432 THE FIGUEES OF EQUILIBRIUM OF A LIQUID MASS 



Investigation of a very small limit below ivMch is found, in the glyceric liquid, 

 the value of the radius of sensible activity of the molecular attraction. 



§ 30. The exactness of the formula p=—— supposes, as we are about to sho-w, 



d 



that the film wliich constitutes the bubble has, at all points, no thickness lesa 



than double the radius of sensible activity of the molecular attraction. 



We have seen (§ 23) that the pressure exerted by a bubble on the air which 

 it encloses is the sum of the actions separately due to the curvatures of its two 

 faces. On the other hand, we know that, in the case of a full liquid mass, the 

 capillary pressure exerted by the liquid on itself emanates from all the points of 

 a superficial stratum having as its thickness the radius of activity in question. 

 Now, if the thickness of the film which constitutes a bubble is everywhere su- 

 perior or equal to double that radius, each of the two faces of the film will have 

 its superficial stratum unimpaired, and the pressure exerted on the enclosed air 

 will have the value indicated by our formula. But if, at all its points, the film 

 has a thickness inferior to or double this same radius, the two superficial strata 

 have not their complete thickness, and the number of molecules comprised in 

 each of tht^m being thus lessened, these two strata must necessarily exert actions 

 less strong, and consequently the sum of these, that is to say, the pressure on 

 the interior air, must be smaller than the formula indicates it to be. Hence it 

 follows that if, in the experiments of §§ 27 and 28, the thickness of the films 

 which formed the bubbles had, through the whole extent of these last, descended 

 below the limit in question, the results would have been too small, but in this 

 case we should have remarked progressive and continued diminutions in the 

 pressures ; which, however, never happened, although the color of the bubbles 

 evinced great tenuity. But all physicists admit that the radius of sensible ao- 

 tivity of the molecular attraction is excessively minute. 



But what precedes permits of our going further, and deducing from experi- 

 ment a datum on the value of the radius of sensible activity, at least in the 

 glyceric liquid. When, after having formed at the adjutage of the apparatus 

 of § 2C) a bubble of this liquid, we introduce the adjutage into the interior of a 

 glass jar, {bucal,) the opening of which is then closed by an obturator through 

 which passes the copper tube df the bubble always manifests a remarkable pht^ 

 nomenon. If we observe it by placing the eye at the height of its centre, the col- 

 ors are at first seen ranged in curved bands, whose order indicates a gradual in- 

 crease of thickness from the adjutage to the base of the bubble: but after a 

 longer or shorter time this arrangement is modified ; we then observe a large 

 central and circular space colored with a uniform tint and surrounded with nar- 

 row concentric rings presenting other colors. If we change our position around 

 the bubble, with the eye still remaining at the height of the centre, the appear- 

 ances turn with the spectator, and if we place ourselves higher the appearances 

 still follow the movement of the eye. We must bence conclude that the lilm, 

 arrived at this point, has a uniform thickness throughout the whole bubble, with 

 the exception, always understood, of the very lowest part, where there is con- 

 stantly a small accumulation of liquid ; the colors of the rings which surround 

 the central space are evidently referable to the obliquity of vision.* The bub- 

 ble having once assumed this aspect, preserves it till bursting ; only the respective 

 tints of the central space and of the rings vary progressively, ascending in the 

 succession of the colors of the rings of Newton, whence it follows that the film 

 continues to grow thinner, but equally so everywhere, still excepting the small 

 portion at the base. 



Now, after the film has acquired a uniform thinness, if the pressure exerted 

 on the air within underwent a diminution, this would be evinced by the mano- 



"This fact had been remarked by Newton, but only as accidental, in reference to hemi*- 

 spbencal bubbles of soap-water. 



