354 THE THEORY OF SCREWS. [323 



radii of gyration of the two bodies, around any one of these three diameters, 

 will not be equal. If, however, it should happen that the radius of gyration 

 of one body be equal to that of the other body about one OX of these three 

 common conjugate diameters, it can be shown that any screw, parallel to OX, 

 whatever be its pitch regarded as an instantaneous screw, will have the same 

 impulsive screw for either of the two bodies. 



If the radii of gyration about two of the common conjugate diameters 

 were equal for the two bodies, it will then appear that any instantaneous 

 screw which is parallel to the plane of the common conjugate diameters, will 

 have the same impulsive screw for each of the two bodies. The corresponding 

 impulsive screws belong to the system of the fifth order, which is defined by 

 being reciprocal to a screw of zero pitch on the third of the three common 

 conjugate diameters. 



Of course, if the radii of gyration coincide on this third diameter, then 

 the two rigid bodies, regarded from our present point of view, would be 

 identical. 



