130 Prof. J. Plateau on the Figures of Equilibrium 



only further to find the angles which the two films and the par- 

 tition form with each other at their junction. On this point I 

 have first to remark, that films of liquid cannot meet each other 

 so as to form angles whose edges are linear : the condition of 

 continuity requires that all along the line of junction of our 

 three films a minute mass should be formed, with surfaces highly 

 concave in the direction perpendicular to this line. With soap- 

 water or with the glycerine solution this small mass is much too 

 slender for the eye to be able to distinguish the transverse cur- 

 vatures ; but they may be seen very well in the systems of films 

 obtained with oil in the midst of an alcoholic liquid, in the man- 

 ner indicated in my Second Series of researches. This being- 

 admitted, it will be seen that this small mass of liquid must have 

 a figure of equilibrium proper to itself : its transverse curvature, 

 however, being enormous as compared with its longitudinal cur- 

 vature, we may disregard the influence of the latter, and reason 

 as if the small liquid mass were straight ; but in this case capil- 

 lary equilibrium evidently requires that the transverse curvatures 

 of the three small surfaces should be the same, whence it follows 

 that the angles formed by the three films must be equal : these 

 three films accordingly meet each other under angles of 120°. 



We may also make use of this equality for determining the 

 radius of the partition in terms of the radii of the other two 

 films, in which case we again arrive at the formula already given. 

 If we suppose a third hemispherical film to attach itself to the 

 other two, the whole group will necessarily contain three parti- 

 tions, which, upon the same principle, must meet each other 

 under angles of 120°. 



From this common value of the angles formed by the junction 

 of all the films under consideration, I deduce a simple graphic 

 method of constructing the base of a system formed by the union 

 of two or three hemispheres with the intermediate partitions, 

 the radii of the hemispheres after their partial interpenetration 

 being assumed to start with. 



I verify this construction by the following experiment : — The 

 base in question being drawn on paper in broad lines, the paper 

 is placed on a table and covered with a thin glass plate, whose 

 upper surface is moistened with the glycerine solution ; either 

 two or three bubbles of the same solution are next placed on the 

 glass above the parts of the drawing which represent the respect- 

 ive bases of the united hemispheres ; the bubbles then immedi- 

 ately form themselves into a partitioned system, and when, by 

 means of a slight artifice described in the memoir, the diameters 

 of the several hemispheres have been modified so as to bring 

 them into accordance with those of the drawing, the base of the 

 system of films so formed is found to be exactly superposable to 



