DYNAMICS OF A RIGID BODY. 139 



given screw of the screw complex. For a couple in 

 a plane perpendicular to the nodal line of a cylindroid 

 may be regarded as a wrench upon a screw recipro- 

 cal to the cylindroid ; and hence a couple in a diame- 

 tral plane of the ellipsoid of inertia, conjugate to the 

 diameter parallel to the screw 0, will make the body 

 commence to twist about the screw 9. 



It is somewhat remarkable that a force directed along 

 the nodal line of the cylindroid must make the body 

 commence to twist about precisely the same screw as 

 the couple in a plane perpendicular to the nodal line. 



If a cylindroid be drawn through two of the principal 

 screws of inertia, then an impulsive wrench on any screw 

 of this cylindroid will make the body commence to twist 

 about a screw on the same cylindroid. For the impul- 

 sive wrench may be resolved into wrenches on the two 

 principal screws. Each of these will produce a twisting 

 motion about the same screw, which will, of course, 

 compound into a twisting motion about a screw on the 

 same cylindroid. 



126. Ellipsoid of ihe Potential. A body which has 

 freedom of the third order is in equilibrium under the 

 influence of a system of forces in conformity with the 

 restrictions of 6. The body receives a twist of small 

 amplitude & about a screw 9 of the screw complex. It 

 is required to determine a geometrical representation 

 for the quantity of work which has been done in effect- 

 ing the displacement. We have seen that to each screw 

 9 corresponds a certain linear parameter v 9 ( 72), and 

 that the work done is represented by 



We have also seen that the quantity VQ- may be repre- 

 sented by 



