DYNAMICAL THEORY OF HEAT. 283 
(17), 
where « will be the reciprocal of the compressibility, and ¢ the coefficient of ex- 
pansion with heat. 
Equations (14), (16), and (3), thus become 
2s SP Reed 
ie Gh), ee: 
2 
K—N=o%F (19), 
Mai Ke : : : : ; : : (20) ; 
the third of these equations being annexed to shew explicitly the quantity of 
heat developed by the compression of the substance kept at a constant tempera- 
ture. Lastly, if 6 denote the rise in temperature produced by a compression from 
0+dv to v, before any heat is emitted, we have 
TaN ee arse een Se ene 8 
50. The first of these expressions for 6 shews that, when the substance con- 
tracts as its temperature rises (as is the case, for instance, with water between 
_ its freezing point and its point of maximum density), its temperature would 
become lowered by a sudden compression. The second, which shews, in terms of 
its compressibility and expansibility, exactly how much the temperature of any 

substance is altered by an infinitely small alteration of its volume, leads to the 
approximate expression 
yp Ke 
Oak 
_ if, as is probably the case for all known solids and liquids, ¢ be so small that 
_ @. «Ke is very small compared with wK. 
51. If, now, we suppose the substance to be a gas, and introduce the hypo- 
_ thesis that its density is strictly subject to the “gaseous laws,” we should have, 
_ by Boye and Mariorrte’s law of compression, . 
dp_ p 
ieee A : 5 : : C (22); 
_ and by Darton and Gay Lussac’s law of expansion, 
dv Ev 
qt = 1482 : : ; } (23) ; 
— from which we deduce 
dp Ep 
