949 
manometer is. Calculation shows, that even with v= 1000 cc. the 
left hand side of the relation is much too small to have an effect, 
and the condition thus becomes with near approximation 
„> 260 OE oO 
<7? dg S2ndg 
In this case the condition for the transition to the unstable con- 
dition agrees, as is at once seen, with that mentioned in the 
beginning, that the change of volume of the bubble becomes smaller 
than that of the gauge. 
In order to make the phenomenon even more prominent than 
with the open gauge, the latter was replaced by a large funnel 
which was connected to the apparatus and placed upside down in 
a large trough of water with its rim just below the water level. 
The area O was now 642 cm’ and moreover the displacement A 
was almost completely confined to the water-surface inside the 
funnel (as the level in the large trough does not change appreciably) 
and thus twice as large as with the open gauge with tubes of the 
same width. In this case hdg = p—p, and the condition becomes 
ee 
Sady’ 
which with the numerical values given above leads to r< 1.1 em. 
as the transition to the unstable condition. In agreement with this 
result the experiment showed, that the bubble could not be made 
smaller than 2 em. in diameter without the bubble gradually be- 
ginning to contract. 
The contraction continues, as long as the bubble is larger than 
a half-sphere; beyond this state 7 begins to increase; the capillary 
pressure thus begins to diminish and the contraction will cease, 
when the capillary pressure has become equal to the pressure 
exerted by the gas present. The condition can now but be stable, 
as a further contraction involves a diminution of the capillary 
pressure and therefore a diminution of the volume in the gauge 
and an increase of the gas-pressure. 
By means of the above relations the further question may be 
solved whether an increase of c in the formula pv =e, Le. an 
increase of temperature or of the quantity of gas, will make the 
bubble larger or smaller. The relation : 
4m 
shows, that in the stable condition the bubble will increase and 
conversely in the unstable condition. 
