1 96 Inquiries into the Principles of Liquid Attraction. 



proach ; but when one has an elevation, and the other a depression, 

 they recede. 



We have 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 of a hemispherical form ; dierefore, 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 have to their volume, a 

 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. 

 It 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. 

 For 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 experiment, that in a capillary tube, the diameter 

 of whose bore is the yi ^ 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 j^o of an inch, will be equal to 



