Art. 3.— K. Hirayaina ; 



r'^xdw=[\+{-\y][\ + {-\y]J -xdw 



Hence the integral vanishes when either l or j is odd, and becomes 



àf'^Xdw 



when both are even. 



7. Applying this result to the equations (8), I obtain after 

 some simplifications 



(9) 



where 







«t'tZtü 



Taking the first integral and expanding 



-, 2 /-I/t 7i-l/3\ .. , (/i-l)(/i-3V3 \-_ . b 



2 



Now 



— / COS ^oau'' 

 7: J 



,_l-3 (i-1) 



2-4 i 



when i is even. Therefore 



T_,_l-1 1/3 \, (/t-l)(/i-3) l-3/^3\- 



^'~ ~^'^\~\r 2^4 2tVtj 



_ (//-l)(/t-3)(/i-5) 1-3-5 / 3 Y^ 

 2 4-0 2-4-6 \ 4 / ■*■ 



