366 Mr. Herapath on True Temperature, and the [Nov. 



temperatures were first equal will equally diminish their temper- 

 atures, if no extraneous temperature interfere. 



Were the two portions similarly exposed at an equal depth, 

 the proposition would coincide with the preceding, and the 

 evaporations would be as the surfaces ; that is, as the quantities 

 of the fluid ; and the temperatures being once equal will always 

 be equal. The converse case under these circumstances is 

 evident. 



Again : because the fluids are the same, the decomposition in 

 each particle at a given temperature is the same, and hence 

 equally affects the temperature of that particle, or an equal por- 

 tion of particles. Therefore if the decomposition or evaporation 

 of p particles produce on a certain quantity Q of the fluid, a 

 given diminution of temperature, the decomposition of n p par- 

 ticles or n times that number will produce the same diminution on 

 n Q, or n times the former quantity of the fluid. That is, the 

 original and resulting temperatures of the fluid being equal, the 

 quantities evaporated will have the same ratio as the portions 

 of the fluid from which the evaporations are made, provided 

 nothing extraneous affects the temperatures. 



And since equal diminutions of temperature are accompanied 

 with evaporations proportional to the quantities of the fluid, it 

 follows conversely, that evaporations proportional to the quanti- 

 ties of the fluid produce equal diminutions of temperature. 



Co/'.— Hence if the decomposition be similar in each particle, 

 the loss of temperature arising from it will be proportional, and, 

 therefore, by knowing the diminution of temperature due to the 

 decomposition of any quantity of the fluid, which we shall here- 

 after show how to compute, and by knowing the deficiency of 

 weight in the fluid, we may easily determine the loss of temper- 

 ature arising from the evaporation ; and hence also the loss or 

 acquisition due to any other cause we wish to examine. 



Scholium. 



Philosophers, by some means, seem very much to have neg- 

 lected, if not to have entirely overlooked this theorem. Having 

 made their experiments in cases where the temperature of the 

 atmosphere or other circumstances have overbalanced the 

 influence of the inequality of depth, they have found that the 

 exposed area has by far the greater influence, and hence have 

 considered the depth and quantity of the fluid as having little or 

 nothing to do with the evaporation. Thus, to give a familiar 

 example, which has often been submitted to calculation as a 

 proof that the quantity of evaporated water is proportional to the 

 exposed surface, let us take two vessels filled with water, of the 

 temperature of the atmosphere, the one deep, and the other 

 shallow ; but both having equal mouths. Then if they are both 

 equally exposed to the atmosphere, the quantities of water eva- 

 porated ia any given time will be very nearly the same in each, 



