Surveying Instruments of Greece and Rome

INST UMENTS AND METHODS

.      

With no hard evidence to base the design on, the reconstruction of a
libra can only be tentative. The sole requirements are that (on the
present argument) it should resemble a balance beam and that its man-
ufacture should be within the capabilities of a Roman metal worker;
and in order to survey the shallow gradients of Roman aqueducts it
must also be more accurate than the dioptra.

A steel beam was therefore made, with each end bent at right angles
to carry iron split sights as on the dioptra, projecting sideways because
the instrument is used only for levelling. The overall length is  ft
(. m) and the weight . kg. From the centre rises a vertical
member terminating in a transverse bar with a knife-edge underneath
on each side. This rests in a slight notch on top of each arm of a deep
U-shaped bracket carried on a heavy tripod intended for a modern
level. The concave base of the bracket imitates that of the level, allow-
ing it to be adjusted on top of the convex tripod head, and a small
plumb-line indicates when the bracket is vertical in both directions.

The knife-edge ensures that the beam can swing with a minimum of
friction; indeed it is so sensitive that a fly settling on one end affects the
reading on the staff. Because its weight is twice that of the dioptra and
its exposed surface is less than a fifth, it is much less liable to swing in
the wind. As an extra precaution, a narrow and shallow case of thin
wood was made, screwed to the inside of the bracket arms and leaving
only a slot at each end for the sights to project through. This shields the
beam and prevents movement even in a moderate wind. When made,
the beam was slightly out of balance and did not hang truly horizontal.
A small quantity of metal was therefore added to one end and pared
away until the beam appeared to be in proper equilibrium.

The libra was tested over the same course as described in Chapter
.,  m long with a difference in height of . m. The procedure
was the same as with the dioptra except that at first only one-way sights
were taken. Early results, giving around . m, were little if any
better than with the dioptra, and the suspicion arose that contrary to
appearances the beam was not in perfect equilibrium and that one-way
sightings were inadequate. As with the dioptra, two-way sightings were
therefore adopted. The final three results were ., . and
. m, whose average differed from the actuality by only  mm.



THE LIB A

. .. Libra reconstruction with shield.

. .. Libra reconstruction without shield.



INST UMENTS AND METHODS

. .. Detail of suspension.

. .. Detail of sight.



THE LIB A

This represents an error of  in ,, which would allow a gradient
of  in  or even , to be derived from levels taken with the
libra. The best result was identical to that with the modern level. The
implications are again discussed in Chapter .. In a later demonstra-
tion for BBC television, the libra was given the task of setting out a
 m stretch of aqueduct around a valley head at a gradient of  in
. The total fall should therefore have been  cm. When the make-
shift trough was installed and water was succesfully flowing, the actual
fall was surveyed with a modern level and found to be  cm, an error
of  in ,. This was probably due to the fact that, time being short,
only one-way sightings were taken with the libra.

The libra’s superiority over the dioptra seems to be accounted for
both by the freedom from movement in wind and by the distance,
three times as great, between the sights. As already observed, the
design, though based on what can be deduced of the original libra, can
only be tentative. That it works is no proof that it is correct. But the
fact that it achieves the results postulated for it on quite different
grounds makes it at least plausible.



 
THE G OMA

. 

The groma was an extremely simple instrument, possibly of Greek
origin, which became almost the trademark of the Roman land sur-
veyor. Because its function was limited to sighting and setting out
straight lines and right angles, its use was restricted to surveying roads
and the like and to establishing the rectangular grids of towns, military
forts and, above all, land divisions. Since roads form the subject of
Chapter , we may here confine ourselves to a brief outline of the
history of surveyed grids.

