The Plan of St. Gall :: :: University of Virginia Library

Reinle believes he has discovered that the Plan of St. Gall
was drawn at a scale of 1:200.[345] He is not the first to
advance this view. Wilhelm Rave had expressed himself
along similar lines in 1956,[346]
and Emil Reisser likewise, in a
study published posthumously in 1960.[347]

The Plan is, indeed, drawn to a scale that comes close to
what we would define today as a ratio of 1:200. But it is one
thing to observe that the Plan was drawn at a scale that
corresponds or comes close to the ratio of 1:200; it is quite
another to claim that it was actually drawn at that scale. In
proposing this view, Reinle is caught in an anachronism.
The concept 1:200 is not a medieval concept and does not
make sense within the medieval system of mensuration. If a
modern architectural drawing is said to be laid out at a
scale of 1:200, this means that one unit on the drawing
corresponds to 200 identical units on the ground. The base
of this ratio is decimal. A medieval architect could not have
expressed himself in these terms, since the two basic units
of measurement with which he worked, the foot and the
inch, were internally divided not into tenths, but into
twelfths and sixteenths (a system that still persists in
England and the larger Anglo-Saxon world) or into
twelfths and twelfths (the pied royal de France, which was
used in France until the introduction of the metric system).[348]

The foot and its primary subdivision, the inch, were
derived from the human body.[349] Twelve thumb-breadths
of a fully grown man equal the length of his foot (fig. 57).
This is the raison d'être for the twelve units of the English
foot. The French word pouce, the Old French poulcée, the
Latin pollex—all meaning "thumb"—reflect the history of
the genesis of this measure. Like the English foot, the
Latin foot consisted of twelve units[350] "Inch," Anglo-Saxon
ynce, comes from Latin uncia = "a twelfth"; and
the duodecimal graduation of the Roman foot is reflected
in the series: uncia = 1/12;

sextans	= 2/12 or ⅙
quadrans	= 3/12 or ¼
triens	= 4/12 or ⅓
quincunx	= 5/12
semipes	= 6/12 or ½
septunx	= 7/12
bes	= 8/12 or ⅔
dodrans	= 9/12 or ¾
dextans	= 10/12 or ⅙
deunx	= 11/12

[ILLUSTRATION]

62. PLAN OF ST GALL: SHOWING 40 FOOT MODULE SUPERIMPOSED UPON
THE ENTIRE SITE OF THE MONASTERY

The human body does not offer reliable guidance for
divisions smaller than the breadth of a thumb. These
smaller units could only be obtained by instrumental
operations, and the simplest, easiest, and for that reason,
probably the oldest, way of graduating a distance into a
sequence of consistently decreasing smaller units is the
method of continuous halving—a procedure by means of
which a whole is reduced to a half, a half to a quarter, a
quarter to an eighth, and eighth to a sixteenth (fig. 58).[351]
This is the procedure that created the sixteen graduations
of the English inch.[352]

We know nothing about the internal divisions of the
Carolingian inch, but whether it was graduated into twelfths
or into sixteenths, this much is certain: there was no
common decimal denominator between a Carolingian inch
and a Carolingian foot that could be expressed in the ratio
1:200.

The modern metric scale is based on a comparison of
parts of like nature, all of which can be understood either
as fractions or as multiples of ten. The medieval scale has
no such common unit of reference. It is a combination of a
variety of different forms of graduation (sedecimal, duo-

1. Corporibus. Scilicet non solum de temporibus.
2. Miliarium. Id sunt mille passus. Legua enim ·I· D· passus.
3. Stadium. Id est ·CXXV· passus. Stadium octava pars miliarii est.
4. Iugerum. ·XLVIII· passus. Iugerum est quod possunt duo boves in una
die arare, id est iornalis.
5. Perticam. Decem pedes . . .
6. Dimidium. Id est medietas.
7. Semis. Scilicet non solum appellatur medietas librae semis, sed etiam
medietas cubiti et ideo dixit in corporibus.
8. Semis. Scilicet ubi semis ponitur, non ponitur et coniunctio.
9. Semissem. Id est dimidium. Accusativus a semis.

"Bede had asserted that the traditional measures had to be adapted to
duodecimals. But the Metz glossator, in introducing these definitions,
gratuitously introduced other schemes of fractions. Granted (2) that a
mile is a thousand paces, a league is 3/2 thousand. A stade (3) is 125
paces, an eighth of a mile. An acre (4) is 48 paces, a rod (5) ten paces. At
this stage of the pattern, medietas (6), the mid-point, becomes a congenial
concept for one half, not only for the semi-pound (7) but for the semicubit,
`and therefore it is used in measuring bodies,' a usage justified
for Bede by no lesser an authority than Moses (Exodus xxv.10) who used
dimidium and semissem in the same sentence interchangably. Hence it
seems that the Metz glossator found it easy, with his mind centered on
the building measurements of Noah's and Moses' arks, to introduce a
scheme of fractions quite at odds with the duodecimalism he was teaching
as the determining ratio of weights and measures."

