768 Sir Oliver Lodge on 



Note that 315 + 378 exceeds 630 + 62 by unity ; also that 

 A 8 = 1 x § x 2 x f x 3 x § x 4 = ^-f- 2 7 . 



Continuing, we find that the positive coefficients for # 9 are 

 the halves of 2835, 5040, and 62 ; while the negative ones 

 are the halves of 6615 and 1320. 



For y 10 the positive coefficients are the halves of 14175, 

 34965, and 1382 ; while the negative ones are the halves of 

 37800 and 12720. 



The law of formation of the terms is fairly simple : — 

 Thus let 



w w _i = A ?1 _iCOS (n — 1)6 — B ?l _iCOS (n—3)6 



+ C n _icos (n — 5)6 — V , 



then 



u n — i{A„_i . 7ZCOSW0 — (A M -.i + B„_i)(w — 2jcos(?i— 2)0 + 

 = A»cosn#— B n cos (n— 2)6 -\ — 



multiplied in each case by y c C\ c 2 ; the last factor 



being c n in the case of y n . Also A»=n l-±-2 n ~ 1 . 



A few minor considerations applicable in a 

 4 circuit machine. 



In first writing down the general equations (1) and (2) 

 for the arrangement diagrammatically illustrated above, the 

 fact that the different branch circuits may have different 

 resistances was ignored. No principle is thus neglected, 

 and general solution is made easier. The only resistance 

 which is not unimportant or unessential from the point of 

 view of radiation is the last of the series, E u , which ought to 

 be large compared with the others. 



The constant which characterizes every expression is of 

 the form jt?M/R, the frequency-constant multiplied by the 

 mutual time-constant of each circuit. There are 4 circuit 

 branches altogether, besides the steady exciting-current circuit 

 of the stator; the circuits of the rotor have been called Hi 

 and R 3 , those of the stator have been called B 2 and R^ ; the 

 latter circuit involves useful dissipation by radiation as well 

 as all hysteresis and ohmic losses. 



