184 The Rev. Dr. Robinson on the Constant of Refraction. 



dR = dQ 



X — f*X3A' + 10A'+7A«) 



+ 1 s%a' + 15a' + 35a« + 21a") 

 &c. 



l+bp 



From the height of the atmosphere given in the preceding note = 7-53 X I, 

 it appears that ¥s is nearly = s\ and, therefore, we need not develope beyond 

 terms of this order, and the equation becomes 



dRzzdQ 

 .X^.e[l + ^&(p'-p)(l + 3tang^0)] 



-^*'X 3^- ^ tl+^^('''-/'H3 + 5tang^0)] 



+ ^s' X ^.0 . [l+5tmg\e-^ih(p'-p) (3+30tang'+35tang*)] 



COS 



- f s*X ^^.0[3+7tang^0+^J(/)'-)t))(15+7Otang^04-63tang*e)] 



OOo 



+ t«'X tS • ^ [1 + 14 tang* + 21 tang* 6 + ^b (/- p) (5 + 

 105 tang* e + 315 tang* + 231 tang^)]. 



-\-ibdpX 



cos" 



These terms are of the form s'dp, and s'p dp. 



The hypothesis of uniform temperature is expressed by the equation, 



1 



as 



p = e ', 



giving the density unity at the surface, and evanescent at an infinite height. 

 Between these limits we have, 



■^\''dp=--^X{n.n-l 2.1) 



C« „ , l-'fn.n — l n 



The hypothesis of uniformly decreasing density gives. 



