268 THE THEORY OF SCREWS. [252- 



Similarly, by omitting the first screw, we can have seven impulsive wrenches 

 which equilibrate, where 



18 



hence we have 



13.28 FK.F& 



Let the instantaneous twist velocity corresponding to F 1S be denoted by 

 F 18 , then, as when seven wrenches equilibrate, the seven corresponding twist 

 velocities must also equilibrate, we must have in the corresponding system, 



12. 38 = VnV* 



13.28 ViV 



But we must have the twist velocity proportional to the impulsive intensity ; 

 hence, from the second pair of screws we have 



and from the third pair, 



F V F V 



^38 38 * 13 13 ) 



hence we deduce 



VlZ ^38 _ ^12 ff 



1^13 ^28 -^13 ^28 



and, consequently, the function of the eight impulsive screws 



12.38 



13.28 

 must be identical with the same function of the instantaneous screws. 



It should, however, be remarked, that the impulsive and instantaneous 

 screws do not exhibit the most general type of two homographic systems. A 

 more special type of homography, and one of very great interest, characterizes 

 the two sets of screws referred to. 



253. Special type of Homography. 



If the general linear transformation, which changes each screw a into its 

 correspondent 6, be specialized by the restriction that the co-ordinates of 6 

 are given by the equations 



fi- 1 



&quot;i 



Pi 



I &amp;lt;* 



6 da 6 



