198 PROFESSOR A. R H. LOVE ON THE 



and therefore, if we put h 3 = and P = in A,, we get 



A _a 2 2AT s 2 a 2 *V ,_ v 



~fr~5~[ 2 + 27I~ ' 



_ 



~2~ ' 2.4...(2K-2)'" 



= 0. 



It follows that A, vanishes to the first order in h 2 and P, and therefore, as has t)een 

 explained, we must evaluate the limit of A t /i~ 2 when /i 2 and P vanish. We have to 

 expand the terms ofyi, s'6 l and adP\/da correctly as far as A 8 ; in calculating the 

 remaining terms of A 1( we may put h 2 and P equal to zero in E^ P\ and QV 



The terms of /*, which are of the first order in h 2 are 



2 r a 2 7.90V /I 1\ . Y 7.9...(2*+S)j-V /I 1 1 \ 1 



L 2.5 2.4.5.7X7 9/ <V ' 2 . 4...2 K . 5 . 7...(2*+3)\7 9 2K+5/'"J' 



.(2*+3) 

 The terms of s 2 ^ which are of the first order in h 2 are 



(-V +1 - + H 



" 



--- - 



55s 2 2.4.5 2.4...2/C.5.7." (2+l)\7 9 ftc+8 



Hence the terms of (fi + s 2 l ) a, 2 /3v which are of first order in h 2 are 



2.4...2K 



1 \1 

 +8/J- 



Again, when we keep those terms only which are of the first order in h 2 and P, we 

 find from (52) of 11, 



1 h 2 



__ __ 

 2 . 4 . 5 5s 2 ' 



