A10 Scientific Intelligence. 
If z, denote the initial temperature then from the equation (1) we 
ri} 
have di=——(pdv--vdp), 
and if we integrate between the same limits as those to which @ is re- 
ferred and multiply by me! we have 
O 
me' (r=) =e /pado+ vdp), (3) 
which subtracted from equation (2) gives 
3 
F—me(r-1)=—(e-e)q (4) 
where g=/ pdv expresses the work done in the change of state. The 
result is therefore as follows. ‘The quantity of heat communicated 
to a gas during any change of volume and pressure consists of two 
parts, one of which expresses the heat necessary to raise the tempera- 
ture at a constant volume, while the other is a constant-multiple of the 
work done.” In particular we infer that this quantity of heat is in 
itself proportional to the work as soon as the initial temperature Is re- 
gained, while the pressure and volume may have other values; as pure 
oss of heat it appears, it is true, only after a complete restoration of 
the original condition. 
Let us now suppose that neither Mariotte’s law nor the law of the 
invariability of the capacities is accurately true. If c and c’ are sub- 
ject to any small changes in consequence of changes of pressure oF 
temperature, we may consider them as functions of p and v and wnite 
equations (2) and (3) as follows: 
_¢O 
5=— ( ve epdv+ fc vdp) 
6 
nf car —( c'pdv--f c'vdp) 
whence by subtraction, 
| 5 
— t —— oc! é 
oo nfe a Sie c')pdv 
Variation in the capacities. . 
the gas be restored to its original volume so that at any time #e° 
must change its sign, the proportional number is no longer necessarily 
