University of Virginia Library

III. APPENDIX III

THE SIGNIFICANCE OF THE PLAN OF ST. GALL TO
THE HISTORY OF MEASUREMENT

LUCIUS AEBUTIUS FAUSTUS, OF THE CLAUDIAN
VOTING DISTRICT,[1] A FREEDMAN OF LUCIUS
AEBUTIUS SURVEYOR AND SEVIR, HAS
ERECTED THIS MONUMENT, WHILE STILL LIVING,
TO HIMSELF AND HIS WIFE, ARRIA AUCTA,
FREEDWOMAN OF QUINTUS ARRIUS AND TO
HIS CHILDREN[2] AND TO HIS FREEDWOMAN
ZEPYRE

[ILLUSTRATION]

535. IVREA, prov. AOSTA, ITALY

MUSEO CIVICO

TOMBSTONE OF

LUCIUS AEBUTIUS FAUSTUS

SURVEYOR [FIRST CENTURY]

The dedication, written in eight lines, is composed within a square space (symbol of
centuriated measure?). Fine letter forms of the inscription, slightly contracted to
compose with pleasing effect in a narrow area, are representative of the period of
high perfection in development of the CAPITALES QUADRATAE (cf. comment on
Trajan's column inscription, I, 291). With restraint, clarity of statement, and
mastery of design by an unknown sculptor we are told, with respectful terseness
bordering on the laconic, of a servant of the empire, by means of a monument of
exceptional character, artistry, and great beauty.

The vertical slab of marble, lower portion lost, depicts above the inscription a pediment
with floral ornaments, left and right, that fill two triangular corner spaces. A
shield and two spears within the triangle of the pediment may indicate former
military service. The remainder of the fragment, below the inscription, depicts
symbols of state and authority, and instruments of the surveyor's profession—cross
arms of a groma (below, p. 140) superimposed on its vertical staff, exactly positioned
on the slab axis. A pair of jasces, axe blades directed outwards, composes symmetrically
about the groma staff. Two plumb bobs, one right and one left, are seen
between the cross arms.

Just above the head of the staff is depicted an object that cannot be identified with
certainty. Its resemblance to a settee with surmounted cushion has provided a tentative
identification. Yet, a bench-like form is also reminiscent of the chorbates, a Roman
levelling instrument used in construction work. The article surmounting the bench
form may in this matter be interpreted as a vessel pouring water, seen issuing at
left, to fill the water-levelling trough of the chorbates below, and of which it is a
part. The plumb bob is essential in use of both groma and chorbates. Whatever the
object may be, a pragmatic efficiency governing and pervading its design dismisses
any notion that it was a whimsical choice made by the sculptor to fill a space.

Noble, imaginative, with a measure of delight, utterly unsentimental, the genius of a
Roman artist has brought to the memorial purpose, a quality of lasting greatness
which in later eras disappears, is lost.

E.B.

THE SIGNIFICANCE OF THE
PLAN OF ST. GALL TO THE
HISTORY OF MEASUREMENT

A LINK BETWEEN ROMAN, AND
ENGLISH AND AMERICAN SYSTEMS OF MEASURE

PREFACE

During a discussion conducted at a meeting of the Herbert M. Evans History of Science Club, early in 1968,[3] where I
reported on my findings on the scale and construction methods used in the Plan of St. Gall, Professors Charles L. Camp
and Hunter Dupree drew attention to the striking similarity between the series 640, 160, 40, 10 and 2½, used by the designer
of the Plan in laying out the primary area divisions of his monastery site[4] and the measurement system embodied in the
American Land Ordinance of 1785.

The latter is familiar to anyone reared on the great western plains or wherever in the vast territory of the Midwestern
United States that land division into sections one mile square, each composed of 640 acres (fig. 539), is quite visible
Internally these are divided into half-sections of 320 acres, quarter-sections of 160 acres, and downward by the same
process of binary division into parcels of 80, 40, 20, 10, 5, and 2½. In the great rural plains of America, as it was subsequently
pointed out by Hunter Dupree, the expression "the back forty" and "the front forty" (for divisions of a section)
or "forty acres and a mule" (to define subsistence, if not plenty) are deeply imbedded in American history and in common
usage even today.[5]

These analogies raised the interesting question whether the American land measuring system of 1785 might be historically
connected with the system used in the Plan of St. Gall. The problem has since become the subject of two fascinating
studies by Hunter Dupree, the first entitled "The Pace of Measurement from Rome to America," published in the Smithsonian
Journal of History, III, 1968, 19-40, a second and more extensive one entitled "Measure is the Measure of All
Things," read at the Annual Meeting of the Society of the History of Technology, in Washington D.C. on Dec. 28, 1969;
and a third, "The English System for Measuring Fields," Agricultural History XLV:2 (1971), 121-29.

