202 PROFESSOR A. E. H. LOVE ON THE 



Stability in Respect of Displacements Specified by Harmonics of the. Second and 



Third Degrees. 



29. When n = 2 and A 2 = 0, tf = 0, we have 



. 2 



2 +3E 2 +3a 2 Q' 2> 

 5 



wnere 



-.A J_ _ / y 



" 







_ _ 



6? 2.7 2.4.7.9 " ' 2.4...2/c.7.9...(2K + 5)'"' 



- a * Sy'a 6 , y 8.10...('2>c+2)8 ii '- 4 a iu 1 



12s 2 2.4.7 2.4.6.7.9 ' 2. 4...2/c.7.9...(2/c+3) "'J' 



- 22 ' 



L_ ' ___ 8sV , y+1 8.10...(2<c+4)s 2 '- 2 a 



___ 



' 



5i> L 6.7.S 2 2.7.9 2.4.7.9.11 >v ; 2 .4. ..2*. 7. 9. ..(2*4-7) "'J' 

 From these we find 



A _ 2Aa 2 [1 sV 8sV , y (2K+2)(2K44)s i V l 



5>/L6 2.7 2.4.7.9 "^ ' 2 .4.6 .7. 9. ..(2*+5) "J 



~~fr~ [677 ~ 2. 7. 9 + 2. 4. 7. 9.11~"^' ' 2 .4.6 .7.9 ...(2x4-7) "J 



"~s 3 "L6~277 + 2.4.7.9~'"^~' 2.4.6.7.9...(2/c+5)'"J 



-HAT-- 4 8g4<t4 , y (2K4-2)(2<c+4)g 2 'a 2l[ 1 



s* [6 2.5 2.4.5.7 "^ ' 2 . 4 .6 . 5 .7...(2/c+3) "'J' 



By means of the identities 



^ 2_ 3 



2/c + 3 (2/c + 3)(2/c+5)' 



(2/c+2)(2/c+4) _ 1 6_ 15 



(2/c+5)(2/c+7) " 2* + 5 (2/c+5) (2c+7)' 



(2/c+2)(2K+4) = _2 

 (2K+l)(2/c+3) 



