the Heat extricated from Air by Condensation. 155 



temperatures and densities. Let us see how it stands the fore- 

 going test, of computing the rise of temperature due to a qua- 

 druple condensation, by a single operation, and by two separate 

 operations. At one operation, we have, putting § = 4, and 



T = 32°F., ando = ^ 



a S e, 



Again, with ^~% we obtain i = 90°. Adding this to 32° 

 makes the initial temperature t= 122°, and the formula, with 

 ^ again = 2, becomes 106°. 875 for the second value of i. Hence 

 the whole rise, computed at two operations, is 90° + 106°.875 

 z= 196°.875, which exceeds 135°j the rise at one operation, by 

 the enormous quantity of 61°. 875. 



A similar inconsistency will come out in whatever way we 

 vary the trial, and whether we use rarefactions or condensa- 

 tions. But I shall now apply a more obvious test. 



In the case just considered, air at the freezing point, or 32° 

 P., had that temperature raised 90°, or to 122°, by having its 

 density doubled. Now it is clear, that, if the new law were cor- 

 rect, the same air, by having its acquired density halved, should 

 just have its temperature lowered 90°, or from 122° to 32° F., 

 being in every respect restored to its original condition. But 

 if, in the above formula, representing the new law of conden- 

 sation, we put T = 122°, a — — — , and § == 4, the depression of 



temperature is no less than 213°. 75 ; and, consequently, the re- 

 sulting temperature, in place of 32°, is 122°— 213°.75 = ~-91°.75 

 F. ; giving the monstrmis error of 123°.75, just double of that 

 in the former example. 



On the other hand, w4ien the formula representing the old 

 law of condensation is tri-ed by the same test, not the slightest 

 inconsistency can be detected ; because this is founded in fact, 

 but the new law in fancy. 



It would be no difficult matter to apply both of these tests in 

 a general way, by means of symbols ; but the above proof, I 

 presume, will be deemed quite conclusive, and will be more ob- 

 vious to a greater proportion of readers. 



