88 DYNAMICS OF A RIGID BODY. 



lem of the determination of the condition that two forces 

 should be unable to disturb the equilibrium of a particle 

 only free to move on a straight line. If P, Q be the 

 two forces, and if /, m be the angles which the forces 

 make with the direction in which the particle can move, 

 then the condition is 



P cos / + Q cos m = o. 



This suggests what it will be well for the reader con- 

 stantly to bear in mind, and that is, the analogy which 

 subsists between the virtual co-efficient of two screws, 

 and the cosine of the angle between two lines. 



82. Particular Case. If a body having freedom of 

 the first order be in equilibrium under the action of 

 gravity, then the vertical through the centre of inertia 

 must lie in the plane of reciprocal screws of zero pitch, 

 drawn through the centre of inertia. 



83. Impulsive Forces. If a wrench of great intensity 

 TJ" act for a short time on the screw j, while the body 

 is only permitted to twist about a, then we have seen 

 in 60 how the twist velocity produced can be found. 

 We shall now determine the impulsive reaction of the 

 constraints. This reaction is a wrench of intensity X" 

 on a screw X, which is reciprocal to a. The determina- 

 tion of X may be effected geometrically in the following 

 manner : Let /u be the screw, an impulsive wrench on 

 which would, if the body were perfectly free, cause an 

 instantaneous twisting motion about a ( 53). Draw the 

 cylindroid (rj, /ui). Then X must be that screw on the 

 cylindroid which is reciprocal to a, for a wrench on X, 

 and the given wrench on i\ y must compound into a wrench 

 on ju, whence the three screws must be co-cylindroidal ;* 



* We shall often for convenience speak of three screws on the same cylin- 

 as cO'Cylindroidal. 



