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Surveying the Old Way: Comparing Primitive and Modern Land Surveying Techniques
Parker H. Zurbuch
College of Technology, Vincennes University
Surveying Management Concentration
April 27, 2023
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Table of Contents
Abstract.......................................................................................................................................... 4
Chapter 1: Introduction ............................................................................................................... 5
Developmental Procedures .......................................................................................................... 5
Statement of the Problem ............................................................................................................ 6
Hypotheses .................................................................................................................................. 6
Null Hypotheses .......................................................................................................................... 6
Research Questions ..................................................................................................................... 6
Statement of the Need ................................................................................................................. 7
Statement of Limitations ............................................................................................................. 7
Statement of Terminology........................................................................................................... 7
Chapter 2: The Literature Review .............................................................................................. 9
Research Methodology................................................................................................................ 9
Theoretical Framework ............................................................................................................. 10
The Big Picture.......................................................................................................................... 11
Ancient Sources......................................................................................................................... 11
Medieval Sources ...................................................................................................................... 14
Modern Sources......................................................................................................................... 15
Chapter 3: The Method .............................................................................................................. 18
Chapter 4: Data Collection (Results) ........................................................................................ 19
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Chapter 5: Conclusions .............................................................................................................. 29
Limitations in Acquiring Data................................................................................................... 29
Answers to Research Questions ................................................................................................ 30
Future Experiments and the Way Forward ............................................................................... 30
References .................................................................................................................................... 32
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Abstract
The use of modern technology in the land surveying profession has often been utilized as a
crutch in the industry; therefore, the results of the ensuing research project provide necessary
evidence to show that these advances are not essential for a competent practice of land surveying
per se. The purpose of this research was to give an overview of the technologies/methods used in
the art of surveying throughout history, for the sake of helping the author determine which
technologies and methodologies should be utilized for the purposes of this study. Non-fabricated
tools were used to measure latitude and longitude coordinates, and the data collected was
calculated via statistical analysis. This primitively acquired data was then compared to the results
from a modern latitudinal/longitudinal coordinate derivation using the Global Positioning System
(GPS). The outcomes of said experiments suggest that the primitive materials and methods used
were inaccurate, but the whole process of research, experimentation, and analysis was an
incredibly advantageous learning experience.
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Chapter 1: Introduction
Land surveys have been conducted for millennia. From ancient Egypt to the present,
property owners everywhere have needed to know where their property ends, and another’s
begins. The location of property corners, having been monumented in a myriad of ways
throughout history, have been one of the most essential functions within human society. In
modern times, there are an abundance of technologies which can give the location of objects
upon the face of the earth. These technologies are becoming more and more relevant and
accessible to the public at-large, but are they necessary for land surveying per se? Can surveyors
still locate objects as our ancestors did, or have they become so dependent upon current
technologies, that they have forgotten the basics of this ancient art?
Through the course of this research project, I hoped to prove that surveyors do not need
to be dependent on newer advancements, and that the old ways still can provide them with much
wisdom. This hope was to show that, even with primitive materials (no electrical, specialized, or
even fabricated equipment), one can still locate objects on earth to reasonable degrees of
accuracy and precision.
Developmental Procedures
I love the process of making a machine or program work, while also understanding each
part of said mechanism. The technology of today has become so complex and intricate that it is
virtually impossible for one person to understand it’s processes, and the equipment used in the
land surveying industry is no exception to this rule. I wanted to understand land surveying. To do
this in the same way our ancestors surveyed the earth, I thought it was vitally important for me to
gain an understanding of how it could be done – from scratch and with basic construction
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materials. This project required a full use of my knowledge of history, mathematics, and
geodesy, as well as my own creativity; a challenge I was eager to accept.
Statement of the Problem
Are individual land surveyors (and the land surveying industry, as a whole) dependent
upon modern technologies – most of which have been developed in the last 30 years? Or can
they utilize their craft as their ancestors did: with a minimum of materials? The goal of this
young surveyor, who considered himself dependent on modern technological advances, was to
prove that someone like me could survey “from scratch.”
Hypotheses
It is a useful and positive learning experience for a young surveyor to be able to find the
location of an object on Earth, while using only primitive materials.
Null Hypotheses
It is not useful, and a waste of time, for a young surveyor to be able to find the location of
an object on Earth, while using only primitive materials.
