of minerals in which he sees stimuli for
the theoretical fields of hydrostatics, aerostatics and aerodynamics.150 The transportation of
commodities stimulated astronomy, magnetism, optics and the mathematical description of a
pendulum swing according to Merton.151 Merton directly links technological improvements
and theoretical research by first stating: ‘[i]n order to discover ways of increasing the speed of
ships, it is necessary to study the movement of bodies in a resistant medium, one of the basic
tasks of hydrodynamics’,152 and he strengthens the link he lays by arguing that: ‘NEWTON,
in his theorem showing the manner in which the resistance of a fluid medium depends upon
the form of the body moving in it, adds: “which proposition I conceive may be of use in the
building of ships”’.153 Thus although Merton is not always consistent in his ideas on the
importance of external influences, he uses the sentence on shipbuilding we are investigating
here to make a direct connection between theory and practice and uses it furthermore to label
Newton as a pragmatist, as someone for whom: ‘Even that “purest” of disciplines,
mathematics, held little interest […] save as it was designed for application to physical
problems.’154
Merton Revisited
Merton’s book has been scrutinised often. In a famous article from 1963 A. Rupert
Hall criticizes Merton’s work on a number of points. One of these points is Merton’s
depiction of Newton. That the history of science had changed quite a bit in the twenty-five
147
Ibidem 176
Cohen The Scientific Revolution 335
149
Merton Science, Technology and Society in Seventeenth Century England 139
150
Merton Science, Technology and Society in Seventeenth Century England 147-150
151
Ibidem 169-175
152
Ibidem 179
153
Ibidem 180
154
Ibidem 182
148
61
years between the first appearance of Merton’s work and the publication of Hall’s reaction, –
entitled ‘Merton Revisited’155 – can clearly be seen in the treatment of Merton’s work by Hall.
The intervening quarter of a century had witnessed the introduction of the analytical tool that
is the Scientific Revolution and that tool was so all-pervasive that Hall could only read
Merton’s work as a search for the cause for the occurrence of the Scientific Revolution, even
though Hall readily admits that he knows that Merton was not explicitly searching for such a
cause.156 By interpreting Science Technology and Society in Seventeenth Century England as
a search for the answer to the question why the Scientific Revolution occurred, Hall regards
the work as much more ambitious than Merton had written it and in the process overlooks the
nuances Merton makes about the impact of external factors.
This is not to say that Hall has nothing sensible to say, on the contrary, Merton still
depicts Newton as a theorist driven by practical problems. Hall’s critique on Merton’s
depiction of Newton is most clearly explained in Hall’s analogy between Newton’s sentence
on shipbuilding and nuclear physics in the 1930’s. He states that Merton’s interpretation of
Newton’s reference to shipbuilding was equal to thinking that, because it became known
around 1940 that usable heat was released during nuclear fission, every nuclear physicist who
had done research prior to that date believed that his research would lead to practical
applications. What Hall wants to point out with this analogy is that external historians always
pretend that scientists already know the future applications of research they have not even
conducted yet. Hall then moves on to show that he does not take any of Merton’s reservation
into account by asking: ‘Was Newton’s interest in physics conditioned by the needs (in
applied hydrodynamics) of the society in which he lived?’157 By using the term conditioned
Hall uses the lingo of Hessen, not of Merton.
All the critiques of Hall on Merton are in the end variations of the same fundamental
point, which is that external influences never become apparent. Hall admits the trivial point
that Newton could not have written his remark on shipbuilding if he did not know of the
existence of ships and that he could not have written the Principia without knowledge of the
existence of moving bodies and pendulums.158 These are external influences that Hall
recognises in Newton’s work, because the Principia is partly devoted to the explanation of
these subjects. Hall could have added planets to this list, if planets had never retrograded and
155
Rupert Hall ‘Merton Revisited or Science and Society in the Seventeenth Century’, History of Science 2
(1963) 1-16
156
Hall ‘Merton Revisited’ 1
157
Hall ‘Merton Revisited’ 8 my italics
158
Ibidem 8
62
if the moon had always moved uniformly in a circular trajectory around the earth then book
III of the Principia would have looked very differently, if it would have been written at all.
Hall does not see the same indispensable role for applied hydrodynamics. That Hall does not
believe that Newton’s reference to shipbuilding shows the influence of a practical problem on
the Principia does not imply that he does not find the sentence intriguing: ‘it is perhaps a little
more interesting that a mathematician should think such a remark worth making at a time
when no master-shipwright employed mathematical theory or would have admitted the
competence of a mathematical physicist to instruct him.’159
Merton’s conclusion that ‘In general, then, it may be said that the contemporary
scientists, ranging from the indefatigable virtuoso Petty to the nonpareil Newton, definitely
focused their attention upon technical tasks made prominent by problems of navigation and
upon derivative scientific research’160 sums it all up for Hall. Merton depicts Newton as an
extraordinary practitioner, as an expert shipwright who wrote his experiences down. Hall is of
the opinion that this analysis confuses mathematical technology and mathematical physics in
a way that bewilders rather than assists the historian of science.161
The solid of least resistance
Newton’s remark that his mathematical method to compare the resistance endured by
objects travelling through rare media could be useful for the construction of ships has not only
been used to support the idea that the Principia was influenced by practical problems, it also
plays a role in the origin story of the calculus of variations. The calculus of variations is that
branch of functional analysis that searches for maxima, minima and saddle points of
functionals. The easiest way to think about functionals is to picture them as functions of
functions. A good example of the calculus of variations is the question: what function
describes a suspended cable with the least potential energy? 162 Another question could be:
what function describes the shape in which a solid travelling through a medium is resisted the
least? Newton asked this question in his paragraph on the solid of least resistance and
moreover the algebraic method Newton employed to find the answer was formalised into the
calculus of variations by Euler and Lagrange a generation later. Because Newton introduces
the problem of least resistance directly following his remark on shipbuilding a number of
159
Ibidem 8
Hall ‘Merton Revisited’ 8
161
Ibidem 8
162
A clear explanation of functional analysis has been given to me by M.F.J. Vermeulen
160
63
historians have concluded that this question originated from Newton’s interest in
shipbuilding.
H.W. Turnbull is one historian who is convinced that Newton’s contemplation on the
use of his work for shipbuilding spurred the birth of the calculus of variations. In his work
The Mathematical Discoveries of Newton he states: ‘[a]nd just as a like problem on finding a
round solid (a surface of revolution) analogous to any given solid had led Barrow and James
Gregory to their study of differential equations so the problem of ship design led Newton to
the calculus of variations’.163 Herman Goldstine is another historian who sees Newton’s
reference to the construction of ships as an important motivation for his contributions to the
calculus of variations.164
Although the calculus of variations did not exist during Newton’s lifetime it would be
wrong to state that only by looking anachronistically at this part of the Principia we can view
it as belonging to the calculus of variations and then with this conclusion – while deeply
sighing about the disregard of mathematicians for historical practice – push this idea aside.
This would be wrong because it is too simplistic, for although the calculus of variations did
not exist for another 50 years the method Newton employed resembles what would become
the calculus of variations to such an extent that it is justified to regard Newton’s work as a
form of the calculus of variations from before the term existed.
I.B. Cohen has tried to refute the claim that Newton was led to the calculus of
variations by problems in the construction of ships along another pathway. In his vision the
shipbuilding sentence and the problem of the solid of least resistance do not relate to each
other because the sentence on the construction of ships refers back to an earlier point in the
scholium – more precisely the addition of a frustum to an ellipsoid – and the problem of the
solid of least resistance is only introduced in the next paragraph. Furthermore these
paragraphs are only partly related to one another.
The other sources
The scholium after proposition 34 of book II has become the focal point for
investigations into the relationship between Isaac Newton and shipbuilding, but, as we have
seen, this does not give a complete picture. Analysing the other sources will contribute to a
much more complete picture of Newton’s interest in the practical problems of shipbuilding. It
163
164
H.W. Turnbull The Mathematical Discoveries of Newton (London 1945) 40
Goldstine A History of the Calculus of Variations 7
64
will also allow us to better assess if Newton was influenced by practical problems of
shipwrights.
It is remarkable that the experimental method from the first edition has never been
used as an argument for the influence of practical problems. After all, it did not come out of
some obscure, unknown manuscript — it was published as part of Newton’s famous
Principia. Although this passage only appears in the first edition of the work and although
this edition has never been translated in English the passage is of such an importance for the
question in what measure Newton was concerned with practical problems that it should have
been known to historians who were actively searching for such passages! The passage would
be especially useful for these historians not only because Newton presents an experimental
method which can easily test new designs but also because he praises the method on practical
grounds, it being performable at small expense.
It would be incorrect to suggest that this experimental method has never been used in
the history of science, but it has been used in a rather unexpected way: not to argue that
Newton was concerned with practical problems, but to show that Newton’s attempt to find a
mathematical way for comparing the resistance of ship hulls was not a sincere attempt at
practical innovation. The argument is that this mathematical attempt is not sincere because
Newton gives a simple and practical alternative at a different point in the same section.165
The manuscript has been overlooked even more in the history of science, which makes
sense since the work was never published. It did appear on the index of Newton manuscripts
from 1888 and its title: ‘General proportions & observations for all the parts & Lines to be
used in any kind of ship or galley & how the proportions do depend on one another after a
most excellent manner observed by my own experience in my practice’ leaves nothing to the
imagination. That the manuscript might have been interesting for historians of science is
shown by how maritime historians have used the manuscript. Under maritime historians the
manuscript, known by them as ‘the Newton manuscript’, is regarded as one of the clearest
attempts of sixteenth-century hull construction.166 They use it as a source on sixteenth century
construction and hail it as source full of technological innovation, a departure from the
construction of the smaller vessels of the Middle Ages and towards ocean going vessels.
165
166
I.B. Cohen ‘Isaac Newton, the calculus of variations, and the design of ships’ 183
Toni L. Carrell From forest to fairway: hull analysis of La Belle A late 17th century French ship (Fife 2003) 308
65
Conclusion
To what extent was Newton influenced by practical problems when he wrote his
Principia? As we have seen the answer to this question depends on the sources being used
and the interpretation of those sources. The only source that has commonly been used is from
the scholium following proposition 34 of book II. However when the sentence: ‘indeed, I
think this proposition will be of use for the construction of ships’ is used, two key questions
are ignored, which has led to a number of misconceptions and untenable conclusions. The
first key question is: where does ‘this proposition’ refer to? ‘This proposition’ refers to a
method for the comparison of two shapes travelling through a resisting rare medium. Phrased
like this it seems as if this proposition could actually have been of some use in practice, but
when we take the difficulty of the calculations involved into account and when we take the
problems trained mathematicians had with replicating these calculations – Huygens being the
sole exception – into account we are forced to conclude that this proposition has not been able
to ease the everyday work of shipwrights. Furthermore, when we look at the definition of
‘rare’ fluids Newton gives to distinguish them from ‘continuous’ fluids we must conclude –
like Newton167 – that water, neither fresh nor salt, is a ‘rare’ fluid and that this proposition,
and the scholium following it, is not applicable to water.
The influence of practical problems in the construction of ships on the Principia
cannot be made tangible either. From the references – both mathematical and experimental –
we can conclude that the construction of ships was on Newton’s mind from time to time but
these references never become more than an afterthought, Newton never presents them as a
cause for the study of a problem or, for that matter, as anything more than a possible
application of independently created theoretical knowledge.
