470 DR G. PLARR ON THE DETERMINATION OF 



We designate them respectively by </» e and by i/^e, so that 



And putting 

 we have now 





^0 + ^1 = ^ 



Generally having, for any vector co, 



>K&) = — 2 — Sooid'H 

 u 



1 6~H 



ty 1 eo = —Y((0(t>-H + <j)- Wico) + ^~ S&n^ - H , 



the conjugates \jj '(o and *//•/&> will be 



with 



"fro'io = — 2 — Yi<fi HSico , 



■f{a> = ( Vco0 - H + Vi<p ~ J 6> ) + -^ Yi<f> ~ HSaxf) ~ H 





The condition which must be fulfilled when the extremity of p is to move on 

 the limiting curve may be stated as follows : — 



Generally the extremity of p is comprised within the inside of the curve in 

 question. In that case two different axes of infinitesimal rotation, say e and e ls 

 will produce variations Sp differing generally from each other in direction and 

 length. We may assume generally, also, that if e and e x be opposed to each other 

 so that 



Ue+Ue^O, 



we will also have 



But when the extremity of p is infinitesimally near the limiting curve, then 



we cannot any more admit this, because if e 

 should bring the point m (extremity of p) to 

 the point m! inside the curve, then the rota- 

 tion e x = ( — e) would have to bring the point 

 m to m{ outside, a circumstance which can- 

 not take place, as it is against the very 

 definition of the curve. 



We may try the supposition that for a point p on the limiting curve the 



