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PROC. OF THE OKLA. ACAD. OF SCI. FOR 1962
The "Scala Graduum Caloris" and Sir Isaac Newton
_tou
ROBERT M. SAYRE, NOrDlu
An anonymous, six page article appeared in the PAUoaophical TTaMfor the months of March and April. 1701. Tb1a paper written in
Latin waa tiUed "Scala graduum calorls: C&lorum descriptiones • signa.u
Several years later in 1731, this article was republished in the Abridged
....,.. of the PIUloIopMeal 2'n1uc1ctiou. Again no author was given.
aDd again it was pubUahed in Latin. However, thls time the tiUe bad
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been translated as "Scale of the Degrees of Beat." l\uthermore. tile
General Index of 1787 to the first seventy volumes of the p ~
TratIBacfi0n3 lists both publications of this article, without an author.'
The "Scala graduum caloris" is of biatorical interest for HveraI
reasons. First, It contains a scale of the degrees ot calor. TbroUl'hout
the "Scala graduum caloris," the author uses the term roJor interchangeably for the present meanings of "heat" and ..temperature'" when tbla
article appeared in 1701, there was not a elear dlatlneUon' between the
terms "heat" and "temperature:' For this reason the Latin term calor
has not been translated
The scale of the degrees of calor is divided into two eolumna: an
arithmetical scale, which eould be direct readings from a thermometet
and a geometrical scale, which had some points in common with the arltb~
metical scale. The arithmetical scale begins with zero for the color of
water beginning to freeze and lists and describes about twenty-two degrea
of calor. For example, the summer air may be as warm as six on th1I
scale. Twelve is given for the degree of calor of the human body. Thirtythree and thirty-four are the degrees of calor of boiling water. Forty-elght
degrees is the calor of melting for a mixture of equal parts of tin and
bismuth, while ninety-six is the melting calor of lead. One hundred ninetytwo is the calor of an ordinary coal, kitchen cooking tire. Beside. thue.
other degrees of calor are described in the "Scala graduum calor1B:'
The second column of the degrees of calor is a geometrical progreasion. The number one in this column is given to the calor of the human
body, which is twelve in the arithmetical column. Two 11 the cGlor of
melting wax or twenty-four units in the first column. Three .. the calor
of melting for equal portions of Un and b18muth or forty-etght in the ftnt
column. Four and five represent the calor3 of melting lead and of a
coal, kitchen fire, corresponding to ninety-six and one hundred ninety-two
in the first column. Each number in this geometrical scale" twice u
great as the preceding one; therefore, the second degree in th1B column
is twice the first, the third twice the second, etc.
The methods by which these scales were determined are a~ of
interest. For the lower degrees ot calor, a theremometer employlnc linseed oil for the expanding fluid was utilized. The calor of water beginnlna'
to freeze was assigned the value of zero on tha. thermometer, and the
calor of the human body assigned the value of twelve. Equal divwtona were
then made between zero and twelve and extended from twelve higher.
The melting calor of lead was the highest degree of calor meaaurable by
this thermometer.
Another method was needed for determining the higher degreea of
calor. By noting the time taken tor the pieces ot difterent metala placed
upon a glowing iron bar to harden, and for the bar and metal piec- to
cool to the degree ot calor of the moving air, the degrees of color of the
hardening metal pieces could be calculated. The caleuJat1on.l require
two postulates; the tirst assumes that UDitormly moving air c:arne.
away from a warmer body calor in proportion to the total dltterence ill
calor between it and the flowing air; the eecond auumea that the excaa
of the calor from the body would be given up In a geometrtca1
While the time of cooling 18 an arithmetical progreu1on. By p
oD17
small pieces ot different metals on the glowing iron bar, the
of
this paper essentially determines that the rate of cooUDc wU1 remaiD
constant-the rate of the bar cooling without metal pleceI. Tberetore,
variations in the rate of cooling of different metaU are eUmtneted. The
author concludes by observing that becatUe ot agreement between theM
two methods for determining the degrees of calor, the aU t.bermometer ..
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200
PROC. OF THE OKLA. ACAD. OF SCI. FOR 1962
a'va1ld indicator ot degreea of color. The concept used In this second
method for determining the degree ot calor is that of Sir Isaac Newton's
"lAw of coollng." Moreover, Newton's "law of cooling" is traced directly
to th18 paper, since this law does not appear In Newton's other works.
However, neither the lIC8le nor the methods for determining caloT
would be of e.epecial interest, if it were not for this connection between
It and Sir Isaac Newton regarding hla "Law of cooling." The "Scala
graduum calorls" was pUblished in Newton's collected works in 1744 and
In 1782, although a reason for ita inclusion was not offered. By 1751
George Martine in his B88ays and Observations on Thermometers informs
his reader of Newton's authorship of this paper but does not present a
reason for doing SO.I However, Sir David Brewster in his Memoirs of Sir
Isaac Newton of IBM offers his version of the circumstances of publication
of this article:
The only chemical paper of importance pUblished by Sir
Isaac, was read at the Royal Society on the 28th of May 1701,
and printed in the Philosophical Transactions without his name,
under the title Scola graduum Oalom.'