Merton’s argument that the influence of practical problems on the contents of the
Principia becomes apparent through direct references like ‘this proposition will be of use for
the construction of ships’ is incorrect on two accounts. First of all Newton is not trying to
solve a practical problem – which would make a connection likely – but he notes a possible
application for his independently gained knowledge. The second way to see that Merton’s
idea does not hold true is to realise that even when you assume that it is not important that no
shipwright could comprehend the mathematics involved because they could receive cut-anddried solutions from natural philosophers and even if you assume that the shipwrights, whom
we saw Hooke depict as archconservative in an earlier chapter, would abandon their own
167
Smith ‘Fluid resistance: why did Newton change his mind?’ 110
66
body of knowledge and traditions to accept these new found shapes, that even then it is
impossible to deny the fact that there existed only two mathematicians at that time who were
capable to use this proposition to calculate the ideal form of ships and that one of those two –
Huygens – realised that the solid of least resistance could never be used as a ship’s hull.
Hessen’s theory does not suffer from the same problems, but has some faults of its
own. The most important of these is that Hessen assumes that the theoretical background of
practical problems was known to seventeenth century knowledge gatherers. Hessen naively
thinks that just because we now know what the theoretical background of a problem is,
natural philosophers in the seventeenth century also knew in which theoretical field they had
to investigate to solve problems of everyday practice. He furthermore pretends that no
problem could be solved and no improvement could be made without the infusion of
theoretical knowledge, as if no channel could be dug without a hydraulic engineer calculating
the amount of water per unit of time flowing through the new channel. 168 Besides, Hessen’s
theory presents not even a hint of plausibility, let alone prove that the eccentric and (before
the 1690s) unworldly Newton was doing anything else than satisfying his own curiosity. It
would also not be consistent to claim that these curiosities were conditioned by practical
problems because there was no practical problem linked to the most important subject of the
Principia. Universal gravitation and another major aspect, the motions of the heavens, could
be calculated precisely enough for any practical application by using Kepler’s laws, meaning
that that part of Newton’s work also did not solve an existing problem.
It is regrettable that neither Merton nor Hessen used any of the other sources discussed
here. Both Newton’s experimental method and his manuscript could have been used by them
to put the treated reference in the context of a reoccurring interest in shipbuilding. These extra
sources would not have supported Hessen’s theory of social determinism but they could have
aided Merton’s more subtle idea of influence. While these sources might have given more
support to Merton’s story of practical influence, the experimental method would also have
undermined the already not that sure footing of Merton’s explanation of the sentence relating
mathematics and shipbuilding even further. The sentence on the experimental search shows
that there went a lot more thought into it than went into ‘I think this proposition will be of
some use for the construction of ships’ because Newton shows he actually thought about the
practical advantages of the test – it could be done at small expense.
168
Cohen The Scientific Revolution 331
67
We should not act as if Merton and Hessen would have written incontrovertible
theories if they only had incorporated both the experimental method and the unpublished
manuscript. In Hessen’s case, the amount of source material would have made no difference,
a dogmatic Marxist historian need not concern himself with the sources, the influence he
perceives is on a subconscious level, and that influence would not have to manifest itself and
Newton would never even have to have had an encounter with an actual ship for the theory to
still hold.
Merton’s case is – not unlike his work – much more nuanced. For him, both the
experimental method and the unpublished manuscript could have been of some use to support
Newton’s connection with shipbuilding. The use of the manuscript would also have been a
mixed blessing for Merton though. It might be that the manuscript showed Newton had a
certain interest in shipbuilding and it might show that Newton had some knowledge of the
problems that could occur when designing ships; it still does not mean that Newton’s
theoretical thinking was influenced by the practical problems of shipbuilding. Even in the best
case, the case that the manuscript was written before the publication of the Principia, there is
nothing that indicates that Newton had processed the text or did anything else with it than
copy it slavishly as a medieval friar – one who could write but could not read. The manuscript
contains no questions that remained to be answered; it contained no marginal notes of
Newton; nor did it contain any observation that Newton added to the text or anything that
could indicate that Newton found a problem or something interesting that spurred him to
investigate the movement of objects through media consisting of particles that are equal and
arranged freely at equal distances from one another. Newton never makes any calculations or
even applies the text, on the contrary, the tables which were added to the end of the text
remained unfinished while it should have been child’s play for Newton to use the proportions
in the manuscript to fill in the blanks. What this manuscript does show is that Newton did
encounter some of the shipwright’s lingo. The manuscript is littered with terms like ‘wales’
and ‘futticks’. If we assume that Newton knew the contents of the private manuscript he
himself wrote down, we must conclude that Newton had a workable knowledge of
shipbuilding jargon, contrary to what Hall claimed. Hall’s commentary on Merton’s work is
also not supported by the lacunas in Merton’s work. Hall views Merton’s work
anachronistically and it seems likely that Hall mistakenly sees Merton’s work as structuralist
because it is an external history and externalism and structuralism have been intertwined in
the history of science for a long time, although they did not both feature in Merton’s work.
68
We have to conclude that Newton’s mathematical work on movement through
resisting media has not improved the practice of shipbuilding. And we also must conclude that
neither the experimental reference nor the manuscript have given results. The only plausible
possibility for the cross-fertilisation of theory and practice in Newton’s work that remains is
the use of the Principia as evidence for the start of the calculus of variations as a consequence
of the search for the least resisted ship hull through the problem of the solid of least
resistance. The claim that the practical problems of shipbuilding led Newton to develop the
calculus of variations rests on two dubious pillars. The first one is that Newton’s reference to
shipbuilding must refer to the problem of the solid of least resistance. Although I.B. Cohen is
right in stating that Newton reflected with that reference on an earlier paragraph while the
problem of the solid of least resistance was not introduced until after that comment, it would
be incorrect to conclude from that observation, that the two are not connected. This is because
both paragraphs of the scholium that come before the reference – and thus are the only parts
to which the remark could be referring – concern themselves with a search for a type of solid
which is resisted less than any of the other shapes of that solid and the last paragraph is only a
generalisation of the earlier two paragraphs with the help of an early form of the calculus of
variations. The connection between the search for a form of a type of solid that is resisted less
than any other form of that solid – which would be of some use for the construction of ships –
and the search for the solid of least resistance – which form of a solid is resisted less than any
other object, where Newton introduces the early form of the calculus of variations – is not
hard to see. The second pillar on which the theory rests, is the credibility of the claim that
Newton really did intend to use this part of his Principia to improve the design of ships. That
this is not the case becomes clear from the experimental reference which was much more
elaborate. It also becomes apparent from the fact that water did not fit in the category of ‘rare’
fluids for which Newton tried to calculate the solid of least resistance, making it unlikely that
the mathematical sentence on shipbuilding was a sincere attempt to improve practice.
In the end the conclusion must be that Newton’s Principia has not contributed any
direct improvements to the design of ships, shipwrights would not have been able to use his
mathematical method even if they believed it could have helped them and the experimental
method has not been tried on a scale in which it would have been useful for any practical
purpose. The reverse influence of practice on theory, in the form of the solid of least
resistance having its origin in a practical problem is also very unlikely because it rests on the
idea that Newton’s reference to shipbuilding was more than a rhetorical device. In Newton’s
69
work shipbuilding is featured but it never becomes more than an afterthought, never is it more
than a reference which could not have been removed without a problem.
70
4. Petty’s Double Bottom
‘The fitts of the Double Bottome do returne very fiercly upon mee’169 with those
words Sir William Petty announced to his confidant Robert Southwell that he would try to
build a twin-hulled ship one last time. It would be his first double-bottom in almost two
decades and the mixed experiences of his former ships were to be washed away by this new
vessel. In this last ship Petty’s theories on shipping and his experience from his former ships
were to come together to form a triumphant mixture.
William Petty (1623-1687) was born, as the son of a clothier on Trinity Sunday
according to the Julian calendar, in the little town of Romsey. From early-modern biographer
John Aubrey we learn that Petty went to France as a cabin boy on a merchant vessel at the age
of 15 where he was marooned at a small inn near Caen with a broken leg. This abandonment
would be a turning point in his life. He was taken in by the local Jesuits from whom he
learned French, Latin, Greek and the Arts. After his studies at Caen were completed he moved
to Paris to study anatomy and while there he met Thomas Hobbes.170 Petty returned to
England where he taught anatomy at Oxon and later, in 1650, became Gresham College’s
Professor of music. Petty acquired great wealth, great status, and a hint of infamy through his
job as one of the land surveyors of Ireland for the Cromwellian Commonwealth. By surveying
– and allegedly shrewd business manoeuvres – he obtained an estate in Ireland, giving him an
astonishing 18.000 pounds per annum which was reduced to a still very respectable 8000
pounds after the restoration of Charles II. Later in life he obtained a county, giving him the
title of earl and he remained a prominent figure in the learned societies of England and Ireland
well into his old age. He died of Gangrene in London on December 26th 1687 and he is buried
in his family’s family grave at his place of birth.
In modern times, Petty is best known as an economical theorist who used an early and
rudimentary form of statistics in his writings. Shipping was an important aspect of the English
economy and it seems that Petty, with his naval experience, was particularly interested in
ships, which he called the most stately, the most useful and the most intricate engine in the
world.171 According to Petty, the ship resembled an animal more than any other inanimate
object and he stated that there was no art more ancient, more pleasant, more profitable or
honourable than navigating. This love of shipping led Petty to design a revolutionary new
169
The Petty-Southwell Correspondence 1676-1687, Henry Petty-Fitzmaurice ed. (New York 1967) 117
John Aubrey Aubrey’s Brief lives Oliver Lawson Dick (London 1975) 237
171
William Petty The Double Bottom or Twin-hulled Ship of Sir William Petty Henry Petty-Fitzmaurice ed.
(Oxford 1931) 4
170
71
craft consisting of not one but two ships – in jargon hulls or bottoms – laid parallel to each
other and connected by a deck on which the masts and eventually the cabins were mounted.
The contraption was steered by two rudders, one mounted on the end of each ship. Petty built
four of these ships, each one more intricate than the former. The ships were christened the
Invention, the Invention II, the Experiment and the St Michael the Archangel.
Before the construction of these full-sized ships Petty had experimented with scale
models. He experimented extensively with parallelepipeds which he pulled through a trough
of water via a string, a pulley and a submerged weight. The weight fell through water because
that way it would descend at a continuous speed, whereas when descending through air it
would keep on accelerating.172 From these experiments Petty learned, amongst other things,
that the longer an object is, the more steadily it would go through the water. He also learned
from these experiments which percentage of a ship must be underwater for it to sail
comfortably.173
Besides the experiments in the trough of water Petty also made larger models which he
could test in open waters: ‘we made a boat to carry 3 men & tried it […] I have also made 2
logs of plain Wood, by which I think I can satisfactorily shew all the material differences
between our new & the usual Way of Shipping’.174 These experiments were hopeful but Petty
could only fully demonstrate his principle, however, with a full-sized ship.
The Invention
The first double-bottom, or twin-hulled ship of Sir William Petty was launched on
Tuesday the 28th of October (Old style) – St. Simon & Jude’s day – in the harbour of Dublin.
The ship was christened the Invention and alternatively called ‘the Simon & Jude’ – partly
after the day she was launched and partly as an obvious reference to the two hulls of which
the ship consisted. The contraption floated on two cylinders which had a diameter of 2 feet
and which were 20 feet in length. These cylinders were held together by a platform was also
20 feet in length and a little over 9 feet wide.175 On this platform wooden benches were
installed for the comfort of inquisitive passengers A 20-foot-mast was raised in the middle of
the platform to accommodate her main means of propulsion, her sails.To ease the Invention’s
passing through the water Petty ordered some attachments to be made which functioned as
heads and which could be mounted on the ends of the cylinders (see figure 4.1). These heads
172
Petty The Double Bottom or Twin-hulled Ship 15
Ibidem 24
174
Ibidem 31
175
Ibidem 29
173
72
could be easily mounted and dismounted and were to slide into the cylinders up and until the
line CD. In Petty’s mind this would result in a boat as in figure 4.2. Note that at the backend
of the ship there were no special forms added to help the boat through the water, these were
added at a later stage.176
On the morning of the ship’s launch a number of curious Dubliners gathered at the
dock where the Invention was built so they could inspect her. On that day the ship was tested
for the first time and from the crowd of spectators a
group of volunteers was chosen to accompany the ship
on her maiden voyage. A day later – on November the
8th in the new style – a more extensive test was done
and Petty wrote down nine observations made during
that trial. Petty noted that his ship was on par with
other ships when sailing almost against the wind; that
Figure 4.1 One of the head that could be
mounted on the Invention
the ship turned as well as any other vessel; that there
was little delay between steering the boat and her
changing direction; that the ship attained a maximum speed of 9 or 10 leagues an hour –
which is either 27 to 30 knots or around 50 to 55 km/h – that she did not heel over very much
even when the wind was unfavourable; that there was no decrease in performance when one
of her cylinders was filled for twenty-five percent; that when all passengers moved to the
stern the head of the ship was raised above
the water; that she drew only 10 inches –
25½ cm – of water and that if whole crew
moved to one side of the ship she remained
stable.
