200 



Professor Baker, On the general theory of the 



also the coefficients a,b, ..., b', h', expressed in Sir George Darwin's 

 notation are, respectively, given by 



a = 



f = 



hh 



2A 



0' 



2CJ'K 



cdc 



b = h 2Co, c= — 



a a 



•^ a ■^ a "^ 



/i' = - 25/^), 6' = 2C'/*^ 



§ 3. For a form of possible rotary equilibrium to which such an 

 expression for SH is appropriate, the equations for 8H to be 

 stationary are 



2x [ax^ + hy + gz + 'Lh'y' - k'l] = 0, 



hx'^ + by +fz - k'm = 0, 



gx^ +fy + cz — k'n = 0, 



h'c 



by 



0. 



The solution x = belongs to the series of ellipsoids; omitting this 

 for the moment, the equations give 



i:h'y' = -i:yx^ 



X 



2 a - S (A'2/6'), h, g\ = k' 

 h , b, f 



9 



, f, c 



, yjk' = etc., z/k' = etc., 



h, g, I 



b, f, m 



f, c, n 



corresponding to two possible forms other than ellipsoids. 



The stability, for displacements in which only x, y, z, y' vary, 

 depends on the quadratic form 



namely 



2ax^e + 2hx^V + ^gxH + 2SA'a;^7y' + ^br^^ +frjl + ic^2 + i26'^'2. 



this is, however, the same as 



+ 



2^^ 



bc-r 



a - I. {h'^/b'), h, g 

 h , b, f 



9 , f, c 



