132 THE THEORY OF SCREWS. 



By similar triangles, 



[144, 



whence 



or, as before ( 141), 



Fig. 24. 



OA . O H O H* 



CO X 



OH 

 OH 



It will be noticed that, for this investigation, H may have been chosen 

 arbitrarily on the circle. We thus see that, besides the two points and , 

 there will be a system of pairs of points of which any one may be employed for 

 finding the instantaneous screw, and for determining the instantaneous twist 

 velocity. 



If we choose any two points (Fig. 25), fl and H , so that 



Fig. 25. 



then A being given, Al determines H, and Hfl determines A , while the 

 twist velocity is proportional to O T/ -=- IH. We can suppose fl at infinity, 