[ILLUSTRATION]

63. PLAN OF ST. GALL: ONE LINE OF A GRID, 160 FOOT MODULE, FIXED THE CHURCH AXIS

decimal, and decimal), whose relation to one another cannot
be expressed in the terms of a decimal sequence.

It would be correct to say that the Plan of St. Gall is
drawn to a scale in which one sixteenth of a Carolingian
inch on the drawing corresponds to one Carolingian foot
on the ground. To convert this scale into a relationship in
which the ratio is expressed in the form of like units
requires that the base value of one sixteenth of an inch be
multiplied first by 16 (the sixteen parts of the inch) and then
by 12 (the twelve parts of the foot): 16 × 12 = 192,[353] the
number of sixteenths of an inch in a foot. The ratio 1:192
is not far from the ratio 1:200, but it is not identical with it
and should, under no circumstances, be confused with it.[354]
In medieval mensuration the scale relationship 1:200 not
only did not exist, it would have been meaningless.[355] This
fact by itself precludes that the axial title of the Church
could have meant what Reinle purports it to mean, and
thus we are taken back to Boeckelmann's interpretation as
the most reasonable explanation of the dimensional incongruities
of the Plan.

[345]

Reinle, op. cit., 93 and 98.

[346]

Rave, 1956, 47: "Die Planung des Baumeisters ist geradeso wie
noch meistens unsere heutigen Vorentwürfe im Masstab 1:200 aufgetragen."

[347]

Reisser, 1960, 53 and 80.

[348]

For general information see the articles "Weights and Measures"
in Encyclopedia Britannica, and "Poids et Mesures" in Grande Encyclopédie,
XXVI, Paris, n.d., 1184-96, as well as the literature there cited.

[349]

Vitruvius, De Architectura, Book 3, chap. 1.5 expresses himself on
this issue as follows: "Mensurarum rationes . . . ex corporis membris
collegerunt, uti digitum, palmum, pedem, cubitum" (see Vitruvius, On
Architecture, ed. Granger, I, 1931, 160ff).

[350]

With regard to the Roman foot, see Jacono, 1935, 167-68; for a
fuller account see Hultsch, 1862, 59ff; 1882, 74ff. Of great importance
for the medieval history of the inch is Bede's chapter "De ratione
unciarum" in his De temporum ratione, chap. 4, which Charles W.
Jones brought to my attention. See Bedae opera de temporibus, ed. Jones,
1943, 184-85.

The smallest unit of measure derived from the human body is not the
inch (uncia) but the digit (digitus), the breadth of a finger. It formed the
base of the Italic foot (equivalent to 11.66 modern English inches) which
had sixteen digits. Four digits formed a hand (palmus) and four hands
formed a foot (pes). See Hultsch, loc. cit.

[351]

Cf. Perry, 1955, 80.

[352]

The tenacious survival in the modern Anglo-Saxon world of the
sedecimal graduation of the inch appears to suggest that this was also the
traditional way of subdividing the inches in medieval England. Yet this
is not born out by a reading of chapter 4 of Bede's De temporum ratione
(used as a standard text without rival in Carolingian times), as Charles W.
Jones brings to my attention. Here the inch is defined as being divided
into twelve and even twenty-four parts, a division retained in all of the
Carolingian glosses to this treatise, of which more than forty sets have
been examined by Jones (see Bedae opera de temporibus, ed. Jones, 1943,
loc. cit.). An analysis of Bede and other related texts may in fact suggest
a dichotomy in the approach to duodecimal and sedecimal systems,
between the theoreticians and the practitioners of measures and weights.
Charles W. Jones, in a personal letter, addresses himself to this subject
as follows:

"Bede (A.D. 725) treated weights and measures, primarily the divisions
of pound (libra) and ounce (uncia), in his classroom textbook, De temporum
ratione, chap. iv (Clavis patrum latinorum, n. 2320; see also Pat. Lat. XC,
cols. 699-702). Therein he recognized no other fractional principle than
duodecimalism, despite his addiction as an exegete to the concept of ten,
its square, and cube. He positively states that duodecimals are used not
only for weights (including numismetrics) but also for times (months,
hours, points, moments) and for lines, planes, and volumes of bodies
(Jones, 1943, 184.2-3; 185.26-28, 44-49).

