( 694 ) 
clearness I will, however, continue to indicate the remaining columns 
by their original rotation-numbers. 
Now we have’) 
vt) = (4), (9:91) = (ww), 
Vl) = — AW), (9192) = — (wa), 
Ul) = AU) + Ul, (19) = (wo) + (ww) 
(Lg) = (lo), (/,9,) = — (lo), 
(l.9,) = — WUlw), (Lg) = 2(lw) + Uw’). 
By means of these relations the determinant can be still further 
simplified. We perform the following operations 
To (7) add 2.(6), From (VJ) subtract 2.(VZ/) 
» UI)» 2.(L), ” (1) ” 2.(2) 
> (10) ,, ° (9), mA) (X) 
» (V) » (ZV), coh) ee (5). 
If now the remaining rows and columns are rearranged in the 
following order 
dE DEE GE c A) reen A0 
EAA VA MUI I VE ee 
then the equation becomes 
=o 0 A 0's 20s - 07) Copan 
0 SOE De OR (BE 
0 O (lw) 09 —e 90 (ww) 0 
Oe, 0. Cay 0 or een 
u ln A 
EO 7 AA 
where the meaning of the coefficients is as follows (I mention only 
those coefficients that will be used below, those omitted all contain 
m, as a factor): 
A. = iK + terms of higher orders 
Ke ee 
hee eee 
A. = = IGG IG [6,61 
TT LGG] mie [G,G,] 
A= GG 
1) These formulas suppose (Ul!) = («w') = (/'@) = (/w') = 0. This is only true if 
the third and higher orders of e are neglected, 