Research Questions
1. What kinds of equipment have been used in the past for surveying land?
2. Which primitive materials were most useful for this endeavor?
3. Would primitive materials yield similarly accurate and precise results as modern
equipment would?
4. What were the statistical discrepancies between the accuracy/precision of primitive
verses modern equipment?
5. What were the differences in time/labor, while yielding the same end goal, for the
usage of primitive versus modern equipment?
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6. What kind of surveying techniques would be most effective with the primitive
equipment used?
7. What benefits would the student accrue while taking-on said project?
Statement of the Need
The use of modern technology in the land surveying profession has often been utilized as
a crutch in the industry; therefore, the results of the aforementioned project should have provided
necessary evidence to show that these advances are not necessary for a competent practice of
land surveying.
Statement of Limitations
Because the research was being conducted by one individual, who is also the subject of
said research, any conclusions about the value of this project for other professionals in the land
surveying industry were general conclusions, at best.
Statement of Terminology
Specialized Equipment: Technologies utilizing the Global Navigation Satellite System (GNSS),
Electronic Distance Measurement (EDM); or equipment requiring specialized manufacturing
such as Theodolites, precision clocks, sextants, astrolabes, etc.
Geodesy: the science of accurately measuring various properties of the earth’s shape/size,
orientation, and gravity.
GPS: Global Positioning System, also known as Global Navigation Satellite System (GNSS), is
the system of satellites used to find precise localities on the face of planet earth.
EDM: Electronic Distance Measurement. A type of modern surveying technology which uses
lasers and prisms to determine the vertical and horizontal distance/direction of points from each
other.
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Theodolite: a type of surveying instrument used from the 18th to 20th centuries to aid a surveyor
in determining distances between points.
Precision Clocks: clocks used in surveying and maritime travel to assist the user in determining
one’s location of longitude from Greenwich, England.
Sextant: a device with a sighting mechanism used for measuring angular distances; especially,
for taking altitudes in navigation.
Astrolabe: a hand-held device used in ancient, medieval, and modern times to model the
universe. It used the positions of the stars to help users find their approximate location on the
earth’s surface.
Ancient: from the beginnings of record keeping until the fall of the Western Roman Empire.
Medieval: from the fall of the Western Roman Empire in the fifth century to the beginning of
the Renaissance in the mid fifteenth century.
Modern: from the beginning of the Renaissance to the beginning of the twentieth century.
Twigs: small branches from a bush or tree, roughly one quarter the width of an average man’s
pointer finger.
Small Sticks: branches from a bush or tree, roughly one half the width of an average man’s
pointer finger.
Large Sticks: branches from a bush or tree, roughly the width of an average man’s pointer
finger.
Primitive Material: a naturally occurring, non-fabricated material.
GMT: Greenwich Mean Time. This is the time in Greenwich, England; used as the base time for
computing latitude.
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Chapter 2: The Literature Review
The practice of land surveying has been utilized for millennia, and there have been
numerous efforts made in historical research to identify when and where land surveying has
played a role in the history of humanity. While the specific hypothesis of this study has not been
researched in the past (as far as I could tell, no young surveyor had ever documented him/herself
attempting to use primitive technology and record its results against contemporary methods),
there is much that can be learned from our ancestors.
Research Methodology
For this reason, the review of the literature was primarily of a historical nature.
Discovering the technologies used in the measurement of length, area, time, and celestial bodies
was of paramount importance. Additionally, the creation of maps, the marking of property
boundaries, and the documentation of said boundaries were aspects of this research. It was all
completed for the sake of determining the best “primitive” technologies to use in this study.
This research was conducted using a variety of sources available in the public domain,
and particularly on the Internet. Most of these references were fully accessible. Some were only
partially accessible, and many could only be known by their titles because they were out of print.
These latter sources were not references in this work, because no substantial information could
be gathered from them.
The work of researching was completed by beginning with the documents that were most
ancient, and then moving to modern sources. Surprisingly, there has been an abundance of work
done in all major historical contexts; except for the Middle Ages. For the purposes of this study,
I categorized history into three sections: Ancient, Medieval, and Modern.
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As is expected, a complete and conclusive compilation of all sourced references to land
surveying throughout history was not feasible, but a limited search to those sources which
referenced technologies and methodologies used for the practice of surveying was possible. Even
still, this study was not an exhaustive search into the subject. It is meant to be an overview of
historical sources, in regard to land surveying technologies and methodologies, for the purpose
of helping the author determine which technologies and methodologies should be used over the
course of this study.
