on the Elasticity of certain Metals. 357 
D the directive force of the wire, i. e. the moment of revolution 
sie s ; ‘ 180 ; 
which it exercises for a torsion angle of —— = 57°-296. 
é the modulus of torsion of substance cosittioattinn the wire, 
we have pt pe i mK 
Di n2K  6¢ 
and (Bone sd pe = ——- mre (1) 
where g denotes the acceleration due to gravity, and « is the 
pane ne quintuple of which (according to the theory of 
Poisson, i. e. when the ratio of the transversal contraction to 
the jongitadiaat dilatation is=4) multiplied by g gives the 
Square of the velocity of sound in the substance. 
When now in consequence of a change of temperature, the 
elasticity and dimensions of the wire vary, the time of vibra- 
tion 7 changes also. If we denote the variations of », /, hi r 
and ¢, occurring for a small change of temperature, by d 
dm, drandd t, we obtain by differentiating 0) Secs aaie 
is é - i om oat 2d 
t 
But on the canpienea oe toe wire jee haces an equal dila- 
dl_dr 
tation in all directions on account of the temperature [= 
Also since m denotes the mass of the unity of length, alee 
dr 
Therefore — a 2. (2) 
The modulus of torsion ¢ is therefore without correction re- 
ciprocally proportional to the square of the time of vibration. 
The definition of the modulus of elasticity assumed here 
a basis, denotes, with regard to the spare mepe the weight which 
must be suspended to a wire, whose unity of length is the same 
as the unity of its mass, to double the length. In practice it is 
customary, though frequently less wc to e peng Aime: the 
section instead of the weight of the unity o 
case, ay above expression (1) must be eltiphea farther or 
the density of the substance, and the coefficient of the ee 
dilatation 3¢ must be subtracted from formula (2), so thai 
de wes 2dt 
t 
os 
pee a 
* m.t=(m+dm) (i+) | 
t 
dm_ di 
eee 
