454 PROFESSOR CHALLIS, ON ATMOSPHERIC TEMPERATURE 



sequently ensues, the warmer parts ascend and are continually being 

 replaced by the descent of colder. The effect of this circulation is to 

 make the gradation of mean temperature from the lower to the upper 

 strata less rapid than it would otherwise be, and so far as this cause 



also operates, -y will be positive. Hence we may assume -7^ to be 



some positive function of a, and as we have no means of determining 

 a priori the form of this function, we will assume that 



-rr- = A + B% + Cx' + &c. 

 az 



Then substituting in equation (5), we have 



G 



de\ A gk B C 



Kdij - m ~ w^oUTF) ^ l+k'"'^ l + k'^^^^'- 

 and. integrating, 



1 / , gk\ B^ C^ , 



supposing = when ^ = 0. 



The empirical formula which Atkinson gives in his Memoir, for 

 expressing the relation between the altitude (h) in English feet above 

 any place on the Earth's surface, and the depression of temperature (n) in 

 degrees of Fahrenheit at that elevation, is the following: 



h = ti {251,5 + f (m- 1)|. 



This in our notation is, 



ss = - 450 9 + 4,86 e", 



from which it will be found, that 



z z° ^ « 



450 ■*" 18750000 390625000000 "^ ^' 



The third term amounts to about 1° for an elevation of three miles, 

 and may, within the heights to which observations can extend, be neg- 



