WITHDEAWN FROM THE ACTION OF GRAVITY. 427 



quite a just idea of the cause of these pressures, which he does not, however, 

 distinguish from one another, and, in order to appreciate them, sets out, as I 

 have done, with a consideration of the concave surface which terminates a col- 

 umn of the same liquid raised in a capillary tube; but, although an ingenious 

 observer, he was deficient in a knowledge of the theory of capillary action, and. 

 hence arrives, by reasoning of which the error is palpable, at values and a law 

 which are necessarily false. 



Professor Henry, in a very remarkable verbal communication on the cohesion of 

 liq^uids, made in 1844 to the American Philosophical Society,* described experi- 

 ments by means of which he had sought to measure the pressure exerted on the 

 internal air by a bubble of soap of a given diameter. According to the account ren- 

 dered of this communication, the mode of operation adopted by Mr. Henry was 

 essentially as follows : he availed himself of a glass tube of U form, of small 

 interior diameter, one of whose branches was bell-shaped at its extremity, and 

 inflated a soap-bubble extending to the edge of this widened portion ; he then 

 introduced into the tube a certain quantity of Avater, and the difference of level 

 in the two branches now gave him the measure of the pressure. Unfortunately 

 the statement given does not make known the numbers obtained, nor does it 

 appear that Mr. Henry has subsequently published them. This physicist refers 

 the phenomenon to its real cause, and states the law which connects the pressure 

 with the diameter of the bubble ; the account does not say whether the experi- 

 ments verified it. But Mr. Henry considers that a hollow bubble may be assimi- 

 lated to a full sphere reduced to its compressing surface; that is to say, ho 

 attributes the phenomenon to the action of the exterior surface of the bubble, 

 without taking into account that of the interior surface. Let us add that, in 

 the same communication, Mr. Henry has mentioned several experiments which 

 he had made on the films of soap and water, and which, from the statement 

 given, would elucidate in a remarkable manner the principles of the capillary 

 theory. It is much to be regretted that these experim.ents are not described. 



In a memoir presented to the Philomathic Society in 1856, and printed in 

 1859 in the Comptes Rcndus, (tome xlviii, p. 1405,) M. de Tessan maintains 

 that if the vapor which forms clouds and fogs were composed of vesicles, the air 

 enclosed in a vesicle of 0.02 millimetre diameter would be subjected, on the 

 part of this vesicle, to a pressure equivalent to \ of an atmosphere. M. de 

 Tessan does not say in what manner he obtained this valuation ; but it is easily 

 seen that he has fallen into an error analogous to that of Mr. Henry, in the sense 

 that he pays no attention except to the exterior surface of the liquid pellicle. 

 According to the formula of the preceding paragraph, the pressure exerted on 

 the interior air by a bubble of water of 0.02 millimetre diameter would, in fact, 

 be equivalent to that of a column of water 3 metres in height, which equals 

 nearly ^ of the atmospheric pressure; M. de Tessan has found then but half the 

 real value, and we know (§ 23) that this half is the action due to the curvature 

 of one only of the surfaces of the film. 



§ 26. After having obtained the general expression of the pressure exerted 

 by a laminar sj^here on the air which it encloses, it remained for me to submit 

 my formula to the control of experiment. I have employed, with that view, the 

 process of Mr. Henry, which means that the pressure was directly measured by 

 the height of the column of water to which it formed an equilibrium. 



From our formula we deduce j)d = 2hp ; for the same liquid and at the same 

 temperature, the product of the pressure by the diameter of the bubble must, 

 therefore, be constant, since h and p are so. It is this constancy which I have 



* Philosophical Magazine, 1845, vol. xxvi, page 541. 



