100 THE THEORY OF SCREWS. [106-109 



a small initial twisting motion. The twist, and the twisting motion, may 

 each be resolved into their components on the n harmonic screws : n circular 

 pendulums are to be constructed, each of which is isochronous with one of 

 the harmonic screws. All these pendulums are to be started at the same 

 instant as the rigid body, each with an arc, and an angular velocity equal 

 respectively to the initial amplitude of the twist, and to the twist velocity, 

 which have been assigned to the corresponding harmonic screw. To 

 ascertain where the body would be at any future epoch, it will only be 

 necessary to calculate the arcs of the n pendulums for that epoch, and then 

 give the body twists from its position of equilibrium about the harmonic 

 screws, whose amplitudes are equal to these arcs. 



107. Remark on Harmonic Screws. 



We may to a certain extent see the actual reason why the body, when 

 once oscillating upon a harmonic screw, will never depart therefrom. The 

 body, when displaced from the position of equilibrium by a twist upon a 

 harmonic screw 0, and then released, is acted upon by the wrench upon a 

 certain screw rj, which is evoked by the twist. But the actual effect of an 

 impulsive wrench on 77 would be to make the body twist about the harmonic 

 screw ( 104), and as the continued action of the wrench on 77 is indis 

 tinguishable from an infinite succession of infinitely small impulses, we can 

 find in the influence of the forces no cause adequate to change the motion 

 of the body from twisting about the harmonic screw 0. 



