DYNAMICS OF A RIGID BODY. 1 7 1 



corresponding instantaneous and impulsive screws be given, 

 then the relation between every other pair is absolutely 

 determined. It appears from 30 that appropriate 

 twist velocities about A^ &c., A 1 can neutralise. 

 When this is the case, the corresponding impulsive 

 wrenches on JR l9 &c., R ly must equilibrate, and therefore 

 the relative values of the intensities are known. It 

 follows that the specific parameter of each pair A RI is 

 proportional to the quotient obtained by dividing the 

 sexiant of A 2 , &c., A^ by the sexiant of R z , &c., R 6 . With, 

 therefore, the exception of a constant factor, the spe- 

 cific parameter of every pair of screws is known, when 

 seven corresponding screws are known. 



When therefore seven instantaneous screws are known, 

 and the corresponding seven impulsive screws, we are 

 enabled by geometrical construction alone to deduce 

 the instantaneous screw corresponding to any eighth 

 impulsive screw, and vice versa. 



A precisely similar similar method of proof will give 

 us the following theorem : 



If a rigid body be in position of stable equilibrium 

 under the influence of a sytem of forces which have 

 a potential, and if the twists abont seven given screws 

 evoke wrenches about seven other given screws, then, 

 without knowing any further about the forces, we shall 

 be able to determine the screw on which a wrench is 

 evoked by a twist about any eighth screw. 



We shall state the results of the present section in 

 a form, which may, perhaps, interest the student of mo- 

 dern geometry. We must conceive two corresponding 

 systems of screws, of which the correspondence is com- 

 pletely established, when, to any seven screws regarded 

 as belonging to one system, the seven corresponding 

 screws in the other system are known. To every screw 

 in space viewed as belonging to one system will corres- 