The following information was obtained from the Journal Book of the
Royal Society entered for 28 May 1701:
There was read a paper concerning the degrees of heat, measured
by the melting of sevl [Beveral] bodies etc. The Author was
ordered the thanks ot the Society and it was desired it should be
printed as being likely to be very useful!.·
Thus, the records of the Royal Society fail to substantiate Brewster's
claim for Newton's authorship. Similarly, in 1703 Gulllaume Amontons
critically reviewed the "Scala graduum calorts" in the M emoires of the
Royale Academie ot Paris. Amontons tailed to note its author also. The
following listings ot Newton's works fall to note a manuscript version of
this paper: the Oatalogue of the Babson Collection ot Newton's works,
George J. Gray's A Bibliography 0/ the Works 01 Sir Isaac Newton, and
the sale Catalogue 0/ the Portsmouth Oollection 01 the N e1vton Papers.
And it also is not '",ted among the Olassi/ied Papers in the Archives 0/
the Royal Society under Newton's name. No one seemed to be aware that
Newton wrote this paper. One might even suspect that Newton did not
write it, if it were not for the circwnstantial evidence that follows:
Passages in two of Newton's works, the Principia and the "Queries"
in the OptwM, indicate Newton's interest in heat phenomena to be similar
to those held by the author of "Scala graduum caloris." In the Principia
Newton gives in several passages ratios between different degrees ot
color. Sometimes Newton's ratios agree with those calculated trom the
"SCala graduum calor1s;" other times they do not. An example of agreement la that seven times the calor of the summer sun is the degree ot calor
of boiling water. Another similarity illustrated in the PriflCipia is Newton'a interest in theories of cooling. This "Law of cooling" is different
from that normally ascribed to him in the "8ca1a graduum caloris." This
other coolin, law supposes that as globes ot various sizes cool; the time
taken to cool la proportional to their diameters. In both the PritlCipfa
and the ·~ueriea" in the Opfic1ca, Newton mentions glowing iron bars.
In the "Queries" he further mentions that bits ot metals were placed on
aJowiDg Iron ban. as did the author ot the "Scala graduum caloris."
Generally, in both the Opticka and in the Pritlcifria, Newton indicates
lntereeta in many more d1tferent problems involving heat phenomena,
thaD. doe8 the author of the ·'ScaJa graduum ealorla.'"
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201
The most conclU8lve evidence supporting Newton's authol'llhip of the
"Scala graduum caloria" is given by David Gregory, who prepared the
third edition ot the Principia. In "Memoranda of Kay ISH," Grepry
says that Newton claimed a glowing iron bar had the same decree of
calor 88 the kitchen tire which warmed it. Thla statement is a1mllar to
one In the "Scala graduum caloria." Gregory continued that Newton
determined the calor using two methods: the time taken for a body to
cool. and an oU filled thermometer. Later Gregory added a note to thue
"Memoranda" stating that the 011 In Newton's thermometer wu either
linseed or olive and that Newton determined the melting CGlor of the fol.
lowing substances: lead. tin, sllver, bl8muth, resin, and wax.' Moreover,
not only did Newton utUize simUar methods to do BlmUar things, as did
the author of the "Scala graduum caloris," but Newton was doing them
or had done them eight years before the "Scala graduum calorls" was
pUblished. The concluding evidence from Gregory appeared in hfs "Memoranda" tor 1705:
[25 Feb. 1705/6] The Table ot the Degrees of heat In the Philos.
Transact. for March I: Aprile 1701 18 Sir Isaac Newtons, as he
told me 25 Feb. 1705/6. and he talks of reprinting it In Addenda
at the end of the Latin Translation of hls Opticks.·
SELECTED NOTES AND REFERENCES
I"Scala graduum calorls: C&lorum deacriptlones • 8lgna," P1Mloeop"kaJ TraaactiotM, XXII (1101), 824-829. "A Scale of the Degrees of
Heat," Tile PhU080pMcal TraMactioM (From the Year 1700 to tile YeGr
1780) Abridg'd under General Head3, IV (In two parts, 2d. ed.: London:
1731), pt. n. 1.... Paul Henry Maty, A General Inde~ to the PhUoeophscal TraMactioM, From the F«r,t to the Btld 0/ the Sevent~tA vor"me
(London: Printed tor Lockyer Davis and Peter Elmsly, 1781), 424. Tbe
"Scala graduum calorls" has been translated In the following work8 into
English: William Franc18 Magie, A Source Book in Phylrics (New York:
McGraw-HUl Book Co., 1935), 125-128: and Isaac Newton, Isaac Newtofl'.