The historical implications of these three studies of Prof. Dupree's are vast and arresting. After brilliant beginnings in
the earlier parts of the nineteenth century, the history of mensuration has fallen into a state of almost complete stagnation.
That my work on the Plan of St. Gall should have inspired Hunter Dupree to stir new life into this subject adds a new
dimension to the Plan of St. Gall and heightens my excitement about my own findings.

I am grateful to Hunter Dupree for allowing me to include in this work a summary from his own pen of those aspects
of his studies which cast light specifically on the historical significance of the Plan of St. Gall as a connecting link between
earlier and later measurement systems. His report is rendered verbatim.

[ILLUSTRATION]

536. THE WORKS OF EDMUND GUNTER. TITLE PAGE

FIFTH EDITION, LONDON, 1673. SHOWN ORIGINAL SIZE

Edmund Gunter wrote his treatise on the sector and other instruments in Latin in 1609. Although it was copied and freely circulated, Gunter did not permit its publication
in English for more than 16 years. It then appeared in an edition entitled The description and vse of the sector, the crosse-staffe, and other instruments,
for such as are studious of mathematicall practise (London, 1609). This treatise formed the "first edition" of Gunter's Works and as such was
then issued (also in London, 1623) in two volumes: De sectore et radio . . . description and vse of the sector, in three bookes, and Description of
the crosse-staffe in other three bookes . . . . Subsequent editions were published posthumously in London.

A second edition (1636) appended Gunter's Canon Triangulorum, the important tables of logarithmic sines and tangents first published in 1620, and was issued under
the rubic "much augmented." A third (1653), "much enlarged by the author" (his death in 1626 notwithstanding), was "amended" by H. Bond, and contained an addition
by Samuel Foster on the use of the quadrant. A fourth edition (1662) was issued with a description of "another sector and quadrant invented by" Foster, as well as
"examined and enlarged" by William Leybourn. The fifth and last edition (1673) was merely "corrected" by Leybourn who also published, in 1685, Description and
use of a portable instrument known by the name of G's quadrant . . ., the last book with which Gunter's name was associated.

The publication history of Gunter's innovative work is reflected in that of a later handbook, similarly indispensable, by Nathaniel Bowditch, whose American Practical
Navigator has been revised and reissued frequently since it was first published in 1802.

E.B., L.P.

WHEN WALTER HORN, through his analysis of the scale and construction methods of the Plan of St. Gall, dispelled
"once and for all, the widespread belief that medieval architectural drawings were not made to scale,"[6] he placed a question
mark on the almost universally accepted version of the history of the measurement of length from Rome to America. The
accepted version, to risk an over-simplification, followed roughly the pattern of the history of mathematics, reaching a
peak with Archimedes and dwindling almost to complete chaos before the rise of modern science reintroduced precision
into the thinking of Western man. Any measurement outside the confines of the metric system, the units such as inch and
foot, were unfortunate and irrational survivals. That measuring units with human-body referents were widely scattered
through time and space in the world's history was well known but unanalyzed, of antiquarian interest only. This slumbering
set of generalizations scattered in the encyclopedias of the world has now been thoroughly disturbed.

Before Horn's analysis of the measurement system used in the Plan of St. Gall it would have been extremely difficult
to construct a single grid of measurements from Rome to America. Not that the general correspondence of the survey land
patterns in the Po Valley and Ohio, for example, had gone unnoticed. Rather a link was missing which roughly corresponded
to the decline of learning—to the old concept of the Dark Ages. Only in the period after the transmission of Greek mathematics
and Indian numerals to the Western world by the Arabs, should a scholar even begin to look for the resumption of
a mathematical activity which might make a measuring system possible. Yet if one conceives of the carrier of a measuring
system not as high mathematics but as language, he might see the whole problem differently. A continuity of measurement
through the Dark Ages would then be as unbroken as the use of the Latin language, and Carolingian times might provide
a cross section of the system.

When Walter Horn elucidated the meaning of the dimensions of the Plan of St. Gall and especially when he derived
the unit of 2½ feet from the length of 40 feet by the process of continuous halving, he laid the basis for a cross section of
a Carolingian measuring grid. Because the Plan itself is a set of dimensions, with 1/16 inch playing an important role,
and because by multiplying by 192 the Plan becomes a monastery on the ground, the significant units include the inch,
the foot, and by implication the step (2½ feet). Significant groupings of the units include the 40-foot side of the crossing
square, and by implication the 160-foot of the supermodule in Horn's analysis, the 480-foot short side of the Plan, and
especially the 640-foot long side of the Plan.

