The motion of the stare 



95 



(93) 



•^30 



(94) 



I add the corresponding expressions for the moments of the fourth order, 

 which may be alternately used instead of the moments of the third order: 



i^o. - 3iVo/ = (a,^-a,T - ^ (f - f ) (a.^—,^) (n, - «,)^ + - (., - n,)^ 



From the equations (92) we get: 



NN I \ 

 ^20 — -^02 = -]vl^( K - »^s)' — — »«a)' )• 



Dividing by (92*), it results: 



N —N 1 



(95) 

 where 



(95*) . •r,^ ^^-^^ 



^1 — »«2 



The product of the two roots of (95) being equal to — 1, one root is always 

 positive, the other negative. For deciding which of these roots is to be used, we 

 observe that, according to (92*), 



N NN 

 (96) f!^.^^ 

 ^ ' [n^ — v^Y NN ' 



so that Yj shall have the same sign as N^^. (Supposing that only positive values of 

 N^ and N^ are taken into consideration.) 



From (93) we deduce 



(96*) N^^in^ — n^] — N^^{m^ — ■},>;) ^ — ^^^[^ ^ F) ^^'^ ^''^ (^'i -'«2) [K" '«2)' - i^i " ^-i 

 or, after some reductions, 



N^N^ fN N 



(97) t-y = 2c, 



where 



(97*) c = 



and 



^30 - ^1 ^( 



03 



2VriN,, {N,,-NJ 



