211] 



PLANE REPRESENTATION OF THE THIRD ORDER. 



217 



point of contact, it follows that every screw on the cylindroid must be at 

 right angles to the direction corresponding to the point of contact. The 

 co-ordinates of the point of contact must therefore be proportional to the 

 direction cosines of the nodal line of the cylindroid. 



If the body be in equilibrium under the action of a conservative system 

 of forces, then there is a conic (analogous to the conic of inertia) which 

 denotes the locus of screws about which the body can be displaced to a 

 neighbouring position, so that even as far as the second order of small 

 quantities no energy is consumed. The vertices of the triangle self-conjugate 

 both to this conic and the conic of inertia correspond to the harmonic 

 screws about which, if the body be once displaced, it will continue to 

 oscillate. 