These observations show that Petty
was quite happy with his first trial. The
remarkable thing is that in a significant
number of observations the inventor states
that the ship performed as good as any
other vessel would, not better. The
observations in which the ship was the
Figure 4.2 Petty's impression of a double-bottom
176
Petty The Double Bottom or Twin-hulled Ship 33
73
equal of any other ship were all connected to steering and manoeuvring, which was an
obvious concern for Petty’s design. With these manoeuvres the greatest stress was put on the
platform connecting the two cylinders.
The trial impressed the spectators and was repeated on a number of occasions. At one
of these trials the number of spectators was around a thousand people if we have to believe
Petty. Besides the large amount of locals who came to inspect the ship Petty reports that all
the Dutchmen present in the harbour – stereotypical good sailors and England’s fiercest
competitors in all affairs naval – were busy studying his vessel, measuring her and testing her
hull strength by kicking. And while Petty took this Dutch interest as a sign of success it was
to be the seed of great opposition to his craft. As we have seen in Petty‘s penultimate
observation of the first trial, the ship drew very little water, meaning she could easily sail in
very shallow water. Petty was eager to capitalise on this trait stating that the Invention would
function as a prototype for: ‘a man of war which will carry 500 men not needing above 4 or 5
feet of water making all harbours of little use’.177 The Dutch interest in the Simon & Jude
combined with this observation set off alarm bells at the Royal Society, to which Petty
reported. They were alarmed because a great advantage of the English on their Dutch enemies
was the larger size of their ships. As the Dutch admiral Tromp had exclaimed desperately
after a lost naval engagement during the first Anglo-Dutch war: ‘there were more than fifty
ships in the English fleet which were bigger, better built, and better gunned’. 178 The size of
Dutch ships was limited by the shallow harbours of the low lying Dutch delta coast, a problem
which did not trouble the English in the least. Petty’s ship would destroy this advantage
completely, a conclusion drawn rather quickly. A month after the first trials with the
Invention in the harbour of Dublin the then president of the Royal Society, William
Brouncker, wrote: ‘since you seem to say […] that [the ship] destroys the advantage we have
in our Ports & Shipping above other nations (especially the Dutch), [you should consider]
whether the prosperity thereof be desirable or not’.179 This concern for the potentially
disastrous implications the ship would have on the balance of maritime powers reached to the
highest political echelons. King Charles II, who mocked Petty’s ideas at first, had recently
warmed up to the idea of Petty’s Invention, he even promised Petty to pay double the cost that
Petty made if he were to successfully pass the King’s test, 180 but he changed his mind, when
177
Petty The Double Bottom or Twin-hulled Ship 32
As told in: C.R. Boxer The Anglo-Dutch Wars of the 17th Century:1652-1674 (London 1974)15
179
Petty The Double Bottom or Twin-hulled Ship 34
180
Ibidem 34
178
74
the potential political detriment became clear and only wished ill on the endeavour from that
point on.181
Petty, in the meantime, did not see the small draught as hazardous to England and
continued to promote and improve his vessel. He experimented with a number of different
heads and tails – differing in shape as well as in size – which could easily be mounted and
dismount from the vessel. These trial voyages of the ship were transformed into wagered
races in which the Invention indiscriminately outsailed her opponents. Not yet satisfied, Petty
kept on rethinking his design and one particular focus area for adjustments was its means of
propulsion. At its launch the Invention used sails for propulsion but Petty was continually
looking for alternative means. He was sceptical about rowing at first but changed his mind on
the matter after three unexpectedly positive tests in which oars were used. Petty even
speculated that ‘horses may row our shipping’,182 presumably by powering a paddle wheel
suspended between the two hulls. Regardless of the particulars, Petty stated that he would not
gamble the success of his ship on this alternate means of propulsion and only used oars in a
combination with sails at which point they did not contribute much.
Although the races should have established the reputation of the Simon & Jude, the
potential threat it formed for the national security hung over it like the sword of Damocles.
This negative connotation was a point of grave concern for Petty and in typical style he went
on the offensive, publishing twelve reasons why the ship would be detrimental to England's
enemies and especially a bane for the United Provinces. That Petty had a very difficult time
negating the opposition to his ship becomes very clear from the point he uses to argue against
the fears of the use of the design by the Dutch. Petty states firstly that: ‘the double-bodied
vessels are of peculiar advantage to the English over the Hollanders, as well in matter of
Trade as in War, either defensive or offensive between those Nations’ and secondly that: ‘the
English by preoccupation of these Vessels may easily oust the Hollander of his Mastery of
trade & particularly that of fishing.’183 The fact that these two points made by Petty were
statements rather than arguments really emphasizes that Petty either did not see the danger of
his design or could not answer the threat this perceived danger formed for his project. The
first two statements, as a consequence, only apply to the case that the English were the only
ones to have double-bottoms at their command. The subsequent points on the inventor’s list
do not remedy this defect although they do give more particulars of how the ship would
181
Petty The Double Bottom or Twin-hulled Ship 64
Ibidem 40
183
Ibidem 44
182
75
benefit the English. One advantage of the ship that Petty points to is the relatively small crew
it needs to operate, meaning that the English could master a larger fleet with the same amount
of seamen. Other advantages included the stability of the twin-hulled ships – ‘[they] perform
[…] in fair Weather [like] a Galley can, & in foul Weather what a Frigate’ – that the ship was
better for the health of both seamen and passengers; that the ship would be an aid for
Christendom; that the vessel would be financially beneficial to the King – ‘use of these
Vessels will raise the price & estimation of several Materials of the growth of his Majesty’s
dominions’ – and that the use of twin hulled-ships would greatly aid in transportation, being
able to ‘sail as well upon the Ice as the Sea’ and ‘encourage the navigating of many Rivers in
England […] making English Horses a good exportable Commodity’.184 Although Petty gives
two points which were especially beneficial for the English – that there would be more men
available and the cost would be lower, these traits were especially beneficial for the English
because the English crown had large debts and with more men available they could
potentially build a fleet that would eclipse those of their rivals – the majority of the arguments
Petty gives are in support of the ship itself not of the use of the ship by the English.
The negative comments on Petty’s vessel did not only come from political figures
though, Petty mentions opponents among the Dublin seamen and while he expected the
support of the Royal Society, it was not univocally forthcoming. This was not only due to the
political concerns, which did matter to a Society so closely associated with the King, but there
was also a genuine debate if a normal flat bottomed vessel would give the same results as
Petty’s contraption. Petty’s reaction to this question was quite agitated and it came quickly
after he first heard this objection, for it was advanced by the Society’s president, Lord
Brouncker, the man who first brought the ‘Dutch threat problem’ to Petty’s attention.
Brouncker’s question to the inventor was if a flat single bodied vessel of the same length,
breadth and burthen would not perform better than a twin-hulled ship. Petty answered that
such a ship could not be created, that if a flat, single-bottomed ship would be built with the
same dimensions as Petty’s Invention that she could carry less than his ship could or that it
otherwise would lay deeper in the water than his ship, making it more susceptible to
resistance from the water.
The London members of the Royal Society would, after their motto, take nobody’s
word for it and, in this matter, certainly not only Petty’s word. To receive extra information
the Royal Society asked all fellows residing in Ireland to report on the ship to the Society.
184
All citations on this page come from: Petty The Double Bottom or Twin-hulled Ship 44-45
76
These individual observations were forged into one report and that report was sent to London
on January 15th 1663. The consolidation of the individual accounts into one report took place
at Petty’s house, who as both host and founding member of the Royal Society had ample
opportunity to influence the contents of the report. In his other role – that of inventor of the
Invention – Petty was allowed to comment on the critiques he himself had helped to write.
The first remarkable aspect of the report is that all of the noted objections were of a technical
nature. The commission questioned the strength of the connection between the two hulls in
various situations and questioned the stability of the vessel while on a rough sea but never
asked what the impact on England would be if the ship fell into the hands of its enemies. Petty
easily negated the critiques that were written down, not only by using theoretical arguments –
for example, he answered the objection that a wave could exert such a force that it would
destroy the connection between the two hulls by stating that it would have to be done by a
wave that was small enough to pass between the two cylinders yet high enough to touch the
underside of the deck, which would make for a very peculiar shaped wave indeed, and that
even in that case such a wave would travel forward between the hulls and not upwards 185 –
but also by pointing to the many – more than 30 at that time – successful trials the ship had
and the many rough seas it had endured during these trials.186 Petty thus fused both theoretical
and practical arguments to convince the Royal Society of the value of his ship.
The many trials and races were the best way for Petty to promote his vessel and Lord
Massereene, one of the fellows who contributed to the report on the Invention to the Royal
Society, attached his eyewitness account of one such trial to the report. The described trial
was a four way race and the prize to be won was a silk flag with a harp in a laurel wreath with
underneath it a scroll with the inscription: ‘Proemium Regalis Societatis Velociori’ which
roughly translates to: ‘Prize from the Royal Society for the swifter’187. Petty won this race
comfortably, being first at the turning point and on the way back surpassing the opponents
who trailed so much they decided to turn at the moment the Invention rounded the turning
point188, resulting in the hoisting of the victory flag, by him and his crew, under loud cheers.
The opportunity of winning the flag from Petty’s vessel attracted a lot of interested sailors,
which led to new races being organised, each ship had to pay an entrance fee of 10 pounds
185
Thomas Birch The History of the Royal Society of London for improving of natural knowledge, I, (London
1756) 186
186
Birch The History of the Royal Society, I, 188
187
Beste Floris ik twijfel hier erg over of de meest passende vertaling is voor de snellere of voor de snelste
188
Petty The Double Bottom or Twin-hulled Ship 53
77
and each ship that defeated the Invention would win a prize of 20 pounds and the fastest of all
would also win the victory flag.
Petty’s ship did not meet her match on the sea but in the royal halls in London. It was
at this moment in time that the king had changed his opinion on the ship from cautiously
positive to wishing it ill success. Petty saw the danger in this loss of royal favour and franticly
tried to change the king’s mind. On March 7th Petty could not yet believe that the King spoke
negatively on his idea. He clung to the encouraging words Charles II had spoken in the past
and the alluring power of the prospects of enormous wealth with which he had made his
sovereign enthusiastic. At this point he even vowed that if he could be convinced that the ship
would be detrimental for King and Country that he would make a bonfire out of his vessel and
his notes on double-bottom shipping. This disbelieve faded rather quickly and Petty instructed
his confidantes back in England to convince high ranking fellows of the Royal Society and
members of the royal courts of the merit of the double-bottom. Apparently some trials were
performed for the King to change his mind but the nature of these trials and their results were
kept hidden from Petty and his supporters. The whole campaign was of little avail: Petty
never received any answers to his pleas and the king did not change his mind on the
Invention.
The council of the Royal Society spoke about the Invention on May 27th 1663. The
secretary at that meeting, Henry Oldenburg, reminded the council that Petty’s invention
‘being a state concern was not proper to be managed by the Society’. 189 The council explicitly
did not forbade any member from commenting on the vessel but the institution would not
support, advocate for or help Petty and his project. This is likely a good representation of the
ruling opinion in the English capital. For, while the Royal Society supported innovation, their
dependence on the crown always superseded their longing for ingenuity.
