ALTERNATE CURRENT GENERATOR. 



71 



and, as it is well known that algebraic methods are applicable to plane 

 rector operators of the type here made use of, we obtain the following 

 infinite determinant vector solution for a^, namely, — 

 t, 1 0.... 



I T, 1 



1 t, 1 (J 



1 T^ 1 



1 tj 1 



1 T, 

 &c., &c. 



T,_ 1 



1 tj 1 



1 T^ 1 



1 t, 1 



1 T„ 1 

 &c., &c. 



or- 



P,a, = 



n„ 



where P, is the infinite determinant operator whose leading term ia 

 t, and n^ that whose leading term is r^. 



7. P,, IIj, Pj, n^,&c., being the determinants whose leading terms 

 are t,, t„, tj, t^, &c., respectively, we find at once by expanding that — 



P, = t.ll, - P3 



n. = T,p, -n,, &c.; 



hence — 



Pi _ P3 _ 



= t. 



ii:/P. 

 1 1 



^' r. - &C. 



SO that — 



= S, say, 

 1 



= — ct. 



where S, is the infinite continued fraction operator whose leading term 

 is ^,. 



Again if — 



■S = -r — 





&(•., &c. ; 



