96 A. Mukliopadhyay — Differential Equations of Trajectories. [No. 1, 

 where M satisfies the quadratic 

 For since 



y = p . 



we have 



whence the quadratic for M becomes 



M(X2+/>t2)=^(MH/^2), 



which may be written 

 the roots of which are 



Taking for the present 



hix JiX 

 M = -f, — . 



A fx 



we have Mx = fx^, 



X ~A2* 



The equation of the trajectory, therefore, on substituting these values, 

 becomes .^^__^ 



-2«tau \/ -;-l+log T- = 0- 



Putting 



h = fji sec <|>, 



C = 2np, 

 where p is a new constant, this becomes 



-y 





•V' "■ 



^^-p2<p + (/)) 





X2 



or 



1 l4.e2n(p + <^) 