An irregular street pattern was normal to early Greek cities; but in
later times a regular rectangular grid became more widespread. Its
introduction was generally attributed to Hippodamus of Miletus who
rebuilt a number of cities in this way in the first half of the fifth century
, and certainly it was a commonplace by   when Aristophanes
lampooned the astronomer Meton as a town planner laying out
Cloudcuckooland.1 But while Hippodamus may have popularised the
grid, he did not introduce it, for there are many Greek instances from
earlier centuries, and even Egyptian and Mesopotamian antecedents.2
It was most commonly applied to Greek colonies overseas, which often
had the advantage of being built on virgin sites. The example of those
in Italy was perhaps imitated to a limited extent by the Etruscans, to
whom folk-memory ascribed a considerable ritual for the founding of
new towns and an emphasis on correct orientation; but maybe their
contribution was exaggerated, for archaeology reveals little planning of
Etruscan cities. Beyond doubt, however, the Greek colonies of Italy
inspired the Romans to adopt the regular urban grid.3

As for dividing agricultural land into a grid, Herodotus says that the
Egyptians laid out square and equally-sized plots (Chapter .); but in
hard fact this seems to have been the exception, although there was

11 Aristophanes, Birds –. 12 Owens , esp. –.

13 See Owens , –; Ward-Perkins , esp. –.



THE G OMA

certainly a complex system of land registration for tax purposes. In
Greece the generally rough terrain militated against geometrical divi-
sion of land; but once again it was around colonies, where land was dis-
tributed de novo, that a rectangular pattern of division is most evident,
sometimes as an extension of and parallel with the town grid.4 The best
examples are in the Crimea, where huge areas of regular oblong plots
of about   have been identified, and in southern Italy, where divi-
sions of the sixth century tended to be in long rectangular strips, not in
squares. The report of commissioners surveying land boundaries at
Heraclea in Italy in about   survives on a bronze tablet;5 and
among the signatories is one Chaireas son of Damon of Naples, geom-
eter (in the original sense of the word).

Nothing whatever is known about how these grids, urban or rural,
were set out in Greek times. Orientation, as we have seen, would be no
problem, and a straight line can quite easily be prolonged over consid-
erable distances with nothing more than rods as markers. The bigger
question hangs over the means of surveying right angles. The dioptra
with its sights and engraved cross would serve very well; but as we have
observed it appeared on the scene at a relatively late date. In Greek con-
texts we shall find that evidence for the groma, the standard instrument
of the Romans, is slender though not non-existent, and possibly it was
employed. If not, the set square or geometrical methods could have
been used (Chapter .). It is easy to check that lines are parallel by
measuring the interval and that plots are truly rectangular by measuring
the diagonals.

The regular division of land reached its ancient climax with Roman
centuriation.6 This was carried out, above all, around new colonies,
which differed from Greek colonies in that their purpose, at least from
the second century , was not so much mercantile as to provide for
veteran soldiers or the landless. Territory conquered or confiscated or
hitherto uncultivated was accurately divided up in systems that were
often extensive and always carefully planned. Although there was much
variation, the normal division was into squares of  Roman feet on
a side, containing  iugera or . ha. Each square was a centuria

14 Dilke , ; Chevallier ; Isager and Skydsgaard , ; Saprykin .
15 IG  .
16 The literature is huge. Useful starting-points are Bradford ; Dilke ;

Hinrichs ; Behrends and Capogrossi Colognesi ; Campbell .



INST UMENTS AND METHODS

which theoretically contained a hundred smallholdings of about half a
hectare. It was demarcated by limites or roads at right angles, known as
decumani (usually east–west) and cardines (usually north–south).
Boundary stones were set up. When the system was complete and the
land allocated, maps were drawn on bronze tablets with details of own-
ership and lodged in the record office. The surveyors were known
originally as finitores, then as metatores or mensores or agrimensores, and
ultimately (from their most distinctive instrument) gromatici. They not
only laid out the divisions but were experts in such varied skills as
measuring irregular plots and understanding the complexities of land
law, and by the late empire had become judges in land disputes.

