1824.] Mr. Herapath on the Theory of Evaporation. 351 



us with the fact, whether this decomposition takes place at the 

 mathematical surface, or at a very small distance beneath ; nor 

 can we from theory alone decide whether the vapour and its fluid 

 have a common temperature, or even nearly so, before the former 

 quits the latter. The well-known fact that the vapour freely 

 ascending from boiling water is, near the surface of the water, 

 not at the very reduced temperature to which the decomposition 

 alone would have brought it, but at the temperature of the 

 water, tends certainly to favour this idea. Hence if it be assumed 

 that every portion of vapour when it quits the water has the 

 same temperature as the remaining water; and if w be the quan- 

 tity of water, t its temperature, and dw the momentary evapora- 

 tion, we shall have by Cor. 1, Prop. 20, Annals for Dec. 1821, 



— g-^- for the number of vaporous particles in d w. Therefore, 



t K' 6 t TV 



11, , 6 w + 5 dw 



——■ a iv + w — a u 1 

 6 



i s the common temperature to which the water and vapour 

 would be reduced by the decomposition of dw quantity of water. 

 Consequently, 



, 6 t w b t d -w 



6 W + 5 d iv 6 re + 5 d r<'' 

 d t H d w 



or, — = - . — 



t D W 



whose integral is t = A w*, 

 A being an arbitrary constant equal to 



U 



5 



"'-6 



where /, and w, are known corresponding, or the primitive values 

 of I and w. 



If, therefore, the transmission of temperature by water was 

 instantaneous, and every portion of vapour had its temperature 

 equalized, as soon as formed, with that of the remaining water, 

 and then quitted the water entirely, the temperature would be as 

 the quantity of water left raised to the £th power; provided 

 evaporation only interfered. But we know that water is not 

 what is called a perfect conductor ofheat, and therefore that the 

 above law is not mathematically true. As the evaporation, 

 however, is generally but trifling, unless in high temperatures, 

 this theorem may probably be found a tolerable approximation. 



Were the number of the particles increased in the ratio of 

 1 to /'by the decomposition, we should have 



I = A w'-\ 



If, therefore, r — 100, t a w". Hence if 7/- be diminished 

 by a hundredth part only, the values of/ corresponding to ir =c 



