Prof. Thomson on the Dynamical Theory of Heat. 171 



an expression for the difference between the two specific heats, 

 derived Avithout hypothesis from the second fundamental prin- 

 ciple of the theoiy of the motive power of heat. 



49. These results may be put into forms more convenient for 

 use, in applications to liquid and solid, media, by introducing 

 the notation : — 



/;> m 



e = ^f I 

 Kat J 



where k will be the reciprocal of the compressibility, and e the 

 coefficient of expansion with heat. 

 Equations (14), (16) and (3), thus become 



4-) 



</N \fJb / KB 



dv dt J ' " ' 

 K-N = t;— (19), 



M=-./ce (20); 



the third of these equations being annexed to show explicitly the 

 quantity of heat developed by the compression of the substance 

 kept at a constant temperature. Lastly, if 6 denote the rise in 

 temperature produced by a compression from v + dv to v before 

 any heat is emitted, we have 



50. The first of these expressions for 6 shows that, when the 

 substance contracts 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 

 siidden compi'ession. The second, which shows in terms of its 

 compressibility and expansibility exactly how much the tempe- 

 rature of any substance is altered by an infinitely small alteration 

 of its volume, leaui to the approximate expression 



if, as is probably the case, for all known solids and liquids, e be 

 so small that e . vks is very small compared with /iK. 



51. If, now, we suppose the substance to be a gas, and introduce 



