402 



Scientific Intelligence. 



author separated these and employed them for various experiments on 

 polarization, double refraction and dispersion, which he promises to de- 

 scribe hereafter. — Pogg. Ann. xcviii, 353, June, 1856. 



2. On the connection between the theorem of the equivalence of heat and 

 work and the relations of permanent gases. — Clausius 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 in 

 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 change 

 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. In 

 the present notice the author deduces the results of Hoppe from this 

 equation in the following simple manner. For the special case in which 

 the state of the body is given by its temperature t and its volume v, U 

 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 



dv. 



W— J*p 



and we obtain from the previous equation by differentiation, 



7 ^ dU ■ IdM \ , 



(2) i Q=- dt + (— + A. P )4», 



In applying this equation to the more special case of a permanent gas we 

 may express the factors of dt and dv in another manner. The first of 



these two factors —j— is evidently nothing but the specific heat at a con- 

 stant volume, and we write for it c. To express the second factor, the 

 specific heat at a constant pressure, c' must be introduced. According to 

 the laws of Gay Lussac and Mariotte, we have 



in which a represents the inverse volume of the coefficient of expansion. 

 Hence we have 



dv= *°' V \ dt. 

 Substituting this value for dv we have 



idt T (a+t 0 )p\dv ~ * J] 

 The sum in the parenthesis [ ] represents the quantity c', and if we sub- 

 tract from it the quantity c — < ^ we have 



* Vol. xu, p. 409. 



