318 



Dr. Roget on the 



This applies to the case, in which the angle formed by C N' 

 with the produced axis is acute, and its cosine positive. When 

 it is obtuse (or C N' N acute), its cosine being negative, the 

 equation is 



c - x = C. 



When the two poles are similar, and consequently the 

 curves divergent, the two radii, which, during their revolution, 

 generate them by their intersections, revolve in opposite direc- 

 tions ; and the points in each which preserve the same perpen- 

 dicular position with relation to one another, will be found to 

 lie on opposite sides of the axis. The intersections of N n 

 are made with that portion of the line S s, which is produced 

 on the other side of the pole S. This is shown in Fig. 8, 



Fig. 8. 



where N, P, are the two similar poles, and Nw, Pjp, the 

 two revolving radii ; the latter being produced beyond P to q. 

 In this position, when N n coincides with the axis, P q is the 

 direction of the tangent to the divergent curve at the pole P. 

 In their positions N n and Pp', the radii intersect one another 

 at the point c'; when they arrive at n" andp", they intersect 

 at c" ; and so on ; P, c', c", &c., being so many successive 

 points of the curve. When N n and Pp become parallel, they 

 indicate the ultimate direction of the curve. 



