330 M. Poisson on the Caloric of Gases and Vapours. 



y being an arbitrary function. From this we obtain 



p=: p''(pq, 

 and because of equation (1) 



1+ « 3 = «?'-/<? 5'; 



^ being another function. The quantity g remaining the same, 

 ifp, g, and fl become p\ g', and I', we shall have 



/ = §' fl^ 1 + a 6' = i g'*-' (p q. ■ 

 Eliminating d^ q and observing that^ = 266°"67 there result 



fl' = (266°-67 + fl). (-^j -266°-67 I 



These equations (5) comprehend the laws of elasticity and 

 temperature of gases, compressed or dilated without changing 

 their quantity of caloric ; such as would take place if the gases 

 were contamed in vessels imperviable to caloric*; or when 

 the compression is so rapid, as in the phaenomenon of sound, 

 that we may suppose the loss of heat quite insensible. In ig- 

 nition {Dans le briquet a air) for example with air, if the vo- 

 lume is suddenly reduced to a fifth, or if we have g' =: 5 g, 

 we find by the preceding value of k 



6' — fl = 221°+ -83 6; 

 in which it is plain that the augmentation of temperature will 

 be the greater the higher the original temperature 9. For when 

 fl = we have 9' = 221°, a temperature which philosophers 

 think sufficient to ignite tinder [V amadou) in compressed air. 



Eliminating g in equation (4), by means of equation (1), 

 we have ^r \~^,, ■ b\'l 



In order to determine the arbitrary function^ we have need 

 of a new hypothesis. M. Laplace's hypothesis in the 12th 

 book of the Mecanique Celeste consists in assuming that the 

 increments of caloric follow the same ratio as those of the 

 temperature, which requires that the function y should be of 

 the first degree with respect to the variable it contains ; from 



which it results that, since a = _ , 



9= A 4-B(266-67 + 6)jo'^~; (6) 



A and B being two arbitrary constants. Whence the specific 



heats are ■„ \-'^ i -r, f -^ 



c= Bp* , c^ = jBp * 



They do not therefore depend on the temperature S, but are 



* Such cases I think could never under any circumstances whatever be 

 subjected to experimental examination. — J. H. 



known 