"I have examined about twenty different sets of glosses for that
chapter, but only the following sets contain remarks pertinent to this
topic: Berlin MS 130, written A.D. 873 at Metz; Munich MS 18158, an
eleventh-century copy from Tegernsee of a ninth-century text; 21557, an
adaptation of 18158; Valenciennes MS 174, written about A.D. 840 at
Saint-Amand (duplicated in Brussels MS 9837-9840, saec. xii/xiii);
Vatican MS Rossi lat. 247, copied in the Loire region [Fleury?] about
A.D. 1018 from an exemplar of ca. 820. (The complete set of glosses from
the Berlin MS will be published in the forthcoming Corpus Christianorum
edition of Bede's Opera didascalica.) Bede's was the basic text on
the subject in Carolingian schools: about 150 codexes containing that
chapter are extant today. The masters seem to have disregarded Isidore's
treatment, Etymologiarum liber XVI, xxv-xvii, although it was in common
circulation. But they do quote Priscian's De figuris numerorum liber ii,
9-iii, 16 (ed. H. Keil, Grammatici Latini III, Leipzig, 1859, pp. 407-11),
sometimes verbatim and several times by name. Priscian dealt with
both decimals and duodecimals, but the glossators quite obviously tried
to eliminate decimalism by recasting his statements. Nor, with one
exception which I will mention, did these glossators introduce any
suggestion of sedecimalism.

"In short, the scholastic evidence points exclusively to duodecimal
measures in Carolingian as in early-English times.

"Such proof by silence might seem to refute use of sedecimals, but we
know that medieval scholasticism often was remote from practice. An
analogue is the void between Boethian and Gregorian music. I agree with
you that a master builder, with rod and plumbline, would be apt to
think in multiples of halves. The Metz glossator (Berlin MS) seems to
lend some support to this surmise. Bede had stated; Item decorporibus,
sive miliarium, sive, stadium, sive iugerum, sive perticam, sive etiam cubitum,
pedemve aut palmun partiri opus habes, praefata ratione facies. Denique et
in Exodo dimidium cubiti semis appellatur, narrante Moyse, quod habuerit
arca testamenti duos semis cubitos longitudinis, et cubitum ac semissem
altitudinis. ("Also you hold to the same fractions in measuring bodies,
whether miles, or stades, or acres, or rods, or even cubits, feet, or hands,
whenever you need to divide. In fact, in Exodus a half cubit is called a
`semis,' because, according to the statement of Moses, the Ark of the
Testament was two and a half cubits in length and a cubit and a half in
height.") The Metz glossator writes:

[353]

That the Plan of St. Gall was drawn to a scale of 1/16″:1′ was first
expressed by me in the French edition of the catalogue to the Council of
Europe exhibition dedicated to Charlemagne: "Le plan est entièrement
dessiné d'après une échelle, ou le 1/16e d'un pouce sur le parchemin
représente un pied sur le terrain. Converti en une relation d'unités
egales, cela signifie 1:192 (1/16 × 16 × 12 = 192/16), rapport de grandeur
qui approche l'échelle métrique du 1:200, mais qu'il ne faut aucunement
confondre avec celle-ci; puisque la relation 1:200 n'existait pas dans le
système métrologique médieval, où le pied est divisé en 12 pouces, et le
pouce en seize seizièmes" (see Charlemagne, oeuvre, rayonnement et
survivances [Dixième Exposition sous les Auspices du Conseil de
l'Europe], ed. Wolfgang Braunfels, Aix-la-Chapelle, 1965, 399).

[354]

I am delighted to find that in an article that became available to me
only after the present study was completed, Konrad Hecht had independently
come to the same conclusion: "Der Masstab 1:200 ist für einen
mittelalterlichen Plan zwar plausibel, aber doch irrig, denn dieser Masstab
setzt die dezimale Teilung des Fussmasses voraus. . . . Der St. Galler
Plan wurde nicht im Masstab 1:200, sondern im Masstab 1/16″:1′ entsprechend
1:192 gezeichnet" (Hecht, 1965, 187-88).

[355]

The figure 200 is not a natural break in a system that is based on
fractions of 12 and 16. It acquired meaning only after the adoption of the
metric system—a system of consistently graduated units of like dimension
which departed so radically from the chaotic, but deeply ingrained,
forms of mensuration which it supplanted that it could have been
inaugurated only under the auspices of a political revolution and enforced
by the mandate of an ensuing dictatorship. For a brief résumé of the
adoption of the metric system, see Arthur E. Kennelly, 1928, 12-27; for
a comprehensive, detailed account of the establishment and propagation
of the metric system and the operations that determined the meter and
the kilogram, see Favre, 1931 and Bigourdan, 1901.

University of Virginia Library

ANACHRONISM IN MENSURATION

62. PLAN OF ST GALL: SHOWING 40 FOOT MODULE SUPERIMPOSED UPON THE ENTIRE SITE OF THE MONASTERY

63. PLAN OF ST. GALL: ONE LINE OF A GRID, 160 FOOT MODULE, FIXED THE CHURCH AXIS

62. PLAN OF ST GALL: SHOWING 40 FOOT MODULE SUPERIMPOSED UPON
THE ENTIRE SITE OF THE MONASTERY