APPENDIX III. 



Figs. 5, 24, and .33 can be greatly simplified if the watt component 

 corresponding to the C~R losses in the primary and secondary of the 

 rotatory transformer are set off from DL instead of from the semi- 

 circle. For it can easily be proved (Fig. 56) that .the ordinates be- 

 tween RCi and RC 2 are exactly proportional to CV? 2 , while the ordi- 

 nates between DL and RCi represent, with extremely little inac- 

 curacy, the watt component corresponding to the ohmic loss in the 

 primary, C*Ri. The proof of this is very simple, for let b be the or- 

 dinate between RCi and RC 2 , or a current Co, then we have 



Co 2 = mbo, 

 where m is a constant. 



Calling the projection of Co on DL, do, and that of C on DL, a, 

 then we have 



DN 2 = C = a 2 

 We also have 



= a (DL a) 

 Hence follows 



C* = - a - . b . DL (a) 



In a similar manner it can be proved that the ohmic loss in the 

 primary may be represented by the ordinates between DL and RCi, 

 RD being equivalent to the ohmic loss produced by the current OR. 



It is now evident that the output P of the motor is represented by 

 the ordinates between the circle and RC 2 , while the ordinates be- 

 tween the circle and Rd represent the torque D of the motor. 



100 



