VIl] 



OF CELL-PARTITIONS 



301 



according to what we have already learned, upon the relative 

 magnitudes of the tensions at the surface of the cells and at the 

 boundary between them*. 



In the typical case of an equally divided cell, such as a double 

 and co-equal soap-bubble, where the partition-wall and the outer 

 walls are similar to one another and in contact with similar sub- 

 stances, we can easily determine the form of the system. For, at 

 any point of the boundary of the partition-wall, 0. the tensions 

 being equal, the angles QOP, ROP, QOR are all equal, and each 

 is, therefore, an angle of 120°. But OQ, OR being tangents, the 

 centres of the two spheres (or circular arcs in the figure) lie on 

 perpendiculars to them ; therefore the radii CO, CO meet at an 



Fig. 108. 



angle of 60°, and COC is an equilateral triangle. That is to say, 

 the centre of each circle hes on the circumference of the other; 

 the partition lies midway between the two centres ; and the 

 length (i.e. the diameter) of the partition-wall, PO, is 



2 sin 60° - 1-732 



times the radius, or -866 times the diameter, of each of the cells. 

 This gives us, then, the form of an aggregate of two equal cells 

 under uniform conditions. 



As soon as the tensions become unequal, whether from changes 

 in their own substance or from differences in the substances with 

 which they are in contact, then the form alters. If the tension 



* In an actual calculation we must of course always take account of the tensions 

 on both sides of each film or membrane. 



