64] DETERMINATION OF CYLINDRQID. 219 



26) 



sn ^> * = sin 2a *> 



cos cc sin 2 



= ^ cos 2 2 + p y sin 2 



as six equations to determine p x , p y , s l} s 2 , a ly cc 2 . We have by 

 elimination 



2 2*1 = . (sin 2a 2 sin2aj) 



or using the first two equations, 



27) A = -J^S cos (oj + ai ) sin y, 



P p x 



28) 



P v p x . 

 = -^ - sin (cc 2 -f KI) cos (K 2 j 



~~ Pi = P* (cos 2 a 2 cos 2 aj) + p y (sin 2 a 2 sin 

 = (Px Py) (cos 2 a 2 cos 2 ^) 

 = (Px -Py} sin (ag + ai ) sin ( 2 - ^); 

 Pz-Pi = (Px - Py) sin (ag + sin y, 



+ (Px -Py) (cos 2 cc 2 - sin 2 aj 



= Pz+Py "f (P* -jPy) COS (^ -f C^ 2 ) COS y. 



From 27) and 29) we obtain 



(_pj -jpj 2 = (p y -p x } 2 sm 2 y ; 



31) ^-^ 



smy 

 From 27) and 30), 



From 29) and 31), 



- **~ Pl 



COS (^ + Oj) = :? = 



32) tan (^ - 



