Let us return to our problem of the arrangement of partition films. When we have three bubbles in contact, instead of two as in the case already considered, the phenomenon is strictly analogous to our former case. The three bubbles will be separated by three partition surfaces, whose curvature will depend upon the relative size of the spheres, and which will be plane if the latter are all of the same dimensions; but whether plane or curved, the three partitions will meet one another at an angle of 120°, in an axial line. Various pretty geometrical corollaries accompany this arrangement. For instance, if Fig. 114 represent the three associated bubbles in a plane drawn through their centres, _c_, _c′_, _c″_ (or what is the same thing, if it represent the base of three bubbles resting on a plane), then the lines _uc_, _uc″_, or _sc_, _sc′_, etc., drawn to the {308} centres from the points of intersection of the circular arcs, will always enclose an angle of 60°. Again (Fig. 115), if we make the angle _c″uf_ equal to 60°, and produce _uf_ to meet _cc″_ in _f_, _f_ will be the centre of the circular arc which constitutes the partition _Ou_; and further, the three points _f_, _g_, _h_, successively determined in this [Illustration: Fig. 115.] manner, will lie on one and the same straight line. In the case of coequal bubbles or cells (as in Fig. 114, B), it is obvious that the lines joining their centres form an equilateral triangle; and consequently, that the centre of each circle (or sphere) lies on the circumference of the other two; it is also obvious that _uf_ is now {309} parallel to _cc″_, and accordingly that the centre of curvature of the partition is now infinitely distant, or (as we have already said), that the partition itself is plane. [Illustration: Fig. 116.]