96 Inquiries into the Principles of Liquid Attraciion. 
proach ; = when one has an elevation, and the other a depression. 
they rece 
We sade seen the action of the contractile surface in resisting the 
pressure of both the common and artificial atmospheres ; let us now 
notice its action in compressing the common atmosphere. 
First, take air bubbles, as they rest on a liquid; they are bodies 
of a spherical, or rather < a hemispherical form; therefore, accord- 
ing to the principles of geometry, as their diameters diminish, their 
volume, and their superficial contents diminish, the former in the ratio 
of the cubes of their diameters, and the latter in the ratio of the 
squares of these diameters ; consequently, as the diameters of air 
bubbles diminish, their superficial contents haye to their volume, @ 
ratio constantly increasing ; but the compressing force of the surface 
is directly as the superficial contents; and these contents having to 
the volume, a ratio constantly increasing as the bubbles diminish, the 
force with which they are compressed increases in the same ratio, 
ft is manifest from this, that as the bubbles may be diminished to an 
almost unlimited extent, the pressure to which the enclosed air shall 
be subjected by the continually increasing force of the contractile 
surface, may at length become equal to the pressure of the atmos- 
phere ; and when it has arrived at this degree of pressure, every new 
diminution of their diameters gives a renewed accession to the com- 
pressing force of the surface, till at length they will be made to sus- 
tain the pressure of several atmospheres. Now water contains air 
in invisible globules, which are doubtless under this amazing pressure- 
or we can come to a definite result on this point, by transferring to 
the globule of air in water, the calculation of the pressure which the 
contractile surface, in diminishing capillary tubes, is found to sustain. 
For it is found by ee that in a capillary tube, the diameter 
of whose bore is the ;3; of an inch, water will be elevated 5.3 inch- 
es, and since it is the upper spherical surface of the column which 
causes the elevation, this surface will consequently sustain a pressure 
equal to that of a column of water of the same height. Now as this 
surface is equal to the hemispherical surface of a bubble of air of the 
same diameter as the tube, the pressure which the air bubble will 
sustain will be equal to that of a column of water of the same height ; 
and since the pressure on diminishing globules of air increases in the 
ratio of the differences between the square and the cube of the di- 
minishing diameters, the pressure which a globule of air will sustain 
whose diameter is diminished to the ;1, of an inch, will be equal to 
