552 Mr. A. R. McLeod on 



slight change of index, da, is given by 



dn , _ , _ 



\-cot<p ad> = 0, 



n T 



or , . , dn 



d<f>=— tan<£— (18) 



» 



The whole deviation of the ray is thus given by the usual 

 formula 



A ^.f%.-p*«^-_ 4 r T7 * do) 



J. I„ n J„ n\/irr l — k z 



the suffix i referring to the upper extremity of the ray. 

 Writing (17) in the form 



n = n -ph + qh 2 , (20) 



_Ch k' p-2qh)dh 



J h ns/a + zbh + ch* 



where 



k = '/? R sin </> — ni(R 4- ft») cos D ( , 



a = w 2 E 2 — P = n 2 R 2 cos 2 </> , 



& = w R(n — pR), 



c = Oo— pR) 2 +2n U(qR—p). 



In the second expression for /c, D;=^ — <^ refers to the 



dip, in the case of observation from the greater height, In, 

 and iii is the corresponding index. 



The factor 1/n in the integrand of (21) may be replaced 

 by unity, with an error, for h = 8 km., of not more than 

 1 in 4500. Hence we may give (21) the approximate form 



This has the solution : 



— ;=• + Vc/*j+ */ a + 2bJu + cht 2 ! 

 k { 2bq\, I \/c 



L v r J 



■^ [ V + 26//,- + ^- <\/a + 2bh + c7i/] . 



. . . (24) 



