642 Mr W. HOPKINS, ON THE EXTERNAL TEMPERATURE OF THE EARTH, 



Hence we must have 



Cl <- 8 +2c 2 j3 +nc„/3"- 1 , 



a 



If we neglect c 2 , c 3 ... c„, we obtain 



1 + OT, 



where /3 = 



and therefore will be in this case the height of the atmosphere subject to the 



condition 



a? 



Now we have 



a = 916,118 feet*, 

 g= 32,172 .... 



Or if we take 100 feet for the unit of length 



a = 9,16118 

 g= ,32172. 



Also — is the decrement of temperature in ascending through a unit of height, as appears 



from the assumed expression for 1 + a£; and this decrement will be expressed in centigrade 

 degrees if we make 



a = ,0003665. 



Hence — must be < — — 



a a a . . 



<10»,4. (C); 



i. e. the above value of /3, in the case we are considering, will give the height of the atmosphere, 

 if the increment of temperature corresponding to the ascent of 100 feet be less than 10°,4 

 centigrade degrees. It is in fact only the fraction of a degree. 



The limit for the values of — would manifestly be less than the above if c 2 , c 3 , ... c n 



a 



were too large to be neglected and were negative. 



At the limit of the atmosphere where z = /8, we have still, as in the former cases, 



1 + ar 2 m 0, 



Tf - - -- - 273° (C.) 



See Miller's Hydrostatics. 



