290 M. J. Plateau on the Figures of Equilibrium 



In order to give an idea of the most convenient dimensions for 

 this apparatus, I will just say that the edges of my cubical frame 

 are 7 centimetres in length, and that the iron wire, of which it 

 is formed, is a little less than 1 millimetre in thickness. I 

 have already employed similar frames in the experiments (men- 

 tioned in my second memoir) for the formation of liquid polyhedra. 



If one of these frames were completely dipped (with the ex- 

 ception of the upper part of the fork) into the glyceric liquid 

 and then withdrawn, it would be expected that the adhesion of 

 this liquid to the solid frame would cause the formation of a set 

 of films, occupying the interior of the frame ; and this does take 

 place; but a most remarkable thing it is, that the arrangement 

 of these films is not a matter of chance ; it is, on the contrary, 

 perfectly regular and perfectly constant for each frame. In the 

 cubical frame, for instance, is invariably obtained a collection of 

 twelve films, starting respectively from the twelve wires, and all 

 converging on a much smaller thirteenth one of quadrangular 

 form and occupying the centre of the apparatus. 



These systems of films, thus prepared in these polyhedral 

 frames, have excited the admiration of all to whom I have shown 

 them; they have a perfect regularity; the liquid edges that 

 join among them the films of which they are composed are ex- 

 tremely fine, and the films themselves after some time exhibit 

 the richest colours ; again, the arrangement of these same films 

 is regulated by simple and uniform laws, which I shall examine 

 from a theoretical point of view in the next series, and of which 

 here are the two principles : — 



I. At one and the same liquid edge never more than three films 

 can meet, and these same are inclined to each other at equal angles. 



II. When several liquid edges meet at one and the same point 

 in the interior of a system, these edges are always four in num- 

 ber, and are inclined to each other, at the point in question, at 

 equal angles. 



I had already obtained, by totally different means, these 

 systems of films with oil immersed in the alcoholic liquid, as 

 will be seen in my second series ; but they are far less perfect 

 and far less easily produced than by my present process. 

 . We now pass on to another subject. It is well known that 

 a soap-bubble exerts a pressure on the air which it contains. 

 Mr. Henry, in an oral communication made in 1844 to the 

 American Society, has described experiments by means of which 

 he measured this pressure by the height of the column of 

 water with which it is in equilibrium ; but I believe that his 

 numbers have not been published. I have looked at the ques- 

 tion in a general way from a theoretical point of view, and have 

 arrived at the following result : — Let p stand for the density of 



