294 



Trof. J. J. 



, Sylvester on Sp) 



\erica I Harmonics, 



Now 



we have identically 







(fi - 



•*'a) r ^ 







H>- 



-*'A)<= ' 





and 











((4 



-*£)+(*£ 



-4)>=°- 



Hence with respect to I as operand 



we have 





(*a - 



-*£)+(*£■ 



-*'A)=°- 



Operate on this 



identity with 







(4- 



' h dt)~\ h 'dF~ 



*£> 



and we 



obtain 









("i- 



~*5s) ~( h dl + k dk) 



and there will be two other equations of like form. Adding 

 all these together, changing all the signs, and remembering 

 that in regard to I as operand 



\dh) + \dk) = ~ \Jl) ' 



\dh') r \dX) \dl'J> 



we obtain 



(4+*a' +I a) ,+8 (*a+4+'a) 



In this formula 



{! L ih +I 4c +l di) 



stands for its algebraical value 



„ d \ 2 „ 7 7 d d 



■ Kdh) 



