946 
Physics. — “On the measurement of the capillary pressure in a 
soap-bubble.” By Prof. J. P. KurreN. (Communication N°. 145a 
from the Physical Laboratory at Leiden). 
(Communicated in the meeting of December 30, 1914). 
In the measurement of the pressure in a soap-bubble by means of 
an open liquid gauge the peculiar case may present itself, that the 
measurement becomes impossible owing to the condition becoming 
unstable. This fact accidentally came under my notice, when an 
attempt was being made to increase the accuracy of the measure- 
ment of the comparatively small pressure by the use of a micro- 
manometer; in this instrument the construction of which is otherwise 
of no importance for the present purpose the pressure to be measured 
acts on a large liquid surface (about 427 em?) which on a change 
of pressure is displaced over the same distance, as if the instrument 
were a simple open water-gauge with two tubes of the same width. 
When this manometer was used, it appeared impossible to work 
with soap-bubbles of less than about 1 em. diameter, as smaller 
bubbles always contracted of their own accord, though no-leakage 
could be discovered in the apparatus, whereas with a gauge with 
narrow tubes a similar difficulty had never presented itself. 
A consideration of the equilibrium-relations had to lead to the 
explanation of the phenomenon and it soon appeared, that it was 
connected with the change of volume in the gauge which accompa- 
nies the displacement of the liquid surface on a change of pressure. 
Starting from a condition of equilibrium between the surface-tension 
o and the excess of pressure p— p, (Pp, = atmospheric pressure), 
in which therefore p— p, =" (r = radius of bubble), and applying 
to the bubble a virtual change, say a diminution of the radius, the 
capillary pressure will increase and this will cause the liquid-surface 
in the gauge to descend, which in its turn involves an increase of 
the volume. Now the condition will certainly be unstable, if this 
increase of volume exceeds the diminution of volume given to the 
soap-bubble; because in the enlarged volume the pressure of the 
gas will be smaller and this* decrease will cause a further contraction 
of the soap-bubble. It now also becomes clear, why the phenomenon 
was observed for the first time in using the wide gauge: the increase 
of volume which goes with an increase of pressure is much more 
prominent in this case. 
One might be inclined to draw the conclusion, that the limit 
