Dictionary of Greek and Roman antiquities. Ed. by William Smith. Illustrated by numerous engravings on wood.

MENSURA. MENSURA. 751
aense, signifies the application of number to quan- the unit of capacity, as the unit of weight. Or
tity; or, to speak more specifically, the comparison we may take a bulk of any substance, without
of different quantities by means of the standard of measuring it, as the unit of weight. In the latter
number. So long as we regard quantity apart case it is evident that, by measuring the solid confrom number, we can only compare two quantities tent either of the unit of weight, or of an equal
by the test of coincidence, by which we ascertain weight of some other substance, we might derive
whether they are equal or unequal, and, if the from our system of weights a system of measures,
latter, which of the two is the greater; as, for in- first, of capacity, and thence of surface, and thence
stance, in the case of two lines. The next step is of linear distance; just as by the opposite process
the comparison of one magnitude with certain de- we pass from the line to the surface, thence to
finite parts, or multiples, of the other, its half or capacity, and thence to weight.
double, third or triple, and so forth. The last The statement of these elementary principles, in
step, by which we attain to a complete method of as brief a form as is consistent with clearness, has
expressing magnitude numerically, is the choice of appeared necessary, in order to the complete unsome fixed magnitude, or UNIT, with which we derstanding of the metrical systems of the Greeks
may compare all other magnitudes of the saee kind, and Romans, the explanation of which is the object
so as to ascertain what multiple, part, or parts of this article.
of the unit each of them is, if they are commen- i Oii fsue.
surable, and, if not, as nearly as we please. Thus h fi s es
the unit, in itself, or in its parts, forms a M11easure of. OLenth.-The first step in the constructio
all magnitudes of the same kind as itself. of a metrical system is obviously that of fixing upon
all magnitudes of the same kind as itself. A set
the unit of length; and nature itself suggests the
of fixed measures, one for each kind of quantity,,
of fixed measubres, ose form each kind of qantSsty choice, for this purpose, of some familiar object, of
ith their subdivisions, forms a etiE yste nearly uniform length, and which is constantly at
The notions which lie at the foundation of ma- hand to be referred to. These conditionsare ffilled
thematical and mechanical science determine of by various parts of the human body; from which
themselves the foundation of every metrical system. accordingly we find that not only tse uiit of
Those notions are Extension and Force; the former
length, but all the measures of length, except
hn its various kinds, the line, the scr/fice, the solid, those which are too smll or too large to be
those which are too small or too large to be moenand the angle;- the latter in that manifestation of 1
and te le the latter in that manifsttion of sured by parts of the body, are derived in every
it which we call sutjght. Now, since extension, metrical system, except the latest formed of all,
whether linear, superficial, or solid, can be esti- the modern French system, which is founded on the
mated by means of one straight line; or by means urement of the earth. support of t
of two straight lines which form a fixed angle withmasretoft ath Inuprtf th
one another, and wich, together with two oth general statement now made we have, besides the
one another, and which, together with two other
antecedent argument from the nature of the case,
lines drawn parallel to them, enclose a surface; or te et f r the nae of the
tetestimony of all writers, the names of the
by means of three straight lines, the planes passing n es amd the general agreement of thei
through which form a fixed solid angle, and, to-les wt the p r of theb
lengths with the parts of the body whose names
gether with three other planes drawn parallel to they bear. (Ren. It. vi. 319, xv. 678, Od. xi
them, form a solid:- -it follows that all these three 310 Vitruv. iii. 1. ~ 2-9, with Schneider's
k]inds of magnitude may be estimated nsuneiica"lly Notes; Hero, CGeos. in Anal. Graec. Paris, 1688,
by fixing upon units which are respectively a vol. i. p 30-315, 38; Diog. Lat. x. 51;
n ~~~~~~~~~vol. i. pp. 308-315, 388; Diet. Lab'rt. ix. 51;
straight line, a parallelogram having two adjacent Ukert, o.. ec.. li. vol t 2
J Ukert, Geog. d. Griech. u. It6m. vol. i. pt. 2,
sidsadaa ngle fixed, and a parallelepiped
sides aid an angle fixed, and a parahlelopiped p. 54.) The chief of such measures, with their
having three adjacent edges and an angle fixed; Greek and Roman names, are the followisg: the
or, simplifying the two latter cases by making the breadth of afilger (8dcrAsos, dcqites) or t/nsi
fixed sides equal and the fixed angles right angles, (polltx); the breadth of the hand, orpalin (?athe units are (1) a strailgt line of fixed length, Aa te, that is the distance
(2) the square of' which that straigit line is c side, from poatsos); the spun, that is, the distance
t e is a side, from the tip of the thumb to the tip of the little
mnd (3) th~e cube of' whichb that line is the edge. f
aid (3) te ce of cic/ imt line is te eg. finger, when spread out as wide as possible
Thus we obtain a metrical system for length, su:fice, (o7riau'i); the length of the fot (wons, Pes)
(aJd capacityj. A
Fo4 h eaueetofad canpacity,, orthe cubit, or distance from the elbow to the tip of
For the measurement of nlar iitc, or, the middle finger (srlXvs, cibcites); a step (P5tma,
which is the same thing, of distance reckoned along geades); a double step, or ace (posses); and the
thie circumference of a circle, one unit is su icient, distance from extremity to extremity of the outnamely, a fixed angle, which will exactly measure stretched arms (dpTmid). With reference to the
thie sum of four right angles, or a fixed are of a lst two measures, t ill be observe tht the
fixed circle, which will exactly measure the cir- i w eved tha e
Romsans derived them from the legs, the Greeks
cumference of'the circle. Th'lus we obta~in- a me1ferenee of'thcicle T seoti from the arms, the passus being one foot shorter
trical systenifor all anuar afide s,ic~dl
inical syuste for all ngluia sscagsitudcs, incluclui'g than the dpyvmd of the other, and the former (5 feet)
Againi ihepetto rc fw tetetbelonging to the decimal system, the latter (6 feet)
Again, with respect to Fosce, of which the test to the duodecimal. The higher measures of
to the duodecim-al. The higher measures of
is weieglt, since all forces may be compared, either length will be referred to presently. Cop. Poldirectly, or through the calculation of the velocities lux. 157, 158who also mentions some ess
n I~~~~~~~lx ii. 157, 1158; who also mentions some less
which they produce, with the force of gravity. iportant measures; namely, the or
There are two ways of estimating weight. Either rv tan meas or esov, which was the same as the
TrVodXoSsx7 or bmlpom,, which was the same as the
its measure may be deduced from the measure of raj the p p, or the length of t
y 7~~~~~~~~racUtffTr; the 5'pOo~opoy,, or the length of the
capacity; for, as the weight of a body depends on
tile quantity of matter in a given space, estimated' This measure was not in the Roman system.
by the effect which the force of gravity exerts upon When they wished to express the Greek span,
it, we may take the quantity of a fixed kind of the proper word was dodlras, that is, three quumatter (water for example) which will exactly fill ters (of the foot).