268 BOOK OF MATHEMATICAL PROBLEMS. 



prove that the repulsive force at any point is inversely proper- 

 1 to the chord of curvature through the centre of force. 



1285. The coordinates of a point P of a rigid body, referred 

 to a system of fixed rectangular axes, are x, y, z\ prove that, if 

 the body receive any small displacement, the displacements of P 

 parallel to the axes may be represented by 



a, /?, y, 6 lt O a , O a being independent of (a;, y, z). Hence prove 

 that the sum of the virtual moments of any forces acting on a 

 rigid body is of the form 



Xy Y, Z being the sums of the resolved parts of the forces along 

 the axes, and Z, M 9 N the sums of the moments about the axes. 