Centuriation originated at least as early as the fourth century  in
Italy; it increased dramatically in the second century  and even more
so in the early empire. Surveyors consequently grew in numbers,
gained in status, and began to assemble a canon of manuals on survey-
ing procedures which has come down to us as the Corpus Agrimensorum.
In its present form this is a compilation of probably the fourth century
, corrupt in text and desperately obscure, but our major source.
Useful information also survives in inscriptions, notably the cadasters
or maps on stone of land surveys at Orange in the south of France7 and
a newly-found fragment on bronze from Spain.8 Above all there are the
hundreds of square kilometres of centuriation still to be seen (most
easily from the air) especially in northern Italy and North Africa.

To what extent Roman grid surveying was influenced by Greek
practice is open to much debate.9 Town plans could readily be imitated
from Greek colonies in Italy. But the Roman tradition of centuriation,
while it has some parallels with Greek practice, seems to be indepen-
dent and early; and although land division utterly dominates the admit-
tedly later Corpus Agrimensorum, it is almost totally ignored by the
Greek surveying manuals. This is not to say that the Roman literature is
innocent of Greek influence.10 Some see connections between Hero’s
Dioptra and Metrics and some parts of the Corpus, notably in so far as
Hero’s methods of calculating the area of irregular plots are not unlike
those of Frontinus and Hyginus. Balbus carried out such typically
Greek exercises as measuring river widths and mountain heights, and

17 Piganiol . 18 Sáez Fernández .

19 For a summary of the question see Hinrichs , –.

10 Folkerts  discusses parallelisms in mathematical procedures.



THE G OMA

his parallel lines could have been set out by the methods in Dioptra 
and . Hyginus’ second method of finding south by gnomon is a very
sophisticated one, dependent on solid geometry, which smacks
strongly of Alexandrian scholarship,11 and it is also one of the only two
sections in the Corpus illustrated by a diagram with reference letters in
the Greek fashion. The standard Greek practice of working by similar
triangles is represented in the Corpus by two instances, which likewise
stand out because they are the only ones. Hyginus’ method (Source
) of establishing parallel lines is in effect the same as that of Dioptra 
and  and of Anonymus , and has the second example of a lettered
diagram. Nipsus on measuring the width of a river (Source ),
although his method is not directly paralleled elsewhere, has an unlet-
tered diagram and relies on similar triangles entirely in the Greek tradi-
tion. One sentence in particular, ‘go to the other side of the
ferramentum and with the croma remaining [unmoved] sight a line’,
might almost be a direct translation of Dioptra , ‘without moving
the alidade, go to the other side, [and] sight M’.12 It has moreover been
thought, and reasonably so, that Nipsus’ Podismus is a straight transla-
tion from a Greek original.13

But these are the exceptions which prove the rule. The essential
difference between Greek and Roman instruments, the difference
between Greek and Latin terminology, and the idiosyncrasies of
Roman land surveying all underline the basic independence of the
Roman tradition. The Greek treatises, where the geometric theory
which underpins them is readily visible, contrast strongly with their
nearest Roman counterpart, the Corpus, which is utterly practical and
virtually innocent of theory. They nicely illustrate Cicero’s famous
dictum: ‘To them [the Greeks] geometry stood in the highest honour,
and consequently nobody was held in greater esteem than mathemati-
cians. But we have restricted these arts to utilitarian measurement and
calculation.’14

Rome was undoubtedly tardy in acknowledging, let alone in imitat-
ing, the scientific attainments of Greece, and it was only in the second
century  that its awakening began. Two examples must suffice. The
story goes that the critic, librarian and geographer Crates of Mallos,

