48 UNIVERSITY OF COLORADO STUDIES 



Comparing the two forms for the equation of the tangent, viz.: 



— cos <b + -4- sin 6=1 

 a 



X cos a-\-y sin a =p 

 we get 



cos ^ cos a sin <^ sin a ,... 



a p "* h p 



Observing that sin a=cos <^', equations (1) show that 



cos ^ sin <^^ sin ^ cos <^' 

 a p '' h p 



By eliminating j9, we get 



tan <^. tan ^' = — , a relation connecting the eccentric angles of 



P and P\ 



This result can probably be made useful, and so far as I know, 

 is new. 