The Roman predecessors of the Carolingian units are readily apparent for the inch and the foot. That the length is
close to that of the foot of Drusus (33.30 cm.) rather than the classical Roman foot (29.60 cm.) or the modern English
foot (30.48 cm.) is of minor importance. The foot of Drusus was itself an inheritance of Roman times and retained its
stability alongside the slightly shorter Roman foot for many centuries. Once a length for a unit has been selected, the
elaboration of a grid can proceed on the same relations as one based on a slightly different unit as measured against a
modern scale as long as the name, in this case "foot," is identical. In addition to the inch and foot, the Roman jugerum
(a measure of land 240 feet by 120 feet) appears as one-half of the short side of the Plan. The Roman stadium, or 625 feet,
has a reflection in the long side of 640 feet. The difference between the two is extremely important, as it represents an
anomaly in the Roman system in halving the Roman mile of 5000 feet (1000 Roman paces or 2000 steps) three times to
625 feet and doubling the 2½ foot step in a sequence 2½, 5, 10, 20, 40, 80, 160, 320, 640. This difference will ultimately
account for 120 feet of the 280 feet added to the Roman mile to make the English mile of 5280.

An examination of the intervals of the grid pattern shown by the Plan of St. Gall indicates that, while the units are
clearly Roman, the changed social setting has seen a regrouping of the Roman units into a grid adapted to the life of a
Benedictine monastery. The 5-foot Roman pace has receded in favor of the 2½-foot step, which is more useful in close
quarters. The short side of the enclosure as analyzed by Horn could be most readily measured in cubits (1½ feet), which
introduces a factor of 3 that is very useful in constructing right angles. Yet the dominant unit of the step (2½ feet), and of
the sides of the nest of modules, which includes that of the crossing square of the church (40 feet), all relate to the long
side of the Plan (640 feet), so that a ratio of 3:4 is readily available both to the planner on the parchment and to the
builder on the ground.

[ILLUSTRATION]

537. PLAT OF THE FIRST SURVEY MADE UNDER THE LAND ORDINANCE OF 1785

NATIONAL ARCHIVES, CARTOGRAPHIC ARCHIVES DIVISION, WASHINGTON, D.C.

ILLUSTRATION is 3/4 of the size of the original drawing

SCALE OF ILLUSTRATION: 1 1/2 INCHES = 80 CHAINS

3/4 INCHES = 40 CHAINS

R.F. = 1:84,480

In the Land Ordinance of 1785 the Congress of the Confederation in the new United States set the pattern for surveying the western lands
north and west of the Ohio River ceded by the states to the national government. Thomas Jefferson and Hugh Williamson of North Carolina,
members of the committee drafting the statute, originally proposed in 1784 a square grid of townships, oriented to true north, each of which
would measure ten miles on a side. Jefferson proposed that the mile to be used should be the "geographical mile," which he took as 6086.4 feet,
quite close to the present nautical mile. He further proposed a decimalization of the geographical mile as follows:

thus:

         

ONE AMERICAN MILE	=	6086.4 feet	[10 LINKS	=	1 PACE]
ONE FURLONG	=	608.64 feet	10 PACES	=	1 CHAIN [100 LINKS = 1 CHAIN]
ONE CHAIN	=	60.864 feet	10 CHAINS	=	1 FURLONG
ONE PACE	=	6.0864 feet	10 FURLONGS	=	1 AMERICAN MILE
[ONE LINK	=	0.6864 feet]

Had this choice of units prevailed, even if the foot were retained, the grid of the Land Ordinance would not have belonged to the tradition of
length measurement carried by the units descending from Rome through Carolingian times and medieval England to the American colonists in the
form of the statute mile. Rather the grid would have derived from the grid of latitude and longitude which the cartography and navigation of
Europeans had developed to a high degree of accuracy since the beginning of the expansion of Europe over the broad seas in the fifteenth
century. However, the population of the new American republic possessed a system of land measuring with as great an agreement on fundamental
units as that used by any people anywhere. The Gunter chain of 66 feet, divided into 100 links, had no rivals. Ten chains made a furlong and
eight furlongs a mile. Hence when, after Jefferson's departure for Paris, the committee drafted the final version of the Land Ordinance in 1785,
it substituted the statute mile of 5280 feet for the geographical mile as the side of a section, 36 of which made a township. One scholar who has
examined the connection between the grid idea and Roman centuration concludes that while such a conceptual link is not impossible, it is highly
unlikely (William D. Pattison, Beginnings of the American Rectangular Land Survey System, 1784-1800) [Chicago:
University of Chicago Department of Geography Research Paper No. 50, 1957], pp. 60-64). Pattison does not, however, address himself
directly to the history of the units of the subdivisions of the sections and their relation to the measurement tradition discussed here.

