162 Voltage Ratios of an Inverted Rotary Converter. 

 obtained by proceeding in the usual way with the above 



expressions. 

 1 < ( V — OK) sin — sm 6 H j* 



dO 



sin— x 4CR(V-CR)sin 7r 



(. w \2>? 4 / 7r \ n n n / 



+ 4C W 1 (4) 

 rf0 



J {(V-CR) S m^in^+^ R } 2 < 



sin^ 77 i 8CR(V-CR)si 



= ( V — OR)- sin J — | q ^— f + 



w ( 2 n 2 ) n 



. 27T -v ~~^„^ ~^v . 7T IT 



Sill — COS - 

 n ii 





The sum of the squares for the period to it is equal to 

 twice expression (4) + expression (5). 

 The value of this is 



/xj nr^2 • s 77 " ^ 4CR(V — CR) . it f a . it 2ir it , 7r") 



(V— CR) 2 sm 2 - — + ^ ^sin— ^ 2sm cos- +2 cos- \ 



n Z n n { n n n n J 



, 8C 2 R 2 7r 2 + 4C-°R 2 (^-2)7r 



+ 7l 3 



Dividing through by 7r, taking the square root, and divid- 

 ing this again by V we get as the value of the ratio of the 

 alternating P.D. to the direct current P.D. 



(V-CR) 2 sin 27r 8CR(V-CR)sin- 



v n v y n ( . it it it it \ 



1 I sm — I- cos cos — > 



z nir (, n n n n ) 



4C 2 R* 

 + -^-(tor + n^V) 



Y 



Let UR = — Then the expression for the ratio becomes : — 

 m' 



(m — l) 2 sin 2 — (m — 1) sin 



\/ V J 71 V J n C . 7T 7T 7T 7T } 4 ,_ 



/ -r- « h 2 \ sin- + cos cos- > +—r-»('2ir + n — 2) 



The corrected ratios of conversion are compared with the 



