( 693.) 
where x and y represent two of the variables /;, gi and p and gq 
two of the variables ZL, G;. The quantities (wy) are of the order 
zero in the masses, the quantities [pq] are of the first order. 
With the aid of the values of y;, which have been derived above, 
it is now easy to write down the determinant A(s). The differential 
{ie ie Or 
coefficients such as ———-—— will have m, in the denominator. To 
03, Vie : 
remove this, and to make all terms of the same type also of the 
saine order in the masses, the five lower rows have been multiplied 
by m,. Then the five upper rows, have been divided by /m,, and 
the last five columns by m,Vm,. Finally every term has been divided 
by 7. The equation then becomes 
| —e 0 0 0 0 COMA mer RN 
pee -¢ Bed 0 U (a4) Cal) Caos) Cans | 
0 0 =P 0 0 (hls) (lala) lala) Clam) (laga) 
0 6 0 —F 0 (hm, Can) (lag) gam) (9,92) | 
” 0 0 0 =F Chg2) laga) laga) (raa) (gga) | 
AAT AANED AT EE VRT oe sa 
—[ZyLe) Ko-[Lala) —[Lale] —-[LoG] —[LeGa] 0 —p Û 0 0 
—[L,L£3) —[Lel,) K3-(Lsl3] —[/sGi] —[ZeG.] 0 a 0 0 
| [AG] (4G) HA LAAT LAG] 0 0 0 —e 0 
CRD AE TEN EE Ee 
For brevity we have put 
3 f 3 d 3 
k, = — —-~ et , tae 
9? 2 2 
we, a, ENGE 
To simplify the determinant (5), we may use the relation, which 
has already been mentioned above, 
(Le) HAU @) + (U, 2) =0, 
where x represents an arbitrary element. We perform the following 
operations, which are here, in order to save space, only indicated 
(the ordinary figures refer to the columns, the roman figures to the 
rows) : 
To (8) add 4.(6) + 2.(7,, From (VZ) subtract 4.(VJZ/) 
EE) wos ELEN 
” II) ” 4 (1) at (ITZ), ” (1) ” 4.(3), 
9 (2) ee ee) 
The determinant then becomes divisible by 9, and the columns 
(3) and (8) and the rows (III) and (VIII) drop out. For the sake of 
