402 : Scientific Intelligence. 
author separated these and employed them for various experiments on 
polarization, double refraction and dispersion, which he promises to de- 
i —Pogg. Ann. xeviii, 353, June, 1856 
connection between the theorem of the equivalence of heat and 
work and the relations of permanent gases—Cuavsius has published 
some critical remarks upon the paper of Hoppe which has been noticed 
in this Journal,* his object being mainly to shew that he himself had 
considered the subject from a different point of view and had arrived at 
essentially the same results as Hoppe. In a memoir “On a change im 
the form of the second principal theorem of the mechanical theory of 
heat,” Clausius deduced the equation 
(1) Q=—U+ A.W, 
in which Q denotes the heat communicated to a body during any cha 
of state, W the external work performed, A the equivalent of heat for the 
unit of work, and U a quantity of which it may be assumed that it is 
perfectly determined by the initial and terminal state of the body. Th 
: J : 
may be considered as a function of these two quantities. When the ex- 
ternal work consists only in overcoming a pressure p which opposes the 
expansion, we have 
w= a8 p dv, 
and we obtain from the previous equation by differentiation, 
dU dM 
(2) aQ=F dt (T+ 4-7) de. : 
In applying this equation to the more special case of a permanent gas we 
may express the ory of dt and dv in another manner. The first of 
these two factors ae. is evidently nothing but the specific heat at a con- 
stant volume, and we write for it c. To express the second factor, the 
— heat at a constant pressure, c’ must be introduced. According to 
é laws of Gay Lussac and Mariotte, we haye 
Be iu. 
P ve i. (a+), 
in which a represents the inverse volume of th i ion. 
Picea Sie th of the coefficient of ce sae 
dy = Po:*o_ gy 
as ; (4-+1,)p 
Substituting this value for dv we have 
* 
a & ee OPET, 
aq=[F, + Cate (2 
; ¢ dt + (4+1,)p dv + AP )] sia 
The sum in the parenthesis [ ] represents the quantity ¢’, and if we sub- a 
tract from it the quantity c= a we have 
* Vol. xxi, p. 409. 
