426 THE FIGUEES OF EQUILIBEIUM OF A LIQUID MASS 



form an equilibrium to tlie same pressure will be to one another in the inverse 



ratio of the densities, and, therefore, if the height of the second is --, that of 



d 



the first will be ~~. Hence, designating by^ the pressure exerted by a lami- 

 nar sphere on the air which it encloses, we obtain definitively^=r— — , p be- 

 ing, as we have seen, the density of the liquid which constitutes the film, 7i the 

 height to which this liquid rises in a capillary tube 1™"" in diameter, and d the 

 diameter of the bubble. If, for example, the bubble be formed of pure water, 

 we have /> = 1, and, according to the measurements taken by physicists, we have, 

 very exactly, h zzz 30'"'" ; the above formula, therefore, will give, in this case, 



pz=:—r-. If we could form a bubble of pure water of one decimeter, or 100™™, 



in diameter, the pressure which it would exert would consequently be equal to 

 0™™.6, or, in other terms, would form an equilibrium to the pressure of a column 

 of water 0'"™.6 in height ; the pi-essure exerted by a bubble of the same liquid 

 one centimetre, or 10""", in diameter, would form an equilibrium to that of a 

 column of water of G™™. As regards soap-bubbles, their pressures, if the solu- 

 tion were as weak as possible, would differ very little from those exerted by 

 bubbles of the same diameters formed of pure water. 



For mercury we have /> = 13.59, and, according to M. Bede, k about equal to 



271 S 

 10™™; the formula would therefore give, for a bubble of mercury pzz: — ~, 



but, from the remark which closes the last paragraph, this value is too weak 



and can only be regarded as a first approximation. It only instructs us that, 



with an equality of diameter, the pressure of a bubble of mercury would exceed 



four times and a half that of a bubble of pure water. For sulphuric ether, we 



have pzziO.715, and conclude from measurements taken by M. Frankenheim, 



{Biblwlheque UniverseUe, nouvelle serie. III, 1S36,) h to be very closely equal 



14.6 

 to 10™™. 2; whence results p== — ~, and thus, with an equal diameter, the 



pressure of a bubble of sulphuric ether would be but the fourth of that of a 



bubble of pure water. 



We know that the product Jip, being the product of the capillary height by 



the density, is proportional to the molecular attraction of the liquid for itself, or 



in other terms, to the cohesion of the liquid; it is, moreover, the result from a 



4: A 'Zhp 



comparison of the values ~ and — —, which have been successively found, in 



§ 22 and in the pi-esent paragraph, to represent the pressure exerted by a lami- 

 nar sphere on the air which it contains ; hence we deduce hp = 2A, and it will 

 be remembered that A is the constant capillary ; that is to say, a quantity pro- 

 portional to the cohesion of the liquid. The formula ^=—j- indicates, there- 

 fore, as must be evident, that the pressure exerted by a laminary bubble on the 

 included air is in the direct ratio of the cohesion of the liquid which constitutes 

 the film and the inverse ratio of the diameter of the bubble. 



§ 25. As early as 1830, a learned American, Dr. Ilough, had sought to arrive 

 at the measure of pressure exerted, whether on a bubble of air contained in 

 an indefinite liquid or on the air enclosed in a bubble of soap.* He conceives^ 



* Inquiries into the principles of liquid attraction. (Silliman's Journal, 1st series, vol. 

 ?vii, page 86.) 



