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THE ROYAL SOCIETY OF CANADA 



whence by putting To = wc where c is some length not otherwise 

 defined we get 



^ ws s 

 tan 6 = — = - 



Putting therefore — = - 

 dx c 



(3) 



we get 



dy 



ds V c^ + s^ 



and taking, for a time, the origin at A, axis of x horizontal and axis of 

 y vertical, we get by integration of this equation 



y = Vc^ + s^-c 



whence s = V(y + c)- — c^. 

 Rewriting (3) 



dy V'(y + c)2-c2 



dx 



we get dx = 



dy 



V(y + c)2-c2 



or changing the origin to a point O which is a distance c below A, and 

 putting Y = y+c, we get 



cdY 

 dx = 



V Y2 - c2 

 Making the substitution Y = c cosh lo, and integrating we get 



Y = c cosh - , (4) 



