20 



L. B. Tucker man 





I — €" . 26 



., P s 2 sin 2 cos 2irN. -+-P V sin 2 7r A 7 ! 



Q, 





2e ... 



Substituting the value of V an d simplifying: 



tg 2 6 = 



tg"2l 



cos 2 7r TV! 



COS 2tt N-- 



Letting 6 o =tgu>, 



, tg2<? 



tg 2 e l 



COS 2 (0 ■ 



I+^ 2 o |[ 2^ "J 2 



Substituting values for 



and for t£2 7rA r ,: 



COS2U): 



cos 2 6 l 

 cos 2 



Using Stokes's notation : 



r — r= 2 0,=— 



2 ' 2 



R'—R= 2< 



2 



-2R=C 



(40 



and the equations reduce to Stokes's form : 



sin(>' — r) sin;; . r tg(>' — r) tgn . . 



COS2o)= . ,_, ^t-=- COS2 7rN,= *„, -—=-5— (42) 



s\n(R'—R) sinr ' tgC^e'— A') tgt 



or in another form usually more convenient for computation : 



|sin(V — ?i) 



S » \tg% 



tg% (c—) l) 

 (* + ») 



tffTrTV; 



H 



sin (c-\-n) 



(43) 



In introducing Stokes's notation it is assumed that the two read- 

 ings of the compensator are complementary when the major axis 

 of the original ellipse is taken as the axis of reference. Care 

 must be taken to choose two out of the possible four sets of read- 



176 



