154 DYNAMICS OF A RIGID BODY. 



given screw complex. Then the co-ordinates of any 

 other screw 6 of the complex may be determined by 



= a, -f + y + i, 



&c.,. &c. 

 0"0 6 = a"a G + |3"j3e + 7'V* + S"S 6 . 



We shall, as before, denote two screws on the reci- 

 procal cylindroid by X, /u. If be a principal screw of 

 inertia, then 



hp, ("ai + /3"j3i + 7'V + "'&) = a a, + /Tft + 77, 

 + X'% + //'jui, 



&c., &c. 



A/. (a"a 6 + ]3"j3 6 + y">y. + S"&) = a'ae + jS'jSs + 7 " 7 6 

 + X"A 6 + /> 6 . 



Multiplying the first of these equations by ai, the next 

 by a 2 , &c., adding the products, observing that a is reci- 

 procal to j3, 7, 3, X, ju, and repeating the operations for 

 |3, 7, 8, we have the four equations 



=o, 

 A = o, 



-t- 7' / S iyi + 



From these four linear equations a", )3 /r , 7", 8" can be 

 eliminated, and we obtain an equation of the fourth de- 

 gree for h. When h is known, then a", j3", 7", 3" are 

 known, and thus the co-ordinates of the four principal 

 screws of inertia are determined. 



144. Application of Euler's Theorem. It may be of 

 interest to show how the instantaneous screw corres- 

 ponding to a given impulsive s<r"w can be deduced 