The analysis of the data collected was completed by searches in Google Scholar, Google
Books, Vincennes University’s Shake Library Online Resource, The University of Michigan
Library, Internet Archive (Archive.org), and Journal Storage (JSTOR.org). The analysis then
required reading through the sources found, and pinpointing sections of the texts which dealt
with surveying technology and methodology. After perusing said sections, the relevant quotes
and citations were documented and compiled in an organizational reference manager.
Theoretical Framework
The research was started with the most ancient of sources and continued until the present
day. The concepts that I dove into included the historical usage of measurements (length, area,
time, and celestial), equipment used, cartography, property boundary markers, and the
documentation of property rights. Each of these topics have been covered by academics in the
field, no matter which historical period they were researching. These were the most common
topics to research on this subject matter. The purpose of this research was to give myself an
overview of the technologies/methods used in the art of land surveying throughout history; so
that I could use the best of these “primitive” technologies/methodologies in my own
observations.
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The Big Picture
Following the flow of history and identifying these concepts throughout the journey of
research showed me how many of these surveying concepts have been utilized commonly
throughout human history, and how there is a massive gap in the literature as regards to the
Middle Ages. This gap was shocking to me, as I did not expect there to be so few sources for the
period. It was unclear whether this lull is due to a lack of contemporary interest in the topic or if
it was due to a lack of preserved documentation. Now, it was time to turn to the sources
compiled, and hear the story of land surveying technology and methods.
Ancient Sources
The first order of this research was to those sources regarding ancient times. This
includes citations about land surveying technology/methodology from the earliest recorded
histories until the fall of the Western Roman Empire in the fifth century A.D. I categorized the
following citations of ancient sources by their subject matter, such as measurements (length,
area, time, and celestial), instruments used, cartography, property boundary markers, and the
documentation of property rights.
First, was a discussion on ancient forms of measurement. Measurements of length were
the most used throughout the ancient societies of Egypt, Assyria, Babylonia, Greece, and Rome.
The tools to measure length would have been the ones most readily available to ancient peoples,
namely, parts of human anatomy. Among these tools were the measurement of hands, being the
width of the palm; cubits, being the width of a forearm; and fingers (Derry & Williams, 1960,
pp. 219-221). Additional measures of length were used in cultures, such as the Babylonians, who
used the reeds of plants as tools to this end. According to Baker (2011), these reeds were used in
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double-reed, whole-reed, or half-reed measurements (pp. 309-310). These ancient examples of
how peoples would measure lengths were an incredibly primitive source of technology; ones
which would be readily accessible to a young surveyor attempting to measure land in such a
way.
The most common measurement of area would have been the acre, as it still is today;
however, in ancient times the acre was defined as “the area that a yoke of oxen could till in a
day” (Derry & Williams, 1960, p. 221). Besides the acre, the Romans used designations for area
called the “Centuria” and “Saltus” (De Nardis, 1994, pp. 7-8). It is said that one of the legendary
founders of Rome, Romulus, allotted citizens certain portions of land:
One hundred of these plots then make up a “Centuria.” A “Centuria” is square in such a
way as to have sides of two-thousand four-hundred feet in all four directions. Further,
four such “Centuria,” joined in such a way that there are two in each direction, are called
'Saltus' in land which has been publicly divided and allocated. (De Nardis, 1994, pp. 7-8)
Today, surveyors still use methods like those of the ancients. Acres, although they now have a
much more precise definition, are still the basis of measuring area today. In most countries, and
especially in the United States of America, land is divided into a type of “grid” system, like the
“Centuria” and “Saltus” used by ancient Romans. The acre, and some sort of gridded system for
organizing the location of land still is a source of indispensable knowledge to any surveyor
today.
Clocks were another form of measuring tool used by surveyors throughout history. In
ancient times, clocks were not as important for the practice of surveying as they became in
modern times. The ancients mostly used solar/shadow clocks; the earliest of which known to
have been in use were in Egypt around 1450 B.C. (Derry & Williams, 1960, p. 224). In this
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contemporary age, clocks are used everywhere, but the most relevant place they are employed
for a surveyor are in Global Navigation Satellite System (GNSS) and Electronic Distance
Measurement (EDM) technology. Both forms of equipment use clocks to determine lengths and
triangulate positions on the face of the earth using said lengths. They can also use clocks to
determine latitude, and thus coupled with astronomical observations, one can determine their
place on planet Earth.