11 Hyginus Gromaticus, Establishment .–.; Dilke , ; Dilke , .

12 Other close parallels are Dioptra , Africanus  and Anonymus .

13 Hinrichs , . 14 Cicero, Tusculan Disputations  ..

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INST UMENTS AND METHODS

who constructed a terrestrial globe some  m in diameter,15 came to
Rome on an embassy from Pergamon in either  or   and broke
his leg by falling into the manhole of a sewer. During his convalescence
he gave lectures which first stimulated Roman interest in scholarship.16
Similarly, the first public sundial in the city, brought back from Sicily as
booty of war, was erected in  . But nobody appreciated that the
change in latitude mattered, and for ninety-nine years it told the wrong
time to a blissfully ignorant populace. Only in   did Rome
acquire its first water clock, given by Scipio Nasica and conceivably
designed by Crates.17 It is against this background, and against the
long-established Roman tradition of land surveying, that we may place
the beginnings of Greek technical influence. Greeks now began to
flock to a city which became more and more cosmopolitan, and some
of them were surveyors. By the end of the first century  Juvenal
could utter his xenophobic outburst against the immigrants: ‘Look,
who do you reckon that chap is? He comes to us in any guise you care
to name: teacher, public speaker, surveyor (geometres), painter, trainer,
fortune-teller, tight-rope walker, doctor, magician. The hungry
Greekling knows the lot. Tell him to fly, and he takes off.’18

While Greek surveyors clearly introduced snippets of Greek prac-
tice, as far as we can tell they had little effect on Roman land surveying.
Nor, as we have seen, is there any sure sign of them greatly influencing
Roman levelling techniques. Yet ironically, as we shall find in Chapter
, an elegant method of setting out long straight alignments for
Roman roads smacks more of Greek than Roman geometry.

.     

It is a curious fact that, although the groma is the only surveying instru-
ment of which actual examples and ancient illustrations survive, the
details of its operation remain unclear. The principle is straightforward
enough. A horizontal cross, its arms at right angles, was carried on a
vertical support, and from the end of each of the four arms hung a cord
or plumb-line tensioned by a bob. The surveyor sighted across one pair
of these cords to project a straight line, and across another pair to set

15 Strabo, Geography  .; Geminus, Introduction .; Aujac , n., .

16 Suetonius, Grammarians . 17 Pliny, Natural History  –.

18 Juvenal, Satires . –.



THE G OMA

out a right angle. He therefore worked only in the horizontal, or more
or less horizontal, plane, and was not concerned with differences of
height. If he encountered a steep-sided valley too wide to measure

across in the ordinary way, he carried out the operation known as cultel-

latio. He held a ten-foot rod horizontal (presumably levelling it by eye,

though we are not told) with one end resting on the ground at the start

of the slope. From the other end he dropped a plumb-line and marked

the point where it hit the ground. He moved the rod, still horizontal,

so that its uphill end rested on this point, dropped the plumb-line

again, and so proceeded down one side of the valley and up the other,
counting horizontal ten-foot steps but ignoring the vertical differ-
ence.19

As Schulten showed, the name groma came to Latin from the Greek
gnoma, not directly but via Etruscan.20 Nonetheless the origin of the

word remains somewhat mysterious. Gnoma and gnome are both by-

forms of gnomon, which most frequently denotes the pointer of a
sundial, but can be a carpenter’s set square, a water clock21 or, in a more
general sense, any indicator or mark. Festus (Source ) equates groma
as an instrument with gnomon, for which no parallel can be found in
Greek literature, unless a cryptic dictionary entry (Source ) has this
meaning. Gnoma and gnome, rather, seem to be words used of the
central point of a camp or town, as in Source ,  and perhaps .
Possibly they reflect the setting up at such places of a stone or wooden
marker bearing a cross, as might be implied by Strabo’s description of

Nicaea in Bithynia as laid out in the classic quadrilateral shape ‘divided

into streets at right angles, so that from a single stone set up in the
middle of the gymnasium the four gates can be seen’.22 The same usage

is found for the Latin gruma and groma in the passages cited in Source
. The instrument may therefore have derived its name from the start-
ing-point of the survey. In Latin, when the word first appears in repub-
lican literature, it is spelt gruma, with the related verbs grumare and
degrumare (Sources –). Under the empire it is standardised as groma
with the variant (in Nipsus, Source ) of croma. It is twice given the
generic name ‘machine’ or ‘little machine’ (Sources , ).

19 Frontinus, Surveying .–. Nipsus, Resighting – seems also to take account of

slopes: see Bouma , –. 20 Schulten , .

