192 Mr Hill, On the effect of [Feb. 20, 



the air which has absorbed it rise into upper regions where much 

 of its heat will be radiated into space, while a circulation of air 

 will be kept up, and evaporation go on continuously. I conclude 

 that in the case of the sea as well as in that of dry land, the 

 vicissitudes of day and night and winter and summer, lower the 

 mean temperature. 



It is requisite to know, for one problem which presents itself, 

 which of these two, radiation or evaporation, has the largest share 

 in producing this result. Evaporation, an explicit function <f> (t) of 

 temperature, is by the equation 



<Kt)+f(t)=h 



an implicit function of the rate of heat-supply. Let us examine 

 the sign of its second differential coefficient with respect to h. 

 Differentiating, taking alternately h and t, as dependent variable, 



n d(b ., „ dt 



whence -~- = 1 — / -y.- 



dh J dh 



/' + </>' 



and is therefore positive. 



Differentiating again, with respect to h, 

 d 2 <j> d ( <£' \dt 





dh 2 dt \f + <j>'J dh 

 (f + Vf 



~U' //(/+*')■■ 



If as above we suppose the radiation for temperature t to be 

 proportional to a* — 1, we obtain for the second term of the bracket 

 log a, and since a is, according to Dulong and Petit, T0077, the 

 value of this is '00767 approximately. Other formula? give a lower 

 value and Newton's makes/" to be zero. 



