482 M. R. Pictet on the Application of the Mechanical 

 thence derive the following principal relation, 



10333(274+*)* (g) _ [x-^-Q]E(V-Q. 



1-2938x274 



274 + t 



(III.) 



Deriving from this equation the value of \—c(t' — t), we get, 

 as the general formula corresponding to our hypothesis, 



10333(274 + 21 (y) 

 X-<*'-0 = X-2938E x 274(^-0' ' ^ V 



If our hypothesis is correct, if it answers to the physical 

 conditions of the problem, it will prove true for all liquids and 

 at all temperatures. We must take any liquid whatever, select 

 arbitrarily two temperatures t and t' , seek in M. Regnault's 

 Tables the pressures P and P / corresponding to the tempera- 

 tures t and tf, and ascertain if equation IV. is constantly ac- 

 curate. If the results do not confirm our previsions, it is 

 because the hypothesis is ill-founded and Carnot's cycle doe's 

 not apply to volatile liquids. 



We w r ill take water for example, which w T as so carefully 

 studied by M. Pegnault, and verity the equation for the tem- 

 peratures £ = 100° and *' = 110°. The constants are P = 760, 



F = 1075-37, S = 0-625, c= 1, E =433*5, ^ = 1-41496. 



\—c(t'—t) = 



10333(374) 2 Z(1-41496) 

 1-293 x 0-625 x 433-5 x 10 x 274 



Here is the calculation in extenso as an example of a parti- 

 cular case : — 



Log 1-41496 = 0-1507400. 



Log 0-1507400 =1-1782285 



- =0-3622157 

 m 



Log 



1-293 = 0-1115985! 

 0-625 = 1-7958800 

 433-5 =2-6369891 



10333 

 374 

 id. 



= 4-0142264 

 = 2-5728716 

 = 2-5728716 



274 

 10 



= 2-4377506 

 = 1-0000000 



5-9822182 



Log numerator... 8*7004138 

 Log denominator 5-9822182 



2-7181956 log 522-63. 



And we have X-10 = 522'63, whence X = 532*63. 



Looking into the Tables of M. Eegnault, we find that, fol 

 the temperature of 100°, X is equal to 536 calories. The dif 