21 Athenaeus, Learned Banquet  quoting Theophrastus on Egypt.

22 Strabo, Geography  ..

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INST UMENTS AND METHODS

The instrument as such is mentioned only once in Greek literature,
by Hero (Dioptra ), under the name asteriskos or ‘little star’.23
Whether it had been imported from Rome or was a survival of an
indigenous Greek instrument is more than we can say. The equation of
dioptra and gruma in a glossary (Source ) need mean no more than
that both were used for the same purpose. If we take Hero at face value,
he implies that in his day the groma was not much used in Greek-
speaking lands, since the dioptra did the same job more effectively.
Possibly, however, his derogatory remarks were aimed at Roman land
surveyors, with the motive of persuading them to abandon their groma
in favour of his dioptra.24

The authors of the Corpus Agrimensorum, to whom the groma was
their everyday tool,25 did not see fit to describe it, and what they inci-
dentally let drop forms our only written evidence for its design. It
clearly consisted of at least two parts, the ferramentum or ‘iron’ which
was planted in the ground, and the groma proper which was placed on
top (Sources , ). More often, however, ferramentum is used of the
whole thing. The groma proper comprised the cross with four arms,
corniculi, from which hung the cords for sighting (Sources , ). The
centre of the cross, by the usual interpretation, had the strange name of
umbilicus soli, the navel of the base or ground, or (if it should really be
solii) of the throne. As it is normally understood,26 the cross could pivot
on a bracket which could itself pivot on top of the upright column of
the ferramentum. If an existing line was to be picked up, the ferramentum
was fixed in the ground one bracket-length away from the centre of the
marker stone or stake and was plumbed vertical by reference to the
hanging cords. The bracket was swung until its end, the umbilicus soli,
was vertically above the marker as checked by another plumb-line, and
the cross was then turned on the bracket until its arms and cords coin-
cided with the desired alignment. The surveyor sighted across diago-

23 Asteriskos does not seem to be a translation of the Latin stella which, though it appears

in a surveying context, denotes not an instrument but a star-shaped bronze plate used

as a marker on central or boundary marks. See pseudo-Hyginus (Source ); Festus

.–; Gaius . and .. 24 Hinrichs , .

25 It is interesting that Groma occurs once as a proper name, at Chester where a tomb-

stone (RIB ) to a legionary of the first century AD was set up by his heir Groma.

Was he, or his father, a surveyor?

26 Bouma , – discusses the evidence of the texts at length.



THE G OMA

. .. Schulten’s reconstruction of the groma (Schulten , ).

nally opposite cords at rods placed exactly in line by assistants at his
direction. If a new alignment was being established, the point vertically
below the umbilicus soli was plumbed and marked. This is by far the best
explanation of what the texts say. For geometrical precision the mark
has to be directly below the centre of the cross, and the ferramentum
therefore has to be significantly to one side. Schulten therefore recon-
structed the groma as in Fig. ., complete with bracket.

In the very year that he wrote, the metal parts of a groma were found
at Pompeii and ten years later were published by Della Corte with a
reconstruction (Fig. .) which in essence followed Schulten’s.27 There
was an iron spike for planting in the ground with a bronze bush on top
to hold a missing wooden column, a long bronze bush for the top of
the column, two small bronze bushes as pivots for each end of a missing
wooden bracket  cm long and two strips of bronze for reinforcing it,

27 Della Corte .



INST UMENTS AND METHODS

. .. The Pompeii groma as reconstructed by Della Corte
(after Della Corte , Fig. ).

and a wooden cross sheathed in iron, with arms  cm long. Until very
recently Della Corte’s reconstruction ruled the roost, being repro-
duced countless times and accepted unquestioningly as fact. Now,
however, Schiöler has cast serious doubts on its accuracy.28 He points
out that not all the components were found together (not even in the
same room) and that, with the weight of the cross, . kg, cantilevered
on a bracket from the top, a wooden column of the diameter dictated

28 Schiöler .

