"i 
Scientific Intelligence. 409 
SCIENTIFIC INTELLIGENCE. 
I. Cuemistry anp Puysics. 
1. On heat as the equivalent of work.—Hopre has contributed a me- 
moir upon this most interesting and important subject which places the 
analytical theory in a remarkably clear, simple, and general point of 
view, so far at least as it relates to permanent gases. We shall give 
the author’s investigation in extenso, making however a slight change 
in the symbols employed so as to assimilate them to those usually em- 
ployed by writers on the calculus, in French or English. The tem- 
perature t of an enclosed permanent gas may be expressed as a func- 
tion of the pressure p and the volume v by the following formula which 
is a combination of the laws of Gay Lussac and Mariotte: 
ma 
p=z(+e) (1) 
In this formula m represents the mass of the gas, a any definite pres- 
Sure, that of one atmosphere for instance, 5 the density at the tempera- 
ture 0° and pressure a. If we consider the temperature to be meas- 
ured by the increments of volume of the gas itself, « will be absolutely 
constant, and Mariotte’s law will be the only fact resting upon experience. 
et + denote the quantity of heat which the mass m of the gas must 
receive from without, in order to produce any changes whatever in p, 
D hen considering p and v as independent variables and 7 as 
& function of both we can make 
d d 
dv dv’ dp dp 
The magnitudes ¢ and c’, defined in this manner, express the capacities 
for heat at a constant volume and at a eonstant pressure, and may for 
the present be regarded as constant. Substituting in these expressions 
the values of the partial differential co-efficients of t as obtained from 
(1) namely 
2 
dv maa dp ma a 
oS de! 
bbe have, ay op 3 ead hen 
dv aa dp ae 
and hence for the total differential of 
o) 
d5—=— (cpdv--c'vdp). 
If now the gas pass from one state to another so that p and » change 
according to any definite law, p, v, and # become functions of each 
ve 
and we ha 
| I= 2 (ofpivteforp). (2) 
Sscoxp Serres, Vol. XXI, No, 63—May, 1856. 
