THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 257 



apiilic'cl one against the other bj their bases. In order that the convex surfoce 

 of eacli of them should be the smallest possible with reference to the volume en- 

 closed between itself and the common base, it suffices evidently that the whole 

 convex surface of both segments together should be the smallest possible in re- 

 lation to the total volume; now, according to a known principle, this last con- 

 dition will be fulfilled if the two segments constitute together a single sphere, in 

 which case each of the two segments will be a hemisphere. Our liquid film, if 

 it contains a sufficient body of air, ought, therefore, to take the hemispherical 

 form, and this is what common observation verifies. 



§ 3. We will advert now to the particulars to which allusion was made a little 

 while ago. In tlic first place, the liquid of the vessel must be slightly raised 

 by the capillary action on both the exterior aad interior face of the laminar 

 figure, as it would be on the two faces of a solid lamina previously moistened 

 with the same liquid and partially immersed ; it must, therefore, form a small 

 annular mass with concave meridian surfaces, and this also is confirmed by ob- 

 servation. Hence the border of the liquid film does not rest immediately on the 

 plane surface of the liquid of the vessel, but on the crest of the small annular 

 mass in question. In the second place, it will be perceived from this, that if the 

 enclo.«ed volume of air is so small that the space circumscribed by the border of 

 the film shall have little diameter, the surfoce of the liquid in this space will be 

 in no part plane, but will present, even in the middle, a concave curvature more 

 or less decided, as in the interior of a tube of small extent. This result is also 

 in accordance with experience, and I have ascertained, by means presently to be 

 iiulicated, that the central portion of the surface in question ceases to appear 

 l^lane when the diameter of the film, at the crest of the little annular mass, is 

 less than about two centimetres. In the third place, even with a volume of air 

 great enough for the surfixce of the liquid, in the space circumscribed by the 

 film, to shoAv itself absolutely plane through nearly its whole extent, this surface 

 must be sunk below the exterior level by the pressure which the film, by reason 

 of its curvature, exerts on the enclosed air, (V, § 21,) and that this is the case 

 may be evinced by the following process : 



In a large porcelain dish placed on a table in front of a window pour a stratum 

 of glyceric liquid (V, § 13) about 2 centimetres in depth, and, after having in- 

 flated, by means of an earthen pipe, a bubble of the same liquid, deposit it iu 

 the middle of the surface of the stratum, when it Avill at once form a spherical 

 segment. We now place ourselves in such a position as to see the sky by re- 

 flection on the surface in question, holding, at the same time, a black thread 

 stretched horizontally at a small distance from the film in such manner that a 

 portion of its reflected image shall be perceived in the space circumscribed by 

 the film. The complete image of the thread now appears to be formed of three 

 parts — two without and one within the laminar figure; the former arc both in- 

 curvated near the film, in consequence of the capillary elevation before spoken 

 of; as regards the third, if the circumscribed surface has, in its middle, a plane 

 portion, we shall find, by suitably adjusting the thread, a position of the latter 

 for which the middle of the image will be rectilinear. This will be the case 

 with films whose diameter exceeds two centimetres, but within that limit the 

 entire part of the image in the interior of the film will appear curved. 



When the film has a large diameter, that part of the image of the thread is 

 rectilinear for nearly its whole length; it curves only toward its extremities, 

 by virtue of the capillary attraction ; but its straight portion is not in the pro- 

 longation of the straight portions exterior to the film; it Avill be seen a little 

 lower. This depression, which shows that the circumscribed plane surface is, 

 as has been said, below the exterior level, becomes less decided in proportion as 

 the diameter of the film is more considerable — a circumstance referable to the 

 diminution of the curvature, and consequently of the pressure of the film, but 

 which is still very perceptible for a film of a decimetre in diameter. 

 17 s 66 



