a 
947 
between stable and unstable must be found in that condition, whére 
the two changes of volume referred to are equal to each 
other. This conclusion appears to be incorrect, however, when the 
condition for stability or non-stability is accurately established. The 
nature of the equilibrium depends upon, whether in a virtual con- 
traction of the soap-bubble the pressure caused by the surface-tension 
increases less or more than the pressure of the gas, and the latter. 
is given by Boytn’s law, if the temperature is supposed to remain 
constant. In the former case the gas-pressure prevails, when the 
bubble contracts, and the condition is stable, in the latter case the 
condition is unstable. 
Calling the volume of the space from the orifice of the tube, on 
which the bubble is blown, to the liquid surface, when the pressures 
inside and outside are equal, v,, the displacement of the liquid / 
and the cross-section of the manometer-tube O, and treating the 
bubble as a complete sphere, the total volume is 
4 
v=v,+ anit r? + hO, 
whereas, d being the density of the liquid in the gauge, 
46 
2hdg =p—p,. Es 
5 
so that 
‘ ae oe i 260 
ZEN ea ee CN . 
3 y 3 rdg 
The change of the capillary pressure is given by the relation 
_ dp-—p,) _ 46 
dnt ie 
whereas for the gas-pressure pu =c, so that 
dp dw 200 260 
ea (4 4 nr? oe me Hens LOE 
dr dv dr 5 
and the condition will be stable or unstable, according to whether: 
46 260 
de Pp 4n oo 2 EE iT er . 
Po ty r dq 
The same result is obtained from the condition, that in stable, 
respectively unstable equilibrium the free energy w of a closed 
system at constant temperature is a minimum, respectively a maxi- 
mum. In our case w may be written in the form: 
w= 8ar' 6 —clogv + Oh? dg + py», 
63* 