The so-called seven ranges of townships on the western bank of the Ohio River were surveyed under provisions of the Land Ordinance of 1785 in
the summer of 1786 and 1787, and the submission of notes and plats was completed in 1788. Although surveying methods were later improved in
detail, the basic method of laying out sections and townships became standard for surveying the public domain as settlement moved westward.
The occasional penciled lines on the original plat show that division of sections into quarter-sections of 160 acres had already begun at an early
date.

The principle which revealed the relations of the units and intervals of the Plan to Horn is that of continuous halving.
Instead of dividing units into tenths, as in a consistent decimal system, Western man usually referred to the units
by language referring to conventionally chosen dimensions of the human body (e.g. 1 foot = 12 inches [thumbs]). Integers
were to them as handy as they are for people of any age, but lacking decimal notation they found that the easy way to
make a fraction was by continuously dividing by 2. Hence the base of the measuring system is 2 arranged in a geometric
progression. . .

   

1	2	4	8	16	32	64	128	256	512	. . . . . .
20	21	22	23	24	25	26	27	28	29	. . . . . .

The gaps in this base progression can be filled in the ranges used in the Plan of St. Gall by multiplying it (as on the short
side) by 3

   

3	6	12	24	48	96	192	384	768	1,536	. . . . . .
3(20)	3(21)	3(22)	3(23)	3(24)	3(25)	3(26)	3(27)	3(28)	3(29)	. . . . . .

On the long side the multiplier is 5

   

5	10	20	40	80	160	320	640	. . . . . .
5(20)	5(21)	5(22)	5(23)	5(24)	5(25)	5(26)	5(27)	. . . . . .

In this last sequence one sees not only the 40 of the crossing square and the 160 of the super module, but the halving of
5 is 2½ of the step, the most frequently occurring unit on the Plan.

Where once was only the confusion of the centuries of the Dark Ages a measuring system adapted to life in a Carolingian
monastery has now become clear. More important, a link between the Romans and the Carolingians having been
secured, the possibility of a link to the still living Anglo-American measuring systems requires the invention of no different
language and no different social institutions from those we already know to have existed. Indeed by 1300 the English
measuring system had, by becoming a part of statute law, placed itself beyond any possibility of a break in continuity
down to the present.

Since the foot (in a length not far from that of the Romans) was available in medieval England, and since the cloth-yard
of 3 feet was already in consistent use, the problems confronting the measuring-system designers of the thirteenth century
had to do not with units but with the layout of agricultural land. The dominant mode of farming in England was of course
in long narrow strips. Hence it is not surprising to find the statute acre defined as 4 rods by 40 rods, both longer and
narrower than the Roman jugerum. Yet the length of the statute rod is 16½ feet, clearly an innovation of some sort. The
story of how the 16-foot rod, 40 of which make 640 feet (the length of the long side of the Plan of St. Gall) was modified
by the addition of a step of 2½ feet at the 32-step mark on the long side of an acre to create the 660-foot furlong has been
told elsewhere.[7]

In the sixteenth century the Roman mile (mille passus, one thousand paces) of 5000 feet became increasingly conspicuous
as the major itinerary measure in England. While in Roman times the mile had consisted of 8 stadia of 625 feet,
the evolution of the measuring system through the Carolingian empire and medieval England had produced a furlong of
660 feet. Therefore to adjust the difference the Roman definition gave way to evolution, and the statute mile of both
Elizabethan times and the present became 8 furlongs of 660 feet, or 5280 feet.

By the early seventeenth century measuring behavior, which continued to be performed by common and uncommon
people alike, came under the scrutiny of mathematicians who were by this time convinced of the advantages of decimal
fractions. Edmund Gunter (1581-1626) not only added the chain of 66 feet to the English grid, but he divided it into

100 links thus adding a decimal element to the English grid. In the meantime the invention of logarithms and the regularization
of decimal notation for fractions had rendered the operation of halving unnecessary in many measuring settings.
and eventually the metric system dispensed with the units of the traditional systems themselves.

