IX FOCAL PLANE OF TELESCOPE. 395 



shows that y «tn not be greater than 1, which it will attain only for 

 x=0. 



Since 



and 



we see that points corresponding- to the roots x n of J l -(x)=0 are the 

 points of inflexion and have tangents parallel to the x axis. The 

 coordinates of these points are x n , J \x n ). 



From the nature of the roots of J" 1 (;r)=0, we see that these points 

 occur at nearly equal intervals of the abscissae little greater than tt, to 

 which the interval will gradually approximate with increasing values 

 of x n ; consequently the curve has neither maximum nor minimum 

 (excepting the point x =0, y = \), but has an infinite number of in- 

 flexional tangents parallel to the x axis. 



In addition to these, we find another series of inflexion points 

 given by the equation 



3J t (x) 



or, since 



2Ji(«) 



= 2J- (aO 



= J<Hx) + Jfr) 



X 



the above equation can also be written 



U*) " 



For any value of x, J"j(ic)<:l, the relation to be satisfied at the 

 inflexion points 



Jjx) _ '2x 



