on the Elasticity of certain Metals. 365 
The modulus of torsion T is derived from these data by 
means of the formula, p. 
mK 
TSG mar 
It is found to be 
for iron =444 kilometers. 
“ copper==217 a 
“ brass —190 i= 
. kilogrammes 
for iron, 3470 pe ASS eyeeeny 
“ copper, 1950 "8 
“ brass, 1600 % 
wire of the same species : 
double the original length), is obtained from the velocity of 
sound e by means of the formula A=—, where g denotes the 
acceleration due to gravity. The value A’ ordinarily employed 
in practice, and made use of by Wertheim, (i ¢., the weight 
which hung on a wire whose section is unity would double the 
length), is obtained as above by multiplication with the density. 
Thus it was found 
Velocity of sound. . Modulus of elasticity. ~ 
Tron, 5050 meters, 2580 kilometers. 20310 Bay 
Copper, 3640 1350 : 12140 9 
Brass, 3380. 1170 9810 
Wertheim gives A’ for iron wire =19445, copper =12536, 
rass =9000 5h a 
According to these observations, the moduli of torsion bear 
to the moduli of dilatation, for all three wires very nearly the 
Same ratio. The ratio fod is 
+ 
for iron, 5°85 
ene, . 9x8 
6 8, 6°15 