The main, and most accurate, ancient cartographer was Eresthenes, a Greek
mathematician who lived in the third century B.C. Using mathematics and some empirical
observations, he estimated the size of the earth to an accuracy that, even today, is incredible to
historians and scientists alike (Derry & Williams, 1960, p. 229). Another main cartographer who
is discussed in the literature is Ptolemy, a Roman mathematician born in the year 100 A.D. His
maps were not nearly as accurate as those of Eresthenes, but he is still hailed as a father of
cartography by many (Derry & Williams, 1960, p. 230). The art of cartography combines one’s
knowledge of mathematics, physics, and art; all three of which are incredibly important skills for
the surveyor today.
Regarding property boundary markers, the sources I found discussed a type of
monumentation used by the Babylonians, Romans, and even surveyors today: stones (Baker,
2011, p. 307). The sources regarding Babylonia did not specify a name for these stones, but the
Roman sources called them “Pati” (De Nardis, 1994, p. 149). These physical monuments were
coupled with documentation of those boundaries and property rights. Evidence from Greece
indicates that at least some of these documents were written on “Ostraca,” which were pieces of
clay pottery or stone used for writing (Schuman, 1944, p. 68). There is also evidence that the
Babylonians used stone “land sale tablets” for this purpose, as well (Schuman, 1944, p. 68).
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Stones, and other types of physical monumentation are still used in the contemporary world to
mark the location of property corners.
Research into the ancient sources of land surveying technology and methodology was
incredibly enlightening. It is always amazing to see how wise our ancestors were. It seems that
the Roman surveyors were especially keen in their understanding of law and the civil order, and
that they developed this keenness for the sake of the better organization of society.
Medieval Sources
The sources regarding Medieval land surveying technologies and methodologies were
few and far between. Besides Derry and Williams (1960), I was only able to find Price (1995)
which describes instruments:
Known to medieval surveyors [i.e.,] variants of the groma (or the Grecian Cross) and the
chorobates; the former consisted of two rods at right angles which supported each a pair
of plummets for use as sighting-lines, the latter was a long plank with a single plumb line,
the surveyor could set out perpendicular lines, establish verticals and horizontals, and do
everything needed to augment direct length measurement. (p. 1)
These forms of surveying technology indicate that the use of simple wood at right angles, plumb
bobs, and knowledge of mathematics can allow one to measure lengths in an indirect way. These
instruments were the precursors to today’s theodolites.
Additionally, Derry and Williams (1960) had various sources of information regarding
certain technologies which had been developed in the Middle Ages. The “English Statute Acre”
was precisely defined in 1305 A.D. by King Henry I, who also standardized the yard by the
length of his own arm (Derry & Williams, 1960, pp. 220-221). Mechanical clocks were invented
in the 13th century, and paved the way for precision clocks to be used in marine navigation
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during modern times (Derry & Williams, 1960, p. 225). Another interesting note regards
cartography in the Middle Ages. In Europe, cartography was mostly practiced by monks
attempting to map the world by the descriptions in the Christian Scriptures, but cartography was
practiced and developed by many in Arab empires at the time (Derry & Williams, 1960, p. 230).
Each of these forms of technology are as relevant to surveyors today as they were then; even if
we use slightly more advanced forms/methods today.
Modern Sources
The modern era rolled in with a wave of continuous developments in land surveying
technology and methodologies. There were several sources which were found regarding this era
– too many sources to have sifted through, and many of which were inaccessible through online
means.
Regarding methodologies used by land surveyors, these included basic and advanced
mathematical operations for determining the shape, area, and topography of land (Hopton, 1611,
pp. 6-15; Jess et al., 1799, pp. 1-10, 100, 138). One author also discussed various methodologies
for dividing land (Jess, Bonsal, Niles, & Jess, 1799, pp. 162-176).
During the 17th Century, a new instrument used for land surveying came on the scene: the
Topographical Glass. It is described in Hopton (1611), which is not just an instruction manual
for said topographical glass but is also a textbook for learning how to survey land in general.
