480 DR G. PLARR ON THE DETERMINATION OF 



namely, 



and for dp =jdy + kdz the result becomes 



Yl 3 dz-W 2 dy = 0. 

 We have, therefore, for the element of the limiting curve, 



d P =(jw s +m 2 )dt' 



— —mw^ l iX)dt' . 



Of course, there are two more conditions to be satisfied in order that the 

 extremity of p be actually on the curve. 



We may remark that £ may also be put under a second and a third form, 

 namely, the first being 



5 m r 



we have also 



t— <£-**-* 



m 

 kz, 



where 



x = Sj<pk, y = SJapi, z = Si<pj . 



Hence if we put by analogy 



we get, it is true, 



- m^,?= (kW 1 + i W 3 ) , 



- muf.^= (i W 1 +j Wj) , 



but these two last expressions are only exceptionally representing da, dr 



respectively, namely, they do so only when Vjdcr, or Ykdr, satisfy an equation 



analogous to xp'Yidp = . 



We put 



f-jW.'+iW,' 

 and 



£b =3 w 3 + k W 2 = - mui/rj f , 

 then we have 



and also 



If we put 



£ =x <f>~H — x l (pi , 

 we have 



6-V*. 



