430 
In weighing the fulerum was shifted from 
place to place, and there were notches for the 
suspending cord, determined, no doubt, with 
known weights, these having been calibrated 
with the balance. This Danish steelyard, 
desemer or bismar had, then, a graduated beam 
whose graduations followed no observable law 
and were wholly empirical. It is this that 
Aristotle discusses in his ‘‘ Mechanical Prob- 
lems,” though without much success. 
The Roman steelyard, “Statera Romana,” 
familiar in modern form and but little im- 
proved since classical antiquity, appeared first 
perhaps in Egypt, perhaps in Campania. I 
ean only quote authorities. 
F. Miller :* 
B.C. 1350. The steelyard with running weight 
is In use among the Egyptians. 
L. Darmstaedter :5 
B.C. 1400. The steelyard with running weight 
is in use at the time of the Egyptian king 
Amenophis IV. 
F. M. Feldhaus :* 
Unequal armed balance with running weight, 
usually called Roman steelyard. This balance has 
a short arm, on which the weighing pan hangs, 
and a long arm, bearing a graduation and notches 
for suspending a running weight. The steelyard 
is known to have been in use in Egypt about B.c. 
1400. 
Against these very definite statements must 
be set the authority of Sir J. G. Wilkinson’ 
and of Dr. L. W. King and Flinders Petrie,® 
and of all others, as far as I know, who have 
published on the subject or answered my in- 
quiries about it, to the effect that the Egyp- 
tians did not have the steelyard till the Roman 
period. Harper’s “Book of Facts” (1905) 
says that it is mentioned B.c. 8315—I do not 
know by whom. 
Incidentally, I may say that I was not a 
4‘‘Zeittafeln zur Geschichte der Mathematik,’’ 
ete., p. 3 (1892). 
5‘‘Handbuch zur Geschichte der Naturwissen- 
schaften,’’ ete., p. 3 (1908). 
6‘‘Die Technik,’’? p. 1251 (1914). 
7‘<Manners and Customs of the Ancient Egyp- 
tians’? (1878). 
8 Quoted by H. L. Roth, 7. ¢. 
SCIENCE 
[N. 8S. Von. XLVIII. No. 1244 
little surprised to find this contradiction, and 
that so well known an instrument of trade 
should have so uncertain an origin. 
I will assume that the Roman steelyard 
dates back to B.c. 400, and was then known 
through Mediterranean civilization. He who 
first graduated it may be called the true dis- 
eoverer of the law of moment equilibrium, 
the law of the lever. With any pry or crow- 
bar, or with the bismar, one would have to 
search for the law deliberately; but this im- 
proved weighing apparatus made for trade 
purposes displays its law to the eye. I im- 
agine the inventor as using a bismar beam, 
but keeping the fulcrum fixed and sliding 
along a rider weight, calibrating the beam by 
means of known balance weights in the pan. 
The unaided eye could see that equal added 
weights in the pan corresponded to equal in- 
erements of length on the graduation; and so 
we may understand how Aristotle (B.c. 384- 
322), long before Archimedes (8.c. 287-212), 
was able to state the law thus’® ... as the 
weight moved is to the weight moving it, so, 
inversely, is the length of the arm bearing the 
weight to the length of the arm nearer the 
power....” This he attempts to demonstrate 
as a consequence of the properties of the circle, 
but with poor success. 
Archimedes, knowing this law of the lever, 
wrote a book on the subject, unfortunately 
lost. Another book of his has come down to 
us, in which he discusses the subject of bal- 
anced bodies and the location of centers of 
gravity in certain plane figures. He does not 
define center of gravity, but from the use he 
makes of the term in his demonstrations it is 
clear that he means by it the point where a 
body balances when there suspended. This 
point he treats as representative of the body, 
and assuming this he attempts a demonstration 
of the law of the straight horizontal lever, or 
law of moment equilibrium. E. Mach? points 
out, however, that this demonstration, super- 
ficially convincing, is seen to be fallacious 
9 ““Questiones Mechanice,’’ E. S. Forster, trans. 
(1913). 
10 Science of Mechanics,’? McCormack trans., 
p. 18 (1902). 