Hopton (1611) discusses basic mathematical operations useful to the land surveyor, how to
measure any observable distance, how to make a protractor and scale, and how to take
astronomical observations (pp. 6-15, 49, 71, 93). It also discussed the uses of other instruments
such as the Plaine Table, Circumferentor, and how to measure the volumes of many types of
geometrical solids (Hopton, 1611, pp. 98, 127, 201). In 1725 A.D., the book The Practical
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Surveyor: Or the Art of Land-measuring Made Easy by Samuel Wyld was published. It
discussed the use of the Plaine Table (as did Hopton in 1611), but also described instruments
such as the Gunter's Chain, Poles, Circumferentor, Theodolite, Scale, and Compass (Wyld, 1725,
pp. 4-5; also see Jess et al., 1799, pp. 43-50). One can see how the equipment for measuring
lengths, angles, and areas have become more refined and industrialized throughout these periods
of history. Even though these instruments could not be replicated for the purposes of this study,
the methodologies and inspiration behind them were successfully utilized.
In the 18th century, the first clock was invented that could accurately determine latitude;
which was a momentous occasion for cartography and maritime travel (Derry & Williams, 1960,
p. 226). Precise clocks have been (and are) used for measuring distances and determining one’s
location on the face of the earth. Both functions are useful to surveyors today, and clocks were
an indispensable resource over the course of this study.
Lastly, the astrolabe was a very ancient instrument used in surveying for measuring
heights, depths, and distances (Hayton, 2012, p. 17). Even though it is an instrument dating back
(in various forms) to the first century A.D, it is worth mentioning. The astrolabe was generally a
difficult instrument to produce and involved very “knowledge-intensive” processes of
construction (Golubinskii, 2017, p. 61). For example, when Russia was being surveyed in the
19th century, one of the factors that slowed down that process was that people in the empire
needed to learn how to produce astrolabes; so, even in the modern era the production of the
astrolabe was considered to be a complicated endeavor (Golubinskii, 2017, p. 67). Because of its
complexity, an astrolabe would not be an instrument that could be constructed using “primitive”
means; however, the methodologies behind its use will prove indispensable to this study.
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Particularly, measuring zenith angles and the distance of celestial bodies proved necessary for a
crude recording of one’s longitudinal position.
The instrumentation used for land surveying started to become more and more developed
in the modern era, making these instruments generally recognizable to many surveyors today.
The more complex instruments mentioned in this section were not useful for the direct purpose
of this study, but the methods needed to use them did prove to be practically valuable.
As the technology developed, the applications for surveying the world were widened. The
first project of topographical triangulation was conducted by C.F. Cassini de Thury in 1744
A.D., in which he successfully triangulated the entirety of France. It took him 39 years to
complete this feat on a scale of 1:86,400 (Derry & Williams, 1960, p. 231). Many other
expeditions were made in or from France to this end. Among these expeditions was the famous
trip to Lapland completed by Swedish surveyor and astronomer, Anders Celsius, in which he
determined an accurate measurement of one degree of arc of latitude (Maupertuis, Camus,
Clairaut, & Le Monnier, 1738). These surveyors, who took such risks in their endeavors,
continue to be an inspiration to the modern surveyor today.
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Chapter 3: The Method
The goal of this experiment was to determine the accuracy of primitive land surveying
methods, as compared to contemporary methods. The said experiment was set up by the creation
and use of a primitive, home-made sextant. Said sextant was used to make astronomical
observations to determine latitude. A basic solar clock was also used to determine longitude. The
data which was retrieved was initially recorded in a field book, and later entered into a data
management software (Google Sheets). Said data was then processed and analyzed. The factors
to be studied were those statistically comparing the latitudinal and longitudinal coordinates
obtained by both primitive and contemporary methods.
The control group was the coordinates obtained using GPS technology. These coordinates
could only be obtained using a smart phone GPS, instead of a land-survey-grade GPS. No access
to a land-survey-grade GPS was available for the purposes of this study. The data was collected
using natural, non-planed wood and a knowledge of mathematics. Other resources could have
been used but would have had been primitive in their origin; nothing which required
sophisticated fabrication was utilized.
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Chapter 4: Data Collection (Results)
The collection of data was completed via celestial and solar observations using primitive
materials. Among these materials were those used in the determination of latitude:
(1) Broken twigs and raw sticks held freely in the hands of the observer,
(2) Using the fingers of the observer.
