128 
CAPTAIN NOBLE AND MR. E. A. ABEL ON EIRED GUNPOWDER. 
heat, during their expansion, from the non-gaseous portions in a very finely divided 
state ? 
To solve this question we must have recourse to certain well-known principles of 
thermodynamics. 
Let <7H be the quantity of heat added to, or drawn from, the non-gaseous portion of 
the charge by the permanent gases, while the latter pass from the volume v' and tempe- 
rature t to the volume v'-\- dd and temperature we then have* 
dH=t . d<p, (22) 
<p being Rankine’s thermodynamic function. 
But if X be the specific heat of the non-gaseous portion of the charge, and if /3 be the 
ratio between the weights of the gaseous and non-gaseous portions of the charge, and if 
we assume further, as we can do without material error, that X is constant, we shall have 
dH=-f3xdt; (23) 
.-.d<p=-t&j, (24) 
and by integration 
<P— <P.=log (25) 
But the value of <p—(p 0 for permanent gases is well known, being readily deduced from 
the general expression for the thermodynamic function. 
This expression being f 
?=Clog.i+lJ|.*' (26) 
(J being Joule's equivalent), and ^ being readily obtained from the equation of elasti- 
city and dilatability of perfect gases, 
_pv'=Ut, 
we deduce from (26), by integration, 
?-? 0 =log.({) C '. (£)' 
since J j=C p —C v . 
Hence, equating (25) and (27), 
* Rankine, ‘ Steam-Engine,’ p. 310. De Saint-Robeet, loe . tit . p. 68. 
t Raneine, loc . tit . p. 311. De Saint-Robert, loc . tit . p. 72. 
J Raekine, loc . tit . p. 318. Claesitjs, loc . tit . p. 39. De Saint-Robert, loc . tit . p. 93. 
