DYNAMICS OF A RIGID BODY. 153 



cylindroid, then the reaction of the constraints may be 

 considered to consist of wrenches on X, /u of intensities 

 X", fi". If we adopt the six absolute principal screws of 

 inertia as the screws of reference, then the body will 

 commence to move as if it were free, but had been acted 

 upon by a wrench of which the co-ordinates are propor- 

 tional to /A, . . ., / 6 6 . It follows that the given impul- 

 sive wrench, when compounded with the reactions of the 

 constraints, must constitute the wrench of which the co- 

 ordinates have been just written ; whence if h be a cer- 

 tain constant, we have the six equations 



7, A n /' \ ff \ " 

 npiVi = TI i]i + A Ai + ILL /ii, 



&C., &c. 



7 A f) " i "\ "\ " 



np$* = TJ rj 6 + X A 6 -I- fj. ju 6 . 



Multiply the first of these equations by Xi, the second 

 by X 2 , &c. : adding the six equations thus obtained, and 

 observing that is reciprocal to X, we have 



= o, 

 and similarly 



= O. 



From these two equations the unknown quantities 

 X", ju" can be found, and thus the initial reaction of the 

 constraints is known, substituting the values of X", ft" in 

 the six original equations, the co-ordinates of the required 

 screw are known. 



143. Principal Screws of Inertia. We shall now show 

 how the co-ordinates of the four principal screws of inertia 

 belonging to the screw complex of the fourth order are 

 to be computed. All the co-ordinates are, as before, 

 referred to the six absolute principal screws of inercia of 

 the body ( 105). 



Let c, j3 7, 8 be any four co-reciprocal screws of the 



