44 



CELL-DIVISION AND GROWTH 



II. i 



bubbles. If these two be now diminished, or the opposite two 

 enlarged, the surface of contact will be between the opposite 

 pair of larger bubbles. On the other hand, it is possible 

 to bring smaller opposite bubbles into contact, while the 

 larger ones remain apart. Again, on four bubbles lying in one 

 plane, four small ones may be superimposed in such a fashion 

 that while two lie at either end of the surface of contact, the other 

 two lie over between the two opposite large bubbles below. If 

 now the two latter small bubbles be enlarged, they will displace 

 the other two until all four come to lie not over but between the 



FIG. 24. Diagrams of systems of soap-bubbles. 



A-C, four small bubbles superimposed on four large ones. In A and B 

 the bubbles are not compressed ; in c the lower bubbles have been 

 circumscribed by a cylindrical vessel. In B the upper bubbles are small 

 enough to show the surface** of contact between each and the two 

 adjacent large bubbles below. These surfaces are invisible in A and c. 



D is a system of eight bubbles in one plane, four forming a cross in 

 the centre. 



In all figures notice the fifth contact surface or 'polar furrow'. 



bubbles below, the usual arrangement when four are super- 

 imposed on four (Fig. 24 A-C). 



The final disposition must depend, therefore, not merely on the 

 principles of least surfaces, but also, provided that the conditions 

 of that principle are fulfilled, on the sizes and initial arrange- 

 ment of the bubbles. 



It will hardly need pointing out that very many ova adopt 

 the form which presents the least external surface, that of a 