In just under seven months the Invention went from its successful launch and the
celebration at the first trials to a danger for the state. Petty had found a working innovation
but had not revolutionised the practice of shipping as he planned, not yet anyway.
The Invention II
Although the report of the Royal Society’s council meeting was the last time there was
a recorded conversation about the Simon & Jude, Petty was already working on another
project. A month before the Royal Society disavowed Petty’s vessel, a contract was signed in
which both Petty and Lord Massereene – one of the signees of the report on Petty’s twin189
Petty The Double Bottom or Twin-hulled Ship 72
78
hulled ship to the Royal Society and the author of the accompanying eyewitness account –
vowed money for the building of a new double-bottom or twin-hulled ship. They agreed to
split all costs and the ownership of the new vessel with the added clause that Massereene
would pay 20 pounds to Petty.
Petty called this new vessel a ‘mongrel’ double-bottom, partly because he wasn’t the
sole parent and partly because he did not fully approve of his own ship, not being at liberty to
design it as he pleased. The ship had other names besides the ‘mongrel’ like ‘the Invention
[II]’190, ‘the Mercury’ – after the roman god – ‘the Gemini’ – Latin for twins – the ‘Castor &
Pollux – after the Greek demigod patrons of sailors – ‘the Zabulon and Napthay’ – after two
sons of Jacob who later founded two Israelite tribes to whose land Jesus fled after the death of
John the Baptist191 – and ‘the Wit and Money’ – after its inventor. The ship was ready in
early July and to promote his new vessel Petty used an old technique. He wagered 50 pounds
that no ship could make the round trip from Dublin to Holyhead in Wales faster than his new
double-bottom. This new race would be held on Monday July 30th 1663. On that morning
only one opponent presented itself, a packet boat named Offroy – the fastest in the fleet
according to Pepys192 – which usually delivered mail between Holyhead and Dublin; it was
thus a vessel with experience on this particular route. The packet boat returned to Dublin
harbour at 8 a.m. on Thursday August 2nd, her crew cheering and full of confidence, for they
had not seen the Invention II since they sailed out from Holyhead together and they were of
the opinion that the Invention II must had been shipwrecked or in any case left behind due to
the foul weather and the rough seas.193 Their cheerful mood vanished like a drop of water in
the desert when they saw with utter disbelief that Petty’s vessel had out sailed them and was
already at anchor in the harbour, she had arrived at 5 p.m. the day before, beating the vessel
and its experienced crew by 15 hours.
The race was an unmistakable success and it led Petty to start a grand campaign to
rehabilitate his idea of double-bottom vessels. He used the race with the Offroy extensively
for this purpose, especially the thought of his opponent that his double-bottom had sunken in
the rough sea or as Petty’s advertisement in a Dublin newspaper related: ‘some said twas
impossible her mast could be sufficiently planted against a strong gale,194 others said she was
190
This has to be a second ship called Invention for the first is talked about in October 1662 but this reference
is from june 19th 1663, two months after the launching of the ‘Mongrel’
191
Matthew 4:13
192
Samuel Pepys, The diary of Samuel Pepys IV, 1663, Latham & Matthews ed. (London zj) 31 July 1663
193
Pepys, The diary of Samuel Pepys IV, 31 July 1663
194
Her mast would be ripped out of the deck by the strong wind
79
gone to land at O Brasile. The Hollander would have her in twa sturcken195 […] but her return
in triumph […] has checkt the dirision of some and becalmed the violence of others’. 196 Petty
once again presents the stability of the ship as one of her major advantages: ‘it blew very
hard, insomuch that a small Holland vessel […] was in appearance often lookt to be overset,
whilst [our ship] inclined not above half a foot’.197 Other lists of the advantages of Petty’s
ship also appeared. In these lists the emphasis was mostly on the economic prosperity the ship
would provide and the detriment it would be for the Dutch.
In one of the pamphlets of Petty’s propaganda campaign due attention is given to the
particulars of the ship’s construction in an attempt to familiarize the general public with the
design. The motivation of the design choices made by Petty give an insight into the
knowledge that Petty applied while he designed his vessel. The feature of the vessel that Petty
most thoroughly justifies is the length of the individual bottoms, which were uncommonly
large. Petty justified this length by stating that it had no negative impact on the speed of the
ship while it also makes sure that the platform between the two hulls never gets immersed
completely. Other aspects of the design of the hulls were also debated. The bodies were
supposed to be slender and all of the same breadth, because this inhibited the ship the least.
The hulls had to have broad keels which would reduce the overall draught. The mast of the
ship was longer than usual on ships with the same dimension for Petty was sure that his
particular design could hoist a larger amount of sails without the ship becoming
uncontrollable. In the explanatory pamphlet the most remarkable feature of the design, the
platform joining the two hulls – or rather the fact that there were two individual hulls linked
together – remained undiscussed. No information was given about how the all-important
platform was mounted on the two individual hulls or what made it strong enough for the ship
not to be ripped in twa sturcken. What does become clear is the way in which Petty went
about designing his ship. The inventor made conscious choices based on existing nautical
theory to attain the practical result desired by him but the particulars of these choices seem to
be determined by traditional knowledge.
Petty’s campaign had a significant result. The king had found a renewed interest in
Petty’s vessel and had asked her to come to Portsmouth so he could see her in action in a race
against one of his own royal yachts. To fully capitalize on the interest of the king Petty made
some proposals to the Charles II. The first proposal of Petty was to build a double-headed ship
195
Twee stukken or two pieces
Petty The Double Bottom or Twin-hulled Ship 80
197
Ibidem 80
196
80
capable of going from Wales to Ireland within 30 hours for the sum of 2000 pounds. Another
proposal was to build a warship, swifter then any single hulled vessel, which could house a
crew of 200 men, the same amount of cannons as a normal man-of-war with that crew size
and with provisions for three months. As a third proposal Petty asked that if the king was
pleased with the first ships he built he would receive a contract to build an additional 30
vessels of the type he designed within seven years. As a last proposal Petty suggested to allow
him to convert those ships of the Royal Navy that were in a bad condition to double-bottoms.
In an attempt to convince the king Petty vowed to add any further quality to the ships the king
demanded and vowed to give insurance that none of the platforms holding the individual hulls
together would break. The only compensation Petty begged for was that he would be paid
promptly when he reached his goals.198 The king did not reject Petty’s proposals outright and
suggested alterations to quite a few of them. He thought £ 2000,- was too expensive for any
new ship and was of the opinion that the provision aboard the warship from the second
proposal should be doubled. Charles II rejected the proposal for thirty ships outright stating
that ‘before 30 can be built […] ye Hollander will build 500’199 – a fear not justified for even
after the successful race to and from Holyhead the Dutch spoke only in derogative terms on
Petty’s undertaking: ‘While [Petty] was making [his new ship] he was ridiculed, like Noach
when he was building his arch, some said: “it will be the equal of the Foolish ship of
Rotterdam”’,200 a clear sign of lack of faith in this venture from the Dutch side. Charles II
further demanded that Petty’s statement that ‘any good quality the king desired would be
added’ would be changed to ‘all good qualities the king desired’ to prevent that every
alteration required an additional contract. He found the insurance promised by Petty a
welcome addition and set the rate to be paid out at 99 pounds per cent lost.
While the bartering on the proposals continued, the call to come to Portsmouth with a
double-bottomed ship still stood. Petty found reason after reason to postpone answering this
call. His first excuse was that he was tied up in a grand legal affair, combatting the
retrocession of parts of his Irish estate to previous owners from whom it was seized by the
Cromwellian government. This court held session until September 1st after which Petty would
be free to go to Portsmouth. The king would depart on the 4th of September to Portsmouth
meaning that both men would arrive there around the same time. Petty however still hesitated
198
Petty The Double Bottom or Twin-hulled Ship 85-86
Ibidem 88
200
Thien boecken der Hollandsche Mercurius, off histoorisch-verhaal aller gedenckwaardighste
gheschiedenissen van de beginne des jaars 1650 tot den jaare 1660, in christenrijck voorgevallen. XIV Augustus
1663, 130-131 My Italics
199
81
to set sail from Dublin, this time citing financial reasons. He had to find a new crew and no
sailor would sail his vessel without a promised compensation for their wives and children in
case of shipwreck, which made for a hefty sum. Besides, the co-owner of the ship, Lord
Massereene, thought that with the royal summon to Portsmouth Petty had received a
substantial sum of money from which he demanded his fair share. The consequence of alls
these excuses was that the order to come to Portsmouth, made in July, wasn’t answered
halfway through September. The king’s sincere desire to view Petty’s ship becomes clear
from the fact that he postponed his journey to Portsmouth until he received a message that
Petty’s ship had arrived there.201 Petty must have seen this arrangement by the king as
profound sign of interest and as a light on the road to royal support. He could not afford to let
the king wait too long and squander this opportunity to redeem himself.
Luck was with Petty and it seems at this point that he comes close to a lasting impact
on the art of shipping with his new type of vessel, devised with the aid of experiments,
because he was close to receiving royal support which could cause it to be implemented into
the Royal Navy. Fate, however, showed its most uncompassionate side when only two days
after Petty had received word that the king would wait for the message that Petty had arrived
at Portsmouth, a storm hit Dublin harbour. The night of the storm only one crewmember was
aboard the double-bottomed vessel and this sailor, out of fear, let the ship drive ashore which
damaged the vessel badly. This meant that Petty again could not leave Dublin.202
The Invention II’s string of bad luck did not end here, for when the ship was finally
repaired – which was not until the third week of October – the crew Petty gathered was
reluctant to go on board. To talk about this unwillingness Petty invited the crew and their
families for a dinner at his house on the evening before the scheduled departure. The families
were picked up by carriage – not an everyday mode of transportation for the wives and
children of sailors – and treated with a banquet of ‘burnt wine, stued prunes, applepyes,
gingerbread, white sopps &milke, with apples and Nuts in abundance […] and other more
solid food for ye men themselves’.203 After much crying, laughing, hoping and fearing Petty
took the floor and told the guests that if they did not trust his ship they should not venture to
go aboard, because the carpenters and seamen of London would not be merciful on them and
neither would the poets, playwrights and court wits. However, the gains for the sailors who
braved this opposition were to be substantial. They would not only be sailing to meet their
201
Petty The Double Bottom or Twin-hulled Ship 90
Birch The History of the Royal Society, I, 310
203
Petty The Double Bottom or Twin-hulled Ship 91
202
82
sovereign, on a vessel that would out sail all others, but when a fleet of twin-hulled vessels
was built these sailors would become captains of their own twin-hulled ships in the Royal
Navy and their spouses might become ladies or even dames. The alcohol, this speech and the
prospects of high standings convinced the whole crew to say their goodbyes and to board the
Invention II which sailed out for Portsmouth the next morning.
The ship finally left, two months after she was first summoned but this was not to
everybody’s liking. Massereene, co-owner of the ship, invested in the vessel with the
intention to use it as a pleasure yacht on his newly acquired lake, Lough Neagh. He now saw
his object of desire sailing from Dublin harbour and he feared that the ship’s success would
prevent her from being returned to him. Petty had admitted that the vessel was originally built
for service on Lough Neagh: ‘ye Invention […] full of ugly faults and eye sores – being built
for a fresh water Lough and to be carried 8 miles over land’,204 but now had other plans for it.
This last sentence reveals the forethought with which Petty designed his ship and the
particulars he took into account– such as the type of water the vessel would sail in.
Massereene repeatedly tried to confiscate the vessel but Petty prevented this time and again,
the case eventually was arbitrated but the outcome of the case remains unknown.
