948 
whence : 
dy 16 e dv 1 20hd dh 4 dy 
— ZZ CC ON nen 3 ig@— +p, —, 
dr 4 v dr iid dr Po dr 
or after reduction 
dw 
—= 16 aro— (p—p,)427r". 
dr 
a bas 6 kern dw 
rhe condition of equilibrium — —0 gives the relation p— p, = 
ar 
46 ; 
= —, made use of above. 
JR 
We have further: 
Ip dp dv 
eat xo —(p—p,) 8ar— eas be del 
dy? dv dr 
k p . 260 > 
=— l6mo+ —[ 427? — — ]427°— 0, 
== 5 ( 1 dg 1 << 
which leads to the same unequality as arrived at above. 
This relation reveals the remarkable fact, that even without the 
manometer the condition may be unstable, viz. when 
45 p Ov 
pits en Mn 
r v Xp 
The value of 7 is limited by the circumstance, that it cannot be 
smaller than the radius of the tube to which the soap-bubble is 
blown, and, as p is of the order 10°, 5 for a soap-solution being 
about 25, the unstable condition cannot be realized unless with a 
large volume v. In order to test the above result a carboy of 30 
liters (v = 30000) was attached to the apparatus without gauge: in 
this case the condition becomes 7 < 0.7 cm. That the condition was 
unstable, was manifested in blowing the bulb in the fact, that, as 
soon as the bubble exceeded the half-sphere, it blew itself up quickly 
to a considerable size. In diminishing the bulb below the given limit 
by letting out air the unstable nature of the equilibrium showed 
itself less clearly. The bubble sometimes remained for a considerable 
time without appreciable change in size; this must be due to a 
retardation the nature of which was not fully explained: as a rule 
by tapping the tube the bubble could be made to contract in accord- 
ance with expectation. 
As shown by the above complete relation, the addition of the 
gauge on which the second term on the right-hand side depends 
will make it possible to realize the unstable condition with a much 
smaller volume, the more easily ‚the larger the section O of the 
