VIl] 



OF LAMARLE'S LAW 



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. 



When we have four bubbles in conjunction, they would seem 

 to be capable of arrangement in two symmetrical ways : either, 

 as in Fig. 116 (A), with the four partition- walls meeting at right 

 angles, or, as in (B), with^ve partitions meeting, three and three, 

 at angles of 120°. This latter arrangement is strictly analogous 

 to the arrangement of three bubbles in Fig. 114. Now, though 

 both of these figures, from their symmetry, are apparently figures of 

 equilibrium, yet, physically, the former turns out to be of unstable 



Fig. 116. 



and the latter of stable equilibrium. If we try to bring our four 

 bubbles into the form of Fig. 116, A, such an arrangement endures 

 only for an instant ; the partitions glide upon each other, a median 

 wall springs into existence, and the system at once assumes the 

 form of our second figure (B). This is a direct consequence of the 

 law of minimal areas : for it can be shewn, by somewhat difficult 

 mathematics (as was first done by Lamarle), tbat, in dividing a 

 closed space into a given number of chambers by means of partition- 

 walls, the least possible area of these partition- walls, taken together, 

 can only be attained when they meet together in groups of three, 

 at equal angles, that is to say at angles of 120°. 



