470 DR G. PLARR ON THE DETERMINATION OF 



Let us call £ the vector, for which we have 

 This equation gives the three scalar equations : 



In developing V. i<f>~ 1 i=V.jk<l>~H } &c, by the formula 



we get easily, employing the notations Xi = Sj(f) l k , ?/ 1 = SA*^>" 1 i, z 1 = Si<f)' 1 j : 



hence 



iCjS^i = 2/xS^j = ^S^ = a scalar =— N; 



hence 



We assume N = a? 1 y 1 2; 1 , introducing thus a factor for the sake of which some 

 precautions are to be taken when two of the three a? lf y x , z Y should vanish at 

 the same time. We have thus 



= 23iyi*i • 

 By i// £ = 0, and having generally 



we get 



This shows that when e takes the direction of £, then the extremity of 6, 

 namely, the centre of the ellipsoid, remains unmoved, whereas the extremities 

 of pi, (Ti, Tj displace themselves by the rotation round the instantaneous axis 

 directed parallel to £. 



We have in this particular case 



where dt has a convenient scalar value. 