Also, materials were used in the determination of longitude were a sundial made using a stick in
the ground.
From the initial observations, calculations needed to be made involving the recorded
angles and times. The observations for longitude were computed via drawing lines between each
observed and recorded point, measuring the sides of the constructed triangle, and using the law
of cosines to determine the angle between Polaris and the horizon (see Figure 1). The
observations for latitude were computed by taking the difference between the solar time (the
local time when the sun is at its zenith in the sky) and the time at Greenwich, England. The
Observation Point (Expected Value) was determined by acquiescing GPS coordinates from the
Google Earth application on a smart phone. These coordinates were measured at a latitude of
41.36° and longitude of -85.14° (see Figure 2). Because of significant digits, all values were
analyzed only to the nearest hundredth of a degree.
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Figure 1
Law of Cosines – Solving for Gamma (Angle)
Note. The function “cos-1” indicates the arc cosine function, which yields the inverse of the
cosine trigonometric function. The variables “a,” “b,” and “c” indicate the sides of the triangle.
The variable “γ” indicates the angle opposite the side “c.”
Figure 2
Observation Point – Google Earth Application
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The data points collected to measure Latitude were the measurements of degrees between
the star Polaris and the horizon. The data points collected to measure Longitude were the
measurement of the difference between local solar time and Greenwich Mean Time (GMT). As
stated above, all values were recorded to the nearest hundredth of a degree, for the sake of
significant digits.
Both the latitudinal and longitudinal analyses (the Observed Values) did not yield terribly
accurate results, when compared to the GPS coordinates (the Expected Values). The calculated
observations for longitude, in particular, were generally precise but not accurate (see Figure 3).
The observed values for longitude differed from the expected value by 2.77 degrees, on average;
the standard deviation was 0.212 degrees; and the average value for all the longitudinal
observations was -87.90 degrees. All things considered, these are decent tolerances for the
primitive materials and methods used.
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Figure 3
Longitude Comparisons
The calculated observations for latitude were neither precise nor accurate (see Figure 4).
The observed values for latitude differed from the expected values by 11.38 degrees, on average;
the standard deviation was 7.78 degrees; and the average value for the latitudinal observations
was 52.74 degrees. This is not terribly surprising, because the materials used are meant to be
primitive. Thus, primitive results are to be expected.
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Figure 4
Latitude Comparisons
Additionally, an analysis of the calculated latitudinal observations was completed by
separating the data points by objects used. This method proved helpful in plotting said data.
There were numerous differences found which are of note by looking at the data in this way.
First, the observations using the large sticks gave the most accurate results (as shown in
Figure 5), with an average reading of 3.08 degrees different from the expected values. This
method also yielded the closest individual measurement of 38.47 degrees; a reading only 2.89
degrees less than anticipated! The second most accurate method proved to be using the small
sticks, with an average reading of 11.97 degrees different than the expected value (see Figure 6).
The use of twigs was the third closest method, with an average reading of 13.49 degrees from the
expected value (see Figure 7). The least accurate method, on average, was the use of the
observer’s hands to determine the angle between Polaris and the horizon. This method yielded an
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average difference of 17.29 degrees from the expected value; however, this method also
procured the third closest individual observation to what was expected. This was a measurement
of 47.24 degrees between Polaris and the horizon – which is only a 5.88 degrees difference from
the anticipated reading (see Figure 8).
Figure 5
Latitude Comparisons – Objects Used: Large Sticks
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Figure 6
Latitude Comparisons – Objects Used: Small Sticks
Figure 7
Latitude Comparisons – Objects Used: Twigs
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Figure 8
Latitude Comparisons – Objects Used: Hands of the Observer
These results may be further demonstrated by depicting the global locations of the most
accurate readings. Only the four most accurate results have been depicted, because to show the
others would make the scale of the figure too large to be usefully plotted. Figure 9 demonstrates
the inaccuracies of the observations using primitive materials as compared to the Observation
Point (the Expected Value). One can also think about these results from another angle: the
average difference in longitude (between observed and expected values) was only 2.77 degrees.
On a normal, store-bought, six-inch diameter protractor, that is generally equivalent to a chord
length of 0.15 inches (0.38 centimeters). The average difference in latitude was 11.38 degrees,
which on an average protractor would be a chord length of 0.59 inches (1.5 centimeters). See
Figure 10 for a depiction of these average angles on a 6-inch protractor.