The Invention II made it to Portsmouth and both Petty and his vessel set sail to
London from there, after which and remained in the capital for at least the next half year. Both
the Invention II and its inventor were quite the talk of the town as we learn from the diary of
Samuel Pepys: ‘to the Coffee House, wither came […] Sir W. Petty, with whom I talked, and
so did many, almost all about his new vessel’.205 The ship itself laid at the Deptford docks just
one bend in the Thames downstream from London Bridge. Pepys took a serious interest in the
vessel and had a favourable opinion of it, admitting that it: ‘hath an odd appearance, but not
such as people make of it, for I am of the opinion that he would never have discussed so much
of it, if it were not better than other vessels’.206 The people that Pepys referred to were
generally less sympathetic to Petty’s invention: ‘[Petty] was abused the other day, as he is
now, by tongues that I am sure speak before they know anything good or bad of [his ship]’.207
Peter Pett, master shipwright and one of the signees on the report on the first Invention to the
Royal Society, was one of those persons, he thought the Invention II to be the most dangerous
thing in the world, and he feared that it would cause the English to lose their pre-eminent
204
Petty The Double Bottom or Twin-hulled Ship 92
Pepys, The diary of Samuel Pepys IV 30 December 1663
206
Pepys, The diary of Samuel Pepys V 22 January 1663/1664
207
Ibidem, V, 22 January 1663/1664
205
83
position in the naval trade to the Ottomans who, on their calm seas, would profit much more
of twin-hulled ships than the English would on the rough North Sea.208 The shipbuilder, and
later Member of Parliament, Anthony Deane was also sceptical about the vessel which he
thought must ‘prove a folly’, a notion with which Pepys disagreed ‘unless it be that the King
will not have it encouraged’.209 The whole endeavour hinged on Royal patronage once again.
However, the bestowing of royal patronage on Petty’s ship seemed likely this time: the king
had promised money and support for the ship if it sailed well and he had summoned Petty to
Portsmouth for which he even delayed his own voyage to that town.
Petty had an audience with Charles II on February 10th 1664 and it was there that the
fate of the Invention II would be decided. Pepys wrote a report of the meeting in his diary.
The audience took place in the chamber of the Lord High Admiral, the future king James II.
The conversation lasted two hours and the result was very clear, Pepys’ report speaks for
itself: ‘The King came and stayed an hour or two laughing at Sir W. Petty [and his boat] at
which poor Petty was, I perceive, at some loss; but [he] did argue discreetly, and bear the
unreasonable follies of the King’s objections and other bystanders with great discretion; and
offered to take oddes against the King’s best boates; but the King would not lay, but cried him
down with words only.’210 The meeting obviously went disastrously, Petty was lampooned,
his ship ridiculed and the possibility of royal patronage had eluded him once again just as the
low hanging fruit above the head of the hungry Tantalus.
The Experiment
Although the Invention II did not disappear immediately after that audience of Petty –
both Pepys and John Evelyn report on it in their diaries until the end of February – the ship
quickly sailed out of the records of history, never to return again. Petty himself was quite
rapidly back on his feet. The most important indicator that Petty was not mentally broken by
the failure of the Invention II must be that on January 1st 1665211 – some ten months after the
audience with Charles II demolished his dreams for the Invention II – the king himself
christened a new vessel built under Petty’s auspices and named it the Experiment. The
Experiment was another twin-hulled ship and it was Petty’s third multi-hulled vessel in just
over two years. The launching of the vessel seems to have been an occasion for the elite of
208
Ibidem, January 1663/1664
Pepys, The diary of Samuel Pepys V 29 January 63/64
210
Ibidem, V, 1 February 1663/1664
211
N.B. this was not a significant date because according to Petty and his English contemporaries it was
December 22nd 1664
209
84
London to show themselves, both Pepys and Evelyn were present as well as the Duke of York
and of course the king himself. Evelyn reported that the reactions on the ship were various,
but Pepys stated that: ‘[The ship] swims and looks finely and I believe will do well.’212 A few
months later Pepys describes the ship as a ‘brave roomy vessel’.213 The ship quickly received
international attention, in the Journal des Sçavans of January 19th a report of five pages
concerning the Experiment was published. The report spoke positively on the vessel and on
double-bottom shipping in general. In the report three points were identified in which the
Experiment was an improvement over normal ships. As a first improvement the author
claimed that twin-hulled ships would be faster than conventional ships; secondly, the article
stated that the Experiment would be more stable than other ships and thirdly it stated that
double-bottoms would handle easier than conventional ships.214 Petty wrote an extended
response on the French article in which he first stated that he thought it too early to hold an
extensive discussion on a ship still being tested, after which he described not three but fifteen
different benefits of his double-bottom. He sent his report to the Royal Society for publication
in the newly established philosophical transactions.215 The council of editors however, feared
the political implications of the article – they still feared the ship would fall into the hands of
the Dutch – and withheld it from publication until they had learned the opinion of the king on
the matter.
Petty had no faith that the royal opinion on the type of vessel he designed had changed
since the audience on the Invention II and devised a new trial to test his ship. This new trial
was a round trip to Portugal through the Bay of Biscay. The Experiment sailed out from
London in late March or early April and made it to Porto without severe problems on the way.
She sailed back north from Porto to the city of Vigo in Spain to prepare for the return voyage
to London. Petty dates the start of the return on the 20th October and states that she wasn’t
repaired before she sailed out for England. Later Petty would write to his nephew that two
thirds of her crew was press-ganged by the Royal Navy in Vigo and that she, as a
consequence, set sail from Vigo to London with a crew of just 17 men instead of the required
50.216 The Bay of Biscay is not an easy gulf to sail for any ship, let alone for an experimental
212
Pepys, The diary of Samuel Pepys V 22 December 1664
Pepys, The diary of Samuel Pepys VI 13 February 1664/1665
214
Journal des Sçavans 19 janvier 1665 34-35: ‘premierement [ce Navire] sera plus viste […] secondement […]
ce Navire sera plus seur que les autres […] troisiesmement […] ce Navire sera encore plus commode que les
autres’
215
Journal des Sçavans 30 mars 1663 156
216
The Petty-Southwell Correspondence 87
213
85
ship with less than half of the crew required to man it. Whatever the precise circumstances
maybe, it is clear that the ship never reached its destination and it is presumed to have sunk on
its way home.
Through the remainder of the year Petty kept the hope that his ship would make it
home. In a note to other investors, written in June of 1666, Petty implicitly admits that the
vessel was lost. A year later the Experiment is featured in Thomas Sprat’s History of the
Royal Society who still had a positive opinion of it stating that although ‘the Experiment itself
is lost, I hope I may securely speak of its advantages’.217 Sprat believed that the ship was
destroyed by ‘a dreadful tempest, as overwhelm’d a great fleet the same night’.218 The ship
had thus fallen victim to the most common bane of seamen, the weather.
Sprat was a real convert to the cause of multi-hulled vessels, calling the ship: ‘the most
considerable Experiment, that has been made in this Age of Experiments’.219 Even the sinking
of the ship did not lessen the trust he had in the design: ‘[the ship] was destroyed by a
common fate, […] so that the Ancient Fabricks of ships have no reason to triumph over that
new Model, when of threescore and ten sail that were in the same Storm, there was not one
escap’d to bring the News.´220 This excuse was of no avail, the uncertain political support
combined with the ship’s visit to Davy Jones´s locker had sealed the faith for double
bottomed-shipping for now. The inventor himself had not accepted the fate of his way of
shipbuilding and kept believing in the principle. He wrote to the financiers of the Experiment
that he was looking for new funds to build a fourth ship. That fourth ship would not be built
for almost two decades and Petty had to wait until then to re-attempt the vindication
potentially revolutionary idea.
An Intermezzo
Petty had built three ships between November 1662 and December 1664. These ships
were of a type as yet unseen in Europe, ships we, in our time, would venture to call
catamarans. Each successive vessel had celebrated some impressive results and in the two
years that Petty had applied himself to this endeavour significant strides were made. Starting
from experiments with models his first full-sized boat was the fastest in races across the
harbour of Dublin; his second vessel was the fastest on the line from Holyhead to Dublin and
217
Thomas Sprat The history of the Royal Society of London for the Improving of natural knowledge (London
1667) 240
218
Ibidem 240
219
Ibidem 240
220
Ibidem 240
86
vice versa and his third ship made it across the Bay of Biscay to northern Spain and Portugal.
Each ship had an improved design and was able to go farther than its predecessor.
The ships can be viewed collectively as one twenty year long experiment, to find the
best double-bodied vessel. But not only if you view the ships in succession are they an
experiment, each ship is an adjustable experiment in and of itself. The first ship, for example,
had changeable heads and tails for the cylinders it floated on, to test a variety of designs.
These tests could learn which heads made the ship go the fastest through the water, which
tails remedied the problem of ‘dead water’ the best – ‘dead water’ is water which flows in the
gap left by the rear of the ship as it moves forward, this water pulls the ship back –and which
combination of heads and tails made the ship go the smoothest through the water. Quite a few
of these heads and tails were actually tested emphasizing the experimental nature of Petty’s
enquiry. Besides the trials with the different heads and tails there were some trials in which
rowing was used as the means of propulsion for the ship.
Although the consecutive ships were improvements on their predecessors and although
they could boast some impressive results – the successful defence of their honorary flag, the
victory in the race across the Irish Sea and their voyage to Portugal – the ships did not have a
direct impact on the practice of shipbuilding, let alone revolutionizing that trade.
The ships lacked the institutional and political support to make them into a lasting
success. The most prominent obstacle that prevented Petty’s vessels from gaining political
support was that they would destroy the advantage in ship size the English had on their Dutch
rivals, a factor not to be underestimated because these nations were almost constantly in
conflict with each other – the first Anglo-Dutch war ended less than a decade before Petty’s
first ship was launched, it ended in 1654, and the second war with the Dutch Republic was
declared a month before the Experiment sailed out for Porto. The general conclusion for these
ships must be that they had the potential for revolutionizing shipping but that the revolution
they could bring about was topped because the country in which it could happen did not
desire it.
Petty, however, could not be freed of his visions of double-bodied ships and returned
to the idea a number of times in his later life. Evelyn reports in 1675 that: ‘[Petty] still persists
that [his double-bottomed ship] is practicable, and of exceeding use; and he has often told me
he would adventure himself in such another, could he procure sailors, and his Majesty’s
permission to make a second Experiment’.221 Petty had kept faith in his design, and this faith
221
John Evelyn The diary of John Evelyn Guy de la Bédoyère (ed.), march 22nd 1675
87
showed itself ever more frequent in the ensuing years. When he wrote to his nephew in early
1681 it reared its head once again: ‘let the dead bury the dead, But I have a Treatise ready to
Vindicate the designe [of my double-bottomed ship] and the necessity of attempting it, which
will make it rise againe after I am dead.’222 It is a this point that we return to the opening line
of this chapter, because two years after the last comment Petty unburdened to the same
nephew that: ‘The fitts of the Double Bottome do returne very fiercly upon mee. I cannot bee
diswaded but that it conteynes most glorious, usefull and pleasant things.’223 It would not take
long for Petty to give in to this urge and he soon started gathering support for a fourth twinhulled ship.
The St Michael the Archangel
Petty attempted to get support for his new enterprise by doing tests with scale models
for spectators. For this purpose he had three models made, one representing an ordinary yacht,
a second one portraying a merchant variant of a double-bottom ship and a third which was a
model of a twin-hulled man-of-war. The experiments were conducted at Petty’s house and
besides these three ship models they also involved three planks modelled as a cross-section of
respectively, a single-bodied vessel, a double-bodied vessel and a single-bodied vessel with a
sharp head and a sharp tail – thus in the shape of a canoe. These planks were drawn through
the water in a manner akin to the first experiments almost two decades earlier, and the result
was clear: ‘it was judged by the company that [the] Body which represented the double
bottome mov’d more quick and streight [through] the water then either of the other two’.224
Of the eight guests present that evening only two, a captain Shiers and the earlier mentioned
Anthony Deane, were not wholly convinced of the desirability of the twin-hulled ship. Deane,
for instance, complemented the success of this trial but: ‘hoped that the same advantage might
be given to a single body by means of less uncouth and less different from those in common
practice, the common people being frighted to adventure upon so great changes all at once.’225
The nature of the uttered critique indicates that Petty’s experiment was convincing, for the
critique was not aimed at the models themselves but on the impact they would have on
society.
