126 THE THEORY OF SCREWS. [136- 



equal and opposite twist velocities on the common instantaneous screw. 

 The body would then not move, and therefore the two impulsive wrenches 

 must equilibrate. But this is impossible, if they are on two different 

 screws. 



137. Two Homographic Systems. 



From what has been shown it might be expected that the points corre 

 sponding to the instantaneous screws and those corresponding to the 

 impulsive screws should, on the representative circle, form two homographic 

 systems. That this is so we shall now prove. 



Let A, B (fig. 20) be a pair of impulsive screws, and let A , B be respec 

 tively the corresponding pair of instantaneous screws, i.e. an impulsive 

 wrench on A will make the body commence to twist about A , and similarly 

 for B and B . Let an impulsive wrench on A, of unit intensity, generate a 

 twist velocity, a, about A , and let /3 be the similar quantity for B and B . 



Let X be any other screw on which an impulsive wrench is to be applied 

 to the body supposed quiescent. The body will commence to twist about 

 some other screw, X , with a certain twist velocity fa. We can determine 

 &amp;lt;Z&amp;gt; in the following manner: The unit impulsive wrench on X can be 

 replaced by two component wrenches on A and B, the intensities of these 

 being 



BX A;X 



~AB AB 



respectively. 



These impulsive wrenches will generate about A , B twist velocities 

 respectively equal to 



BX 