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Figure 9
Global Representation of the Four Most Accurate Observations (Latitude and Longitude)
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Figure 10
Protractor Depiction
Note. The blue line signifies the average difference in longitude observed from what was
expected (2.77 degrees), and the red line signifies the average difference in latitude observed
from what was expected (11.38 degrees).
Figures were not constructed to aid in the visualization of the longitudinal data, because
the same stick was placed in an identical spot of ground for all observations of this kind.
Therefore, there were no notable differences to be used in creating comparable datasets via the
type of object used, or any other discernable differentiation.
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Chapter 5: Conclusions
The practice of land surveying is continually in flux. The technologies used have always
developed for the sake of the precision and accuracy of measurements. Throughout the course of
these experiments, the hope was to prove that a young surveyor can acquire relatively accurate
and precise results using only primitive, non-fabricated materials. The results of said experiments
suggest that the hypothesis is inaccurate, but the whole process of research, experimentation, and
analysis was incredibly advantageous to this young land surveyor.
Limitations in Acquiring Data
There were a number of practical problems which prevented the acquisition of additional
data; chief among them was weather. In northeastern Indiana during this spring semester (2023),
the nights where Polaris was visible were few, and the amount of those clear nights that could be
utilized by the observer were fewer still. This latter point was mainly due to the business of life:
academics, work, family, etc. Similarly, getting clear days for the solar observations necessary to
a longitudinal calculation on the same day as a clear night to view Polaris made the days usable
incredibly few. This is the reason for such few data points. For the sake of future experiments, it
will be interesting to see how more observations will tighten up the results.
Problems in the data were not just limited to the quantity of the observations, but also the
quality of them; namely, the clear and ever-present risk of human error. The fact that these
observations were completed using primitive materials meant that the observer had to stand as
still as possible while conducting the experiments, and then attempt to keep the materials (sticks
or hands) at the same angle long enough to record it on paper. This made the whole endeavor
quite difficult and introduced a large chance for human error in the actual observations
themselves.
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Answers to Research Questions
Throughout this process of research, experimentation, and analysis multiple things were
learned. The types of equipment used historically by land surveyors to do similar types of
experiments, as were done in this project, were a point of discussion. Additionally, the primitive
materials to be used was determined. The statistical discrepancies between modern means and
primitive means of measurement were analyzed. It was discovered, as was expected, that
primitive means take much longer and require significantly more effort to procure any results –
not simply accurate results, and accurate observations using primitive materials would require
almost no human error in technique. This human error could be mitigated by more stable,
properly constructed instruments of observation.
Lastly, and of the most significant importance, the student accrued an immense number
of benefits from completing this project. To get connected with one’s roots in nature via solar
and celestial observations was chief among these benefits. To understand that, if using the
correct materials, one does have the ability to survey using nature itself as one’s guide – not
simply buttons and codes in a machine. Even though the results procured were not as accurate as
expected (as is clearly demonstrated by Figure 9), when zooming out and looking at this
experiment, one finds that the degree of accuracy was in fact relative to the materials used (see
Figure 10). The materials were primitive, so primitive accuracy was expected. Surely, the more
refined the materials and techniques used become, the more accurate the results will be.
Future Experiments and the Way Forward
Further experimentation with more refined (but not contemporary) instruments will be
needed to see the full effects of this endeavor in surveying land without a dependence on
modern-day technologies. A more complex and permanent arrangement of materials could be
31
constructed out of lathed or straightened twigs, sticks, or branches. There are methods of
straightening wood which can be completed using fire and steam. A basic lathe could be
constructed using a knife and could help in straightening the branches into true rods. These
straightened materials could be fixated into the ground by either digging a hole or even using a
basic form of concrete, and wooden pegs would be used as pivot points to create a rudimentary
sextant. This increase in uniformity and stability of the materials would greatly aid the
procurement of more accurate latitudinal and longitudinal observations by decreasing the
possibility of human error.
This student hopes to continue these experiments past graduation; possibly by seeking the
project’s publication. To create a non-fabricated, stable mechanism out of primitive materials for
the procurement of more accurate readings would be incredibly helpful to this endeavor. More
research into the history of land surveying, especially focusing on methods used in the Middle
Ages and earlier may additionally prove advantageous, because taking the advice from past
experts is always a surer path to success than trying to blaze ahead on one’s own.
32
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