where we have put 
lw)? lo’): 
Ee) tn eee 
(il) (er) 
We thus find that 9’ is determined by an equation very similar 
to (7). For the coefficients B;; we find easily 
6 = (ww) — 
B,, = i, ae H,, 
bi =H 
B,, = H,+ H 
where 
oR ie ieee 
ne, 
O77’, 16 u‚a,a, €? 
òR 1 u, B Us ! 
i ea Tea 16 RR ete : 
= E es B 
Een 
For the cases (6), (2) and la ), which are the only ones that we 
need investigate, all these expressions are negative. For H, and H, 
this is at once evident. For H, we find: 
Sol. (6) Sol. (2) Sol. (7) 
i Lie 
zr Oe ee en ie a 
: 16a’,€*, 16a',e°, 16at.e, 
which is also negative in all three cases. The equation determining 
the first term of o/ now becomes 
oe — (4+ 4,)6+(4,+4,)o}y" + [4,.4,+4,.H,+ H,.H,}00'=0, . (9) 
The condition that this equation shall have two real and negative 
roots is again that o and o’ are both positive. Now we have 
6 = (ww) — ee) ; 6 = (ww!) — ey 
s s 
It is only necessary to investigate those cases where s and s’ are 
both positive. The conditions of stability thus become 
s.(ww) > (lw)?’, s'. (w'w') > (Vo)? 
The values of s and s’ have already been given above (8). For 
the other quantities we find 
47 * 