To gain political support, Petty started a correspondence with Sir John Werden,
secretary to the highest commander in the Royal Navy, the future James II. Werden responded
222
The Petty-Southwell Correspondence 87
The Petty-Southwell Correspondence 117
224
Petty The Double Bottom or Twin-hulled Ship 117
225
Ibidem 117-118
223
88
encouragingly to Petty’s letter and Petty guaranteed himself of Werden’s support by sending
him the three ship models he used in his experiments as Christmas presents. Werden was
thankful for his gifts and asked Petty to refute the objections a conversation partner of him
had raised against his models. This conversation partner turned out to be no less a person than
the king himself, who, after terminating the success of earlier vessels by laughter and political
concerns was now questioning the internal strength of the double-bottom. Charles II had
perceived two distinct flaws in Petty’s idea, the first flaw was that the experiments done with
scale models were not exact enough and that as a consequence the result could not
successfully be translated to full-sized ships; the second objection was that he thought it
impossible that any twin-hulled ship would be strong enough to endure a voyage on the full
seas. This last objection was fuelled by Petty’s own observation that for every doubling in
size the amount of materials needed to ensure the internal strength had to be cubed. Charles II
backed his critiques with wagers to be won by Petty’s ship in a trial race between a new
double-bottomed vessel and his royal yacht. Petty jumped on this possibility to receive the
royal patronage he so long hoped for by first writing a long reply to the king’s objections
followed by a summary of that same reply not a week later. To this summary he attached a
proposal for a wager containing twenty-one points.
Petty’s replies to the flaws the king perceived show his confidence. The inventor tries
to negate the first objection by emphasizing the high quality of the materials he used for the
models. In the answer to the second point Petty states that he can show that the ship will hold
the added weight of the extra materials by laying extra burden on the models or, alternatively,
by pointing to the earlier double-bottoms that were built and which were able to carry the
extra load. Although Petty points here to his previous ships he is quick to distance this new
ship from the ill-fated Experiment, going as far as devising a new class of ships for his new
project: ‘the double-bottoms which wee now insist upon are very different from those
[double-bottoms you have already seen] and therefore we now call our vessels not doublebottoms but sluice builts’.226 The fact that the King wagered money against his boat did not sit
comfortable with Petty who rather had His Majesty been the referee for the wager – according
to Petty the current situation was very similar to the hypothetical situation in which Petty had
presented the philosophers’ stone to the king, for in the current situation the king would
always come out beneficial, if Petty lost the wager the king would gain money by winning the
bet and if the king lost the bet he had gained intimate knowledge of an invention that would
226
Petty The Double Bottom or Twin-hulled Ship 123
89
easily earn him more money than he had lost on the bet. The trials for the wagers were to be
conducted with models and open for anyone to enter with one vessel, except for the king who
was allowed to use up to ten vessels. Petty pledged that his ship would be superior 21 distinct
ways including that she would: be cheaper, faster, stronger, more stable, with less draught,
less inhibited by adverse winds and that she would need no ballast, and he promised a 21st
part of 10 pounds – comparable with a 1000 pounds in today’s money – for every point and to
every competitor who would outperform Petty’s sluice built.
Petty’s search for support did not only pay off in Royal circles, in April 1684 he had
found fourteen people ready and able to invest in building a full-sized ship. This ship would
be christened as the Saint Michael the Archangel and it would become Petty’s fourth and last
double-bottom – or his only sluice built. Work on the vessel started at Lazar’s hill near Dublin
on July 10th and while Petty complained in August about the deplorable skill of the workmen,
the ship was reported to be almost ready when, in the middle of September, the investors had
to pledge money for a second time. A first trial voyage was done in early October and the
results were less than satisfactory. The vessel did not seem to have enough buoyancy and the
gap between the individual hulls – the actual sluice – was completely submerged.227 Petty’s
solution to this buoyancy problem was to change the amount of sail used and he assured
everyone that his ship would be fine when it was completely fine-tuned. That the St Michael’s
trial might not have been a success did not deter its inventor to try and win still more support
for her and to that end he intensified his writing campaign. He addressed every person who
might seem receptive and who had some influence in the naval affairs of the country. Petty
was eager to emphasize his ship’s ability to go faster, steer better, carry more and be stronger
than any other ship, to anyone who wanted to listen.
Petty’s campaign sorted great effect, not only influential people like Deane seemed to
change their opinion on the matter – writing to Petty: ’I hope […] you may have the pleasure
of knowing how the St Michael deals with the “Dragon” […] I mean the Wind & Seas’228 –
but Petty also received an increasing amount of requests for information to satisfy Charles II’s
curiosity. It even seems that in the beginning of December 1684 Petty’s mouthpieces at court
had convinced the king of the advantages of sluice boats. The king presented Petty’s
experiments to his own subordinates, who, to be honest, were not all as convinced by them as
227
228
Petty The Double Bottom or Twin-hulled Ship 131
Ibidem 135
90
their overlord seems to have been.229 Besides that, Charles II offered a prize for a new trial
race between a ship of his own fleet and the St Michael.
Two of the subjects to which the king showed the experiments, Anthony Deane and
Samuel Pepys – Deane had uttered fear of the great shock that this radical new design would
cause but had appeared to have become more positive recently and Pepys had not given his
opinion on this vessel but had supported the Experiment – severely doubted the claims of
Petty and laid heavy wagers against the St Michael. The wagers amounted to a total of £2500,– more than four times the cost of the St Michael – an amount they would double if Petty
would go aboard his own ship during the trial. They doubted Petty’s claim that the Archangel
was faster than any other vessel – for £200 – that it steered quicker than any other ship – for
£100 – that she could go from Dublin to Chester in England regardless of day, hour or tide –
for £500 – and so on.230 Petty did not receive these proposals until after the trial was
completed, but these wagers show that there was potentially a lot of money at stake.
The stage was set, the royal support within reach and the potential for lucrative
government contracts around the corner, the stakes were high indeed. The S t Michael the
Archangel was tested on the 15th & 16th of December in Dublin harbour and the results were
very clear, the secretary of the Dublin Philosophical Society, William Molyneux, wrote to his
colleague at the Royal Society, Francis Ashton: ‘Sr Wm Petty’s Shipp was tried […] but she
performed soe abominably, as if Built on purpose to disappoint in the highest degree’.231 Petty
admitted his defeat to his confidantes at court and in a letter to Deane and Pepys he revealed
that all his partners had defected and that he had resigned himself in the fate of his vessel and
in his own fate as the king’s ‘naval Scaramouch’.232 He ended his letter to Deane and Pepys
with a long list of those parts of the wagers the addressees proposed he felt affronted by –
most explicitly the provision of him going on board the ship for the trial and the practice of
offering rewards through wagers in general.
Petty talked about the idea of double bottomed vessels infrequently in the few years
that he had on this earth – even rejoicing about a rumour of a double-bottom built in Kerry in
the month before his death, stating: ‘the devill cannot long stiffle what I had so amply
demonstrated’233 – but he would never built another twin-hulled ship.
229
Ibidem 138
Petty The Double Bottom or Twin-hulled Ship 142-143
231
Ibidem 139
232
Ibidem 144
233
The Petty-Southwell Correspondence 330
230
91
Conclusion
In many respects Petty’s last ship was the opposite of his earlier vessels, where they
could all boast some maritime successes but lacked political and institutional support, there
this last ship had political and institutional support but lacked the actual performance during
the trials. None of the ships, however, could claim to have had a lasting influence on
shipbuilding. The double-bottoms raised some eyebrows, won some races and used theoretical
knowledge to improve their practical results but they always failed in an important department
at a crucial time, the progress from model to model is clear and so are the positive test results
but the ship was never implemented on a large scale until much later. This means that the only
viable conclusion must be that Petty’s double-bottom ships did not have the lasting effect on
the practice of shipbuilding the inventor envisaged let alone that they revolutionised shipping.
92
Conclusion
To what extent was the practice of seventeenth century shipping improved by theory?
Taking all four case studies into account, we have to conclude that in none of our cases
practice was improved by either mathematically or experimentally driven attempts. Hooke’s
theory to use straight sails instead of bunting ones did not improve sailing because it was
never put into practice; Du Son’s miraculous ship was never launched; Newton’s method of
calculating a solid of least resistance was hardly understood by professional mathematicians
and the one mathematician who did understand it saw that it could not be used to design the
hull of a ship; and Petty’s double-bodied vessels either lacked the political support or, in the
case of the St Michael, did not live up to the expectations created for it.
These results fit in with the pictures sketched by Davids and Cohen. Davids did not
find any long-term applications of science-based technology developed in the seventeenth
century, and Cohen’s investigations into a variety of attempts to develop science-based
technology in the seventeenth century also yielded very few positive results. Davids did see
some improvements in navigation in this period but these improvements were not developed
by theorists. The increasing amount of detail on the VOC’s navigational charts of Asia, for
example, was due to the increasing frequency of voyages to those regions. More and more
landmarks were added to these maps by navigators and the coordinates of these landmarks
were described with more and more accuracy. These landmarks and their coordinates
functioned as an easy way to find a ship’s position on the globe. Davids also describes another
method introduced in the second half of the seventeenth century which supports this idea of
improvement of practice by craftsmen themselves and not by theorists, for it happened to be
that most ships travelling to Asia were part of a mercantile fleet and in these fleets the
estimations of the coordinates of all navigators present were compared to form a mean, this
mean was assumed to be the best estimation of the position of the fleet on the globe.234
Cohen’s research discerns the same two groups as this investigation does, one
mathematical and one experimental. For the mathematical sciences Cohen concludes: ‘the
usual gap between craft practice and mathematical science yawned almost as widely as it had
at the onset of the [Scientific] Revolution.’235 Cohen identifies four impediments that
prevented theory to be applied to practice without intermediary steps: ‘(a) The weightiest
impediment was a serious underestimation of the real world’s messiness. […]. (b) The
mathematization of second-order effects required the ability to handle nonuniformly varying
234
235
Karel Davids Zeewezen en Wetenschap 177
Cohen How Modern Science came Into the World 323
93
magnitudes, which the Euclidean [mathematics used at the time] was inherently incapable of.
[…] late in the century, [however,] the calculus began to make it possible. (c) […]
craftsmen’s ability and/or readiness to grasp the esoteric language of mathematics were very
limited […] (d) [communication between craftsmen and mathematical scientists was]
impeded by social distance. [Many a mathematical scientist] tended to regard the equal
footing required for fruitful exchange as beneath his dignity.’236 Our two mathematical cases
support these claims to a large extent. Hooke’s inability to convince sailors of the validity of
his mathematically derived argument to use straight sails is a perfect example of craftsmen
unwilling to grasp the esoteric language of mathematics. Moreover, Hooke’s failure to clearly
define which parts of the ship he took into consideration and which not, serves as a good
example of an underestimation of the real world’s messiness. This underestimation finds its
crescendo in Hooke’s catch-all term ‘power of wind and water’, which not only shows
Hooke’s underestimation of the diverse and capricious nature of both wind and water but also
shows the limitations of Euclidian mathematics. Hooke, by relying exclusively on Euclidian
geometry, did not possess the tools to factor in the rapidly changing nature of both of these
elements.