Papers" Letter, on Natural PhUoaophy atld Related Docunumt8, L Bernard Cohen (ed.), ass18ted by Robert E. Schofield (Cambridge: Harvard
University Press, 1958), 259-268.
IGeorge Martine, Buags and ObaervGtWtu em the CotI8tnccttota 0fId
Graduatton 01 Thermometer8 (Edinburgh: PrInted for Alexander Donaldson, 1780), 53-54, 18, 67, 116, 123, 188, ef palMm. Cf. George Martine,
Di8serlati0ta8 aur Ja c1aale1lr, avec del obaenxatioM tIO""eUe8 aur rca cc*strvctWn et la comparataon de.s fhermometru (Parts: Chez Jean-Thomu
Herlssant, 1751). Isaac Newton. 18t1Cri Newtoni, BCl"Uta AtU"Clt«, OJ*8CI'IcJ
Mathematica, phU08ophtco et phUogjca, Job. Cutlllloneus (eeL) (Genevu:
Marcum-M1chaelem Bousquet &:: Soc1oa, 1144), n, 419-428. IAac Newton,
1,aaci Newton, Opera Quae Bzatant Omnta. samuel Horsley (ed.) (Lond1n1: Joannes Nichola, 1782), IV, 403-407.
'Sir David Brewster, Memotra 01 t1&e lAle and wrUmgs 01 Sir lBaIIC
Newtcm (2 Vola.: Edinburgh: Thomas Constable and Co., 1886), I,
aa.
ltIany biographers of Newton use oaly Brewster's 1Dt0rmaUon coneendJIC
the "Scala graduum ca1oria."
~tter from R. W. Smith. Loudon, England, AugD8t 28, 1M2. Dr.
Smith transcribed thla puaage from the Journal Book of the Royal SocIety
during a reeearch trip to London.
'*
'Guillaume Amontons, "Remarquea 8U1' 1& table
degra de cJIaJeur,
extraIte des Transactions PhiIoaoPhlqua du mo18 d'AvrU 1701; Iue par K.
Geofroy en l'A88emblee du Kardy 24 JuIl1et 1708," JlfImOfrw, 200-21J, III
202
PROC. OF THE OKLA. ACAD. OF SCI. FOR 1962
BUtotre • J'A~4e Boyale tIu Bcfenee3, (1703). A Deacriptivs Ca.fGJoI1flS 0/ fM GnJc6 lC. BClNOtI Collect"", 01 the Worb 01 Brr Itf(J(JC NewtOtl
CJtId file JrotericIJ B6lGtitag to Mm
the BOO8on IMtituts LtbTary, BOO8Ot1
!Park, JraM., Introduction by Robert Babson Webber. (New York: Herbert
Kelchner. 1950). Gerald Vernon Wallop 9th earl ot Portsmouth, CattJlogve
01 tM N 6'Wton Pa.P61'8 Bold by Order 0/ the Vfecoutlt I4/ndtlgton, Gr6tJtN,.,. 01 '''' 18GaC Newton. Which WW Be 8014 by Auction by Mee8T8.
Bot1Hlby mad Co. July 13th, 1986. and !ollowing Day (London: by H.
Davy, 1986). George J. Gray. A BUJllogra.phy 0/ t1le Works 01 8rr IMMJC
Newton: Togethe1' ~th a. LMt 01 Books mvetrating hie W01'ke (2d. ed.;
cambridge: Bowes and Bowes, 1907). See Do 4, above.
'ti
'I8aac Newton, PhiloeophitJe NGtu.ra.lie PrindpiG MGthematicG (LonJU18U Societatis Regtae ac typls Josephi Streater, 1687), ·05-418,
498-499, 237, 238, et f.HJ&'tm. Isaac Newton, Opticks or a Tf'eatiee 0/ the
BeflecttoM, Be/rtJetiOtl8, In/lecti0n3 cC Colours 01 Light (Based on the
d1nl:
fourth edition; London: Dover Publications. 1952), 339, 340, 3·41-3, 345,
848-9, 874-8. 398, 399, et paesim.
'l8aac Newton, The Cor1'68Pondence Of 1800C Newton, H. W. Turnbull
At the University Press, 1961). m, 313, 318, 322 n. 15.
(ed.) • (cambridge:
'David Gregory, David Gregory, Isaac Newton and their Circle: B~­
troct8 from Dooid Gregory's Memoranda. 1611-1'108, W. G. Hiscock (ed.),
(Oxford: Printed for the Editor, 1937), 32-33. In a note Hiscock observes
that the "Scala graduum caloris" was not· published with the Optick8. I.
B. Cohen also reports this quotation in Gregory's Memoranda; see I. Bernard Cohen, lI"mnkZ«" and Newton: an Inquiry into Speculative NewtoniGn
sc,erimB1&ta.l 8cience and lI"'ranklin's Work in Electricity as an .B~ample
T1HI1'e 01 (PhUadelphia: The American Philosophical Society, 1956), 68.