The American republic was struggling with the problem of a surveying system for its western lands in the 1780s just
before the metric system became available, its introduction hastened by the French revolution. Although Thomas Jefferson,
acquainted with French thinking on the subject, toyed with an innovative decimal system, the Congress of the Confederation
settled on a grid based on the English mile. A mile square, 640 acres, was divided by continuous halving into 320
acres, 160 acres, 80 acres, 40 acres and so on (fig. 537). The mile, an itinerary unit, thus became part of field measure, and
the subdivision followed the same sequence—640, 320, 160, 80, 40, 20, 10, 5, 2½—that characterizes the Plan of St. Gall,
Thus the American land system resembles the measuring system of the Plan of St. Gall, and when all the adjustments
are made this demonstration leads to the conclusion that the American system is the St. Gall system. A single measuring
system has survived within narrow limits of accuracy from Rome to America.

The actual and continuous existence of the grid opens a new set of perspectives on social history in the Western world.
That people had measures, kept them stable, passed them from one generation to another without a single break, and
adapted them to changed modes of life gives both shape and continuity to a numbering system running through hitherto
unquantified ages. More fundamentally, the Rome-to-America grid ties measurement to the life of people in each age
traversed and makes it a part of their language and culture.

A.H.D.

[ILLUSTRATION]

538. THE WORKS OF EDMUND GUNTER LONDON 1673, fifth edition

A TABLE FOR THE USE OF THE CHAIN illustration shown same size as the original

This table sums up the adjustments from Roman times to the English system in essentially final form as available in the American Colonies at the time of
the Revolution. "Acre" in the heading could read "furlong" and "Cent." could read "link."

[The original concept acre, the area that could be plowed by a yoke of oxen in one day, in
England, became limited by statutes under Edward I, Edward III and Henry VIII as a
piece of land measuring 40 poles (one furlong[8] ) in length by 4 poles[9] in width (= 4840
square yards or equivalent area). Interpreted as feet, this is a plot 660 by 66. The width to
length ratio 1:10 of the plot is significant. By designating as existing statutory measure,
4 poles or 66 feet as a CHAIN, and by extending the decimal notion a step further, Gunter's
"centesimal" was created as a LINK on the ratio 1:100, the link length to chain length, of
0·66 feet = 7· inches. E.B.].

[ILLUSTRATION]

539. AERIAL PHOTOGRAPH VERTICAL VIEW, A SECTION, STATE OF KANSAS

NATIONAL ARCHIVES, CARTOGRAPHIC SECTION, WASHINGTON D.C.

SOIL CONSERVATION SURVEY, DATE 7 JULY 1938, NUMBER AYG. 9.89

Even more clearly than in the hilly country of the seven ranges in Ohio, the rectilinear grid based on the mile square section of 640 acres
determined land-use patterns on the relatively flat prairies and the Great Plains. The aerial photograph of a section of land in Marion County,
Kansas shows the 160-acre quarter-sections which were the size that a settler could obtain free from the government under the Homestead Act of
1863. The forty-acre fields are a common size for fields within a farm. The blocks in the townsite in the northwest corner are, allowing for
spacing by two-chain streets, very close to 2 1/2 acres. The modules from 2 1/2 acres through 10 acres, 40 acres, 160 acres, and 640 acres are
all visible.

Recent research has shown that once the land grid had been laid down, its effect has continued to shape land use, road patterns, property
boundaries, administrative units in a way which differs from similar terrain surveyed unsystematically (Norman Thrower, Original Survey
and Land Subdivision: A Comparative Study of the Form and Effect of Contrasting Cadastral Surveys [Chicago:
Rand McNally & Company, 1966]). A safe prediction is that after two thousand years at least some of the American land grid will be as
visible in an aerial photograph as the Roman centuriation has proved to be.

For visual comparison, a metric scale is included with the Anglo-U.S. scales of feet, miles,
chains, together with indication of the furlong. One furlong appears in coinciding alignment
with 0·2km. The actual relationship is one furlong equals 0·217km. Thus five furlongs equal
1·0058km, irrelevant perhaps but interesting.

[ILLUSTRATION]

DIAGRAM SHOWING SUBDIVISIONS OF LINEAL AND AREAL MEASUREMENTS IN RELATIONSHIP TO
A TYPICAL U.S. LAND DIVISION PLOT ONE MILE SQUARE

The units—mile, acre, furlong, chain, rod, feet—and the ratios among them were
the carriers of continuity with the Carolingian grid. The subdivisions within the
sections were not even specified in the Ordinance. It is the grid within the sections
and not the idea of a grid itself which connects by the units and their ratios to the
Plan of St. Gall. The only change between the ninth century and the eighteenth
century was the addition of 1/2 foot to the rod of 16 feet to create the statute of
16 1/2 feet in English laws just before and after 1300.

*

[ILLUSTRATION]

540.A GROMA based on Matteo delle Corte, 1922

INSTRUMENT OF THE GROMATICI

a professional title, with AGRIMENSOR surviving after the instrument
became obsolete

E.B.