Newton’s case can be used, with some imagination, to support both the idea that
craftsmen were unable to grasp his mathematical language and the idea that the spread of
Newton’s work was impeded by social distance. The case, however, most likely deserves a
category of its own. This category would be (e): some theories are far too advanced to be
applied at the moment. This category would be the best choice for Newton because it is hard
to maintain the position that Newton’s calculations were never put into practice because
craftsmen were unable to learn Newton’s work on the solid of least resistance. It was not so
much the inability of the craftsmen as it was the inability of most other theorists to understand
this part of the Principia that caused it never to be implemented. Besides, Newton can also
not be taken as feeling too haughty to explain his work to craftsmen; it was not Newton’s lack
of contact with the maritime world that caused the failure to implement this part of the
Principia. It might be true that, unlike Hooke, Newton never went to the docks to convince
sailors, but even if he did it would not have been easy to explain to a shipwright a
mathematical theory which was not understood by the large majority of the brightest
mathematical minds of the era. Furthermore, as Huygens noted, Newton’s idea was not
adaptable for the messiness of the real word — yes, a solid of least resistance could be found,
236
Cohen How Modern Science came Into the World 325
94
but it could not be used as the shape for a ship. Newton’s case does not fully support Cohen’s
analysis. The story about the solid of least resistance casts serious doubts on the second part
of Cohen’s statement under (b). For although the calculus was better able to cope with nonuniformly varying magnitudes, this new calculus was too unknown and too difficult to be
applied in full to any practical problem on the short term.
The experimental sciences did not fare much better in Cohen’s analysis: ‘the general
rule is […] no different from the case of mathematical science and the crafts’.237 The reasons
for the failure of the experimental sciences to improve crafts given in Cohen are slightly
adjusted forms of the four points he identified for the mathematical sciences. The largest
adjustment is the marginalisation of the restraint the limiting language provided for Euclidian
mathematics; it had no counterpart in the experimental sciences. The differences in the other
three reasons that the gap between science and practice was not bridged are a matter of
difference in shade not in colour. Most experimentalists were much better aware of the
world’s messiness than their mathematical colleagues, but the methods these experimentalists
employed to account for this messiness differed to such an extent from the methods used by
craftsmen that they too were not adopted in everyday practice. Esoteric language was also less
of a problem for experimentalists than it was for mathematicians: well-devised experiments
present their results with more force than well-devised mathematical theories, as Petty’s trial
races illustrate.
Du Son and his ship is mostly an example of the inability of theorists to take the
messiness of nature into account. The French inventor did not take into account that
mechanisms which performed successfully on a small scale would not necessarily perform in
a like manner on a large scale. Petty’s twin-hulled vessels – especially the first three – are in a
different category altogether. While you could say that Petty underestimated the messiness of
the world, to do this you would have to interpret the term ‘messiness of the world’ in a
fundamentally different manner. Petty underestimated the messiness of court politics and
underestimated the consequences of introducing an improvement which was feared to be
detrimental to the nation it was introduced in. You cannot say that these political reasons sit
comfortably in any of Cohen’s categories nor can you say that Petty’s case can be placed in
the category devised for Newton, so that a new category has to be invented yet again, a
category (f): for applications derived from theory that were actively thwarted by either
political or social factors. Petty had a string of successful experiments resulting in a number
237
Cohen How Modern Science came into the World 482
95
of race-winning ships. There were no technological reasons why Petty’s idea of doublebodied vessels was not accepted, there were only political motives. Most of his ship
accounted quite well for the messiness of sailing, sailors could easily understand the principle
and if they didn’t Petty would gladly explain it to them, or show it in a race. It was the explicit
fear that the Dutch would be able to build far larger ships with this new method that hindered
its acceptance. If Petty had won as many races in the Dutch Republic – where due to the
shallow coastal water the low draught of the ship would be its main advantage – as he had
won in Ireland, it is not unlikely that the ship would have had a much better chance of being
put into practice. Du Son’s case also has aspects that are best put in this new category: he was,
in the end, also stopped by social circumstances. The French inventor could have spent
decades more searching for ‘iron with the right temperament’ if he had not made a fool out of
himself by missing his self-imposed deadlines time and again, and in the process letting down
everyone who came out to support him.
None of the four cases discussed succeeded in improving practice through theory.
Three sorted no effect at all and Du Son’s miraculous ship even was used as a deterrent for
later attempts to start the flywheel of science-based technological progress in shipping. All
cases had different reasons why they failed: Hooke could not convince practitioners that his
method held anything of value for them; Du Son could not find the right materials; Newton’s
mathematics were too advanced; and Petty could not secure the political support he so
desperately craved. These attempts did not bridge the gap between theory and practice but
they illustrate the deep chasm between them, they also illustrate the diverse nature of the
multitude of problems that had to be solved before this gap could be bridged, but these cases
most of all show that the fruitful collaboration between science and technology did not start at
the moment that theorists claimed they found useful applications for their work. And with this
last conclusion both the idea that short-term results boasted the reputation of the new
philosophy and the idea that practical results carved out a special place in society for what
would transform into science have to be rejected, meaning that improvement of everyday life
is not a plausible answer to the question why science became a dominant force in early
modern society.
96
Bibliography
Primary Sources
A Perfect account 183, 5th – 12th July 1654
Aitzema, Lieuwe van Saken van staet en oorlogh In, ende omtrent de Vereenigde Nederlanden III, beginnende
met het Jaer 1645, ende eyndigende met het jaar 1656 (The Hague 1669)
Aubrey, John Aubrey’s Brief lives Oliver Lawson Dick (ed.) (London 1975)
Bacon, Francis New Atlantis: A work unfinished (London 1627)
Birch, Thomas The History of the Royal Society of London for improving of natural knowledge, I, (London 1756)
Boyle, Robert New experiments physico-mechanical, touching the spring of the air (Oxford 1660)
Burch, Thomas (ed.) A collection of the State Papers of John Thurloe, 1638-1660 (London 1742)
Cambridge University Library manuscript Ms Add. 4005 53r
Cort-verhael van het wonderherlijcke schip tot Rotterdam (Rotterdam, 1653)
Du Son Terror Terroris, werelts-wonder-schrick seldsame, noyt-gehoorde noch bedachte vondt, mitsgaders
grondige omstandelycke beschryvingh van seecker wonderbaerlyck, schrickelyck, en onverwinnelyck vaer-tuygh,
ghenaemt den Oorlog-blixem ter Zee (The Hague, 1654)
epitheton seu, super navis, istius rarae gallicae avis fabrica, nuper editae censurae Appendix (Rotterdam, 1654)
Evelyn, John The diary of John Evelyn Guy de la Bédoyère (ed.) (Woodbridge 1995)
‘Extrait d’une lettre escrite de Londres, touchant la description d’un Navire de nouvelle fabrique, inventée par
le Chevalier Petti, Anglois’ Journal des Sçavans 19 janvier 1665 33-36
Hooke, Robert ‘The Cutler lectures of Robert Hooke’ R.T. Gunther (ed.) Early Science in Oxford vol. VIII (Oxford
1930)
Hooke, Robert Posthumous Works of Robert Hooke Richard Waller ed. (London 1705)
Huygens, Christiaan Oeuvres complètes de Christiaan Huygens, XXII, Supplément à la correspondance, J.A.
Vollgraff ed. (The Hague 1950)
Huygens, Constantijn Koren-bloemen Nederlandsche gedichten van Constantin Huygens I, (Amsterdam 1672)
Het Malle Schip van Rotterdam. Aen monsieur du Son, vinder ende autheur van’t Malle Schip (1654)
Mercurius Politicus 180, 17th-24th November 1653
Mercurius Politicus 183, 9th-16th December 1653
Mercurius Politicus 213, 6th – 13th July 1654
Mercurius Politicus 215, 20th – 27th July 1654
Mersenne, Marin Correspondance du P. Marin Mersenne religieux minime, P. Tannery & C. de Waard (ed.) XI
(Paris 1932-88)
97
Newton, Isaac The Mathematical Papers of Isaac Newton VI, 1684-1691, D.T. Whiteside ed. (Cambridge 1974)
Newton, Isaac Philosophiæ Naturalis principia Mathematica A. Koyré & I.B. Cohen (ed.) 1, (Cambridge 1972)
Newton, Isaac The ‘Principia’: mathematical principles of natural philosophy: a new translation by I. Bernard
Cohen and Anne Whitman: preceded by A guide to Newton’s ‘Principia’ by I. Bernard Cohen I.B. Cohen & A.
Whitman ed. (Berkeley 1999)
Perfecte Afbeeldinge: van ‘t Wonderlycke Schip, Gemaakt tot Rotterdam 1653 (Rotterdam 1653)
Pepys, Samuel The diary of Samuel Pepys IV, 1663, Latham & Matthews ed. (London 1970-1983)
The Petty-Southwell Correspondence 1676-1687, Henry Petty-Fitzmaurice, ed. (New York 1967)
Petty, William The Double Bottom or Twin-hulled Ship of Sir William Petty Henry Petty-Fitzmaurice ed. (Oxford
1931)
‘Philosophical Transactions, A Londres, chez Jean Martin & James Allifry, Imprimeurs de la Societé Royale, & se
trouve à Paris chez Jean Cresson, ruë S. Jacques’, Journal des Sçavans 30 mars 1663 156
Sprat, Thomas The history of the Royal Society of London for the Improving of natural knowledge (London 1667)
Staat van de inkomsten van het Gereformeerd Burgerweeshuis van de vroegste tijden af tot 1796 toe
(Rotterdam city archive, Hoog Collection: 37-05_18)
Thien boecken der Hollandsche Mercurius, off histoorisch-verhaal aller gedenckwaardighste gheschiedenissen
van de beginne des jaars 1650 tot den jaare 1660, in christenrijck voorgevallen.
Ware en correcte afteekening naer ’t leven gedaen, van ’t wonderlijcke schip dat tot Rotterdam gemaeckt is / Le
vray Poutraict[!] de cette admirable navire ou machine faicte a Roterdam par le Sieur de Lisson grand ingenieur
de ce temps (Amsterdam, 1653)
Weekly intelligencer 114, 4th – 11th July 1654
Secondary Sources
Barker, Richard ‘A manuscript on shipbuilding, circa 1600, copied by Newton’ Mariners mirror 80 (1994) 16-29
Bennet, Jim et al. London’s Leonardo: The life and work of Robert Hooke (Oxford 2003)
Boxer, C.R. The Anglo-Dutch Wars of the 17th Century:1652-1674 (London 1974)
Carrell, Toni L. From forest to fairway: hull analysis of La Belle A late 17 th century French ship (Fife 2003)
Coates, J.F. ‘The authorship of a manuscript on shipbuilding, C. 1600-1620’ Mariners mirror 67 (1981) 286
Cohen, H.F. How modern science came into the world; four civilizations, one seventeenth-century breakthrough
(Chicago 2010)
Cohen, H.F. Isaac Newton en het ware weten (Amsterdam 2010)
Cohen, H.F. The Scientific Revolution: A Historiographical Inquiry (Chicago 1994)
Cohen, I.B. ‘Isaac Newton, the calculus of variations, and the design of ships: An Example of Pure Mathematics
in Newton’s PRINCIPIA, allegedly developed for the Sake of Practical Applications’ in: R.S. Cohen, J.J. Stachel,
98
and W. Wartofsky (ed.) For Dirk Struik: Scientific, Historical and Political Essays in Honor of Dirk J. Struik
(Dordrecht 1974) 169-183
Cohen I.B. (ed.) Puritanism and the rise of modern science: the Merton thesis (New Brunswick 1990)
Davids, C.A. Zeewezen en Wetenschap: De wetenschap en de ontwikkeling van de navigatietechniek in
Nederland tussen 1585 en 1815 (Amsterdam 1986)
Diekerhoff, F.L. De Oorlogsvloot in de zeventiende eeuw (Bussum 1967)
Epstein, S.R. & M. Prak (ed.) Guilds, Innovation and the European Economy, 1400-1800 (Cambridge 2008)
‘Espinasse, Margaret Robert Hooke (London 1956)
Feingold, Mordechai ‘Robert Hooke: Gentleman of Science’ in: Michael Cooper and Michael Hunter (ed.) Robert
Hooke: Tercentennial Studies (Aldershot 2006) 203-217
Goldstine, Herman H. A History of the Calculus of Variations from the 17 th through the 19th Century (New York
1980)
Graham, L. ‘ The Socio-Political Roots of Boris Hessen: Soviet Marxism and the History of Science’, Social Studies
of Science 15 (1985) 705-722
Hall, A. Rupert ‘Merton Revisited or Science and Society in the Seventeenth Century’, History of Science 2
(1963) 1-16
Hessen, Boris ‘The Social and Economic Roots of Newton’s ‘Principia.’’ In: N. I. Bukharin (ed.) Science at the
Cross Roads (London 1931)
Hunter, Michael S. The Royal Society and its Fellows 1660-1700. The Morphology of an Early Scientific
Institution. (Oxford 1994)
Inwood, Stephen The Man Who Knew Too Much (London 2002)
Jansen, H.G ‘Iets over het Malleschip’ in: G.A. Tindal & J. Swart (eds.) Verhandelingen en Berigten betrekkelijk
het Zeewezen en de Zeevaartkunde, III (Amsterdam 1842) 133-148
Joseph, S.H. ‘Assessment of the Scientific Value of Hooke’s Work’ in: Michael Cooper and Michael Hunter (ed.)
