( 696 ) 
The solutions (16), (12) and (13), ie. those with a negative value 
of x, are thus certainly unstable. For (2) s will be positive if 
Ae,— Be, > 0. 
é . 
By using the value of — found above, this leads to the condition 
é, 
eae 
Q< 2— B = 7.41. 
a, 
Similarly we find for (7) that s’ will be positive if 
Q EP Uh oan 
ET Foe 
For the family consisting of the solutions (2) and (7) we thus find 
that s and s’ are both positive for all values of Q between the 
limits — 0.46 and + 7.41. For the Jovian system we find Q=- 4.14. 
For the solution (6) both s and s’ are always positive. 
This is, however, not sufficient to prove the stability of these 
solutions. We must also consider the four remaining roots of our 
equation (6). To determine these I divide the last two rows and the 
5th and 6 columns of that determinant by Wm, Introducing then 
oe Wins Aij= m, Bij, 
the equation becomes 
| —p'V Mm, 0 (Ul) 0 0 0 (lo) 0 
Oe sans 0 (iv) 0 0 0 (et) 
A); Ajo —p'V mg, 0 ByV img ByuV me 0 0 
Ay Aas 0 Vn, Bagh mg BosV me 0 0 
A @)= = 0 
0 0 (lo) 0 —p’ 0 (aw) 0 
0 0 0 (Ua) 0 —f-' 0 (wo) 
Buma Bam 0 0 Bas Bas il 0 
Buma Bama 0 0 Ba Bu 0 =e 
If now again we neglect all terms which appear multiplied by 
Vm,, and if we perform the operations 
From (7) subtract .(3), from (8) subtract (il) . (4), 
we find 
—o 0 on ih) 
Ao en 
WA On Aan BB Sd 
Bar 0 —@ 