Robert Hooke: Tercentennial Studies (Aldershot 2006) 89-108
Keblusek, Marika ‘Keeping it Secret: the Identity and Status of an Early-Modern Inventor’ History of Science 43
(2005) 37-56
Merton, Robert K. Science, Technology and Society in Seventeenth Century England (1938; 2nd 1978 New Jersey)
Nooteboom, Christiaan De Brederode: het leven van een admiraalsschip (Rotterdam 1955)
Pennington, D. H. Europe in the Seventeenth Century (2nd edition: London 1989)
Prak, Maarten The Dutch Republic in the Seventeenth Century (Cambridge 2005)
Roberts, Lisa et al (ed.) The mindful hand Inquiry and invention from the late Renaissance to early
industrialisation (Amsterdam 2007)
Schoor, Arie van der In plaats van uw aardse ouders: geschiedenis van het Gereformeerd Burgerweeshuis te
Rotterdam (Rotterdam 1995)
99
Shapin, Steven & Simon Schaffer Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life
(amended edition; Princeton 2011)
Smith, G.E ‘Fluid resistance: why did Newton change his mind?’, In: Richard H. Dalitz & Micheal Nauenberg The
Foundations of Newtonian Scholarship (Singapore 2000) 105-136,
Truesdell, Clifford ‘Reactions of Late Baroque Mechanics to Success, Conjectures, Error, and Failure in Newton’s
Principia’ in: Robert Palter ed., The Annus Mirabilis of Sir Isaac Newton, 1666-1966, (London 1970) 192-232
Turnbull, H.W. The Mathematical Discoveries of Newton (London 1945) 40
Westfall, Richard S. Force in Newton’s Physics. The Science of Dynamics in the Seventeenth Century (London
1971)
Westfall, Richard S. Never at Rest: A biography of Isaac Newton (Cambridge 1983)
Westfall, Richard S., ‘Robert Hooke, Mechanical Technology, and Scientific Investigation’, in: John G. Burke
(ed.), The Uses of Science in the Age of Newton (Berkeley 1983) 85-110
100
Appendix A
The working of Hooke’s lamp from lampas explained with modern physics
In the description of his continuous fuel
Definition of symbols:
𝑟
= radius of the bowl
statements on how the lamp should function, for
𝜏𝐶
= torque of the counterpoise
example: ‘let the upper part [the counterpoise] be
𝜏𝐿 = torque of the liquid
lamp from Lampas, Hooke makes a number of
filled with some material of half the weight of the
Oyl, Spirit, or other material, or because that will
be somewhat difficult to do, let there be a
counterpoise of Lead or another ponderous matter
fixed somewhere […] so that the said upper
Hemisphere shall have half the gravity of the
under Hemisphere upon the Center of motion’.
If we assume, like Hooke, that only the
force of gravity is relevant for this lamp – this
means that no external forces work on the
counterpoise or on the liquid and that there is no
friction – if we also assume that the burning
𝐹𝑔,𝐶 = force of gravity working on
the counterpoise
𝐹𝑔,𝐿 = force of gravity working on
the Liquid
𝑟𝐶 = distance from the centre of
rotation to the line of action of the
force of
gravity working on
the counterpoise
𝑟𝐿 = distance from the centre of
rotation to the line of action of the
force of
gravity working on
the liquid
𝑚𝐶 = mass of the counterpoise
substance is a liquid with a homogenous mass
displacement, and that the lamp, and with that the
𝑚𝐿 = mass of the liquid
counterpoise, has to have a vertical plane of
𝑔𝑒 = gravity of the earth
symmetry exactly down the middle of the
𝐴𝐶 = area of the counterpoise
contraption, then that means that we can reduce
the whole problem from a three dimensional
problem to a two dimensional problem. We take
the centre of the bowl of the lamp as the origin in a
𝐴𝐿 = area of the liquid
𝜃̅
𝜌𝐶 = density of the counterpoise
𝜌𝐿 = density of the liquid
Cartesian coordinate system (0,0). The bowl of the
lamp has a circular form in this plane with a given
radius r, which for Hooke is a prerequisite if his
lamp is to function. Because the liquid has a
homogeneous mass displacement, the only acting
force (i.e. the force of gravity) acts on the centre of
101
2𝜃̅ −
𝜋
2
𝜃̅
2𝜃̅
gravity. For the counterpoise roughly the same is true, it is either a counterpoise with a
homogenous mass displacement – giving it a centre of gravity in a way similar to that of the
liquid – or a hollow float (with a negligible mass) in which a mass is be placed at any given
point (which allows the user to pick a the centre of gravity). Because the counterpoise is a
semicircle which rotates around the centre of the bowl, the point of rotation is at (0,0). For the
liquid and the counterpoise to be in balance the equation 𝜏𝐶 = 𝜏𝐿 has to hold, or in words: the
torque applied to the counterpoise has to be equal to the torque applied to the liquid. Because
only gravity is active we know that 𝜏𝐶 = 𝐹𝑔,𝐶 ∗ 𝑟𝐶 = 𝑔𝑒 ∗ 𝑚𝐶 ∗ 𝑟𝐶 or the torque applied to the
counterpoise is equal to the standard gravity multiplied by the mass of the counterpoise
multiplied by the distance from the centre of rotation to the line of action of the force of
gravity. The liquid has a comparable equation 𝜏𝐿 = 𝐹𝑔,𝐿 ∗ 𝑟𝐿 = 𝑔𝑒 ∗ 𝑚𝐿 ∗ 𝑟𝐿 . Hooke states that
the weight of the counterpoise is half the weight of the liquid in the case that the upper
semicircle is filled with the counterpoise and the lower semicircle is completely filled with
liquid, this only holds if we assume, like Joseph and Westfall, that weight in this context is
meant to represent the modern concept of density: 2 ∗ 𝑔𝑒 ∗ 𝑚𝐶 = 𝑔𝑒 ∗ 𝑚𝐿 = 2 ∗ 𝑔𝑒 ∗ 𝐴𝐶 ∗
𝜌𝐶 = 𝑔𝑒 ∗ 𝐴𝐿 ∗ 𝜌𝐿 because in this case both areas are the same (both are a semicircle) we
1
know that 𝜌𝐶 = 2 𝜌𝐿 . We can substitute both masses with the given densities and the areas,
which are given in both cases: 𝜏𝐿 = 𝐹𝑔,𝐿 ∗ 𝑟𝐿 = 𝑔𝑒 ∗ 𝐴𝐿 ∗ 𝜌𝐿 ∗ 𝑟𝐿 and 𝜏𝐶 = 𝐹𝑔,𝐶 ∗ 𝑟𝐶 = 𝑔𝑒 ∗
𝑚𝐶 ∗ 𝑟𝐶 = 𝑔𝑒 ∗ 𝐴𝐶 ∗ 𝜌𝐶 ∗ 𝑟𝐶 , because the area of the counterpoise remains a semicircle 𝐴𝐶 =
1
2
1
1
𝜋𝑟 2 this leads to 𝜏𝐶 = 𝑔𝑒 ∗ 2 𝜋𝑟 2 ∗ 𝜌𝐶 ∗ 𝑟𝐶 = 4 ∗ 𝑔𝑒 ∗ 𝜋𝑟 2 ∗ 𝜌𝐿 ∗ 𝑟𝐶 . When we substitute
these formula’s in the formula 𝜏𝐶 = 𝜏𝐿 we get 𝑔𝑒 ∗ 𝐴𝐿 ∗ 𝜌𝐿 ∗ 𝑟𝐿 =
1
4
∗ 𝑔𝑒 ∗ 𝜋𝑟 2 ∗ 𝜌𝐿 ∗ 𝑟𝐶 or
simplified 4 ∗ 𝐴𝐿 ∗ 𝑟𝐿 = 𝜋𝑟 2 ∗ 𝑟𝐶 .
The distance 𝑟𝐿 from the centre of rotation to the line of action of the force of gravity
working on the liquid is the same as the absolute value of the 𝑥 component of the centre of
gravity of the liquid. Because the liquid is always shaped as part of a circle 𝑟𝐿 =
̅|
2𝑟 sin|𝜃
̅
̅ | cos 𝜃
3|𝜃
in which 𝜃̅ is the angle from the positive 𝑥 axis to the axis of symmetry in the liquid, for a
homogenous fluid shaped as the part of a circle this means that 𝜃̅ is always half of the angle
between the horizontal and the interface between the counterpoise and the liquid.
The distance 𝑟𝐶 depends on the angle between the horizontal and the symmetry axis of
𝜋
the counterpoise which is always 2𝜃̅ − 2 as a consequence 𝑟𝐶 =
102
4𝑟
3𝜋
𝜋
cos( 2𝜃̅ − 2 ). Filling 𝑟𝐿
and 𝑟𝐶 into 4 ∗ 𝐴𝐿 ∗ 𝑟𝐿 = 𝜋𝑟 2 ∗ 𝑟𝐶 the equation becomes 4 ∗ 𝐴𝐿 ∗
4𝑟
3𝜋
𝜋
cos( 2𝜃̅ − 2 ) which can be simplified into
2𝐴𝐿
̅|
𝑟 2 |𝜃
some goniometric formulas the equation reduces to
𝜋
cos(−( 2 − 2𝜃̅ )) which is the same as
𝜋
cos( 2 − 2𝜃̅) = sin(2 𝜃̅), this means that
𝐴𝐿
̅|
𝑟 2 |𝜃
𝐴𝐿
̅|
𝑟 2 |𝜃
̅|
2𝑟 sin|𝜃
cos 𝜃̅
̅
3|𝜃|
= 𝜋𝑟 2 ∗
𝜋
∗ sin|𝜃̅| cos 𝜃̅ = cos( 2𝜃̅ − 2 ). Using
𝐴𝐿
̅|
𝑟 2 |𝜃
∗ (sin(|𝜃̅| − 𝜃̅) + sin(|𝜃̅| + 𝜃̅)) =
𝜋
∗ sin(2 𝜃̅) = cos( 2 − 2𝜃̅) and because
∗ sin(2 𝜃̅) = sin(2 𝜃̅) which results in 𝐴𝐿 =
|𝜃̅|𝑟 2. Hooke’s lamp idea is theoretical sound if the area of the liquid is the same as half of
the angle between the horizontal and the interface between the counterpoise and the liquid,
multiplied by the radius squared. That this holds true is easily seen from the area of a circle:
1
𝜋𝑟 2 , the area of a semicircle: 2 𝜋𝑟 2 and of the area of
103
15
37
part of a circle:
15
37
𝜋𝑟 2 .