946 ON THE SHAPES OF EGGS [ch. 



on Laplace's diiferential equation*; but we have little difficulty in 

 seeing that the various forms represented in a series of sea-urchin 

 shells are no other than those which we may easily and perfectly 

 imitate in drops. 



In the case of the drop of water (or of any other particular liquid) 

 the specific surface-tension is always constant, and the pressure 

 varies inversely as the radius of curvature; therefore the smaller 

 the drop the more nearly is it able to conserve the spherical form, 

 and the larger the drop the more does it become flattened under 

 gravityf. We can imitate this phenomenon by using india-rubber 

 balls filled with water, of different sizes ; the httle ones will remain 

 very nearly spherical, but the larger will fall down "of their own 

 weight," into the form of more and more flattened cakes; and we 

 see the same thing when we let drops of heavy oil (such as the 

 orthotoluidene spoken of on p. 370) fall through a tall column of 

 water, the httle ones remaining round, and the big ones getting 

 more and more flattened as they sink. In the case of the sea-urchin, 

 the same series of forms may be assumed to occur, irrespective of 

 size, through variations in T, the specific tension, or "strength" 

 of the enveloping shell. Accordingly we may study, entirely from 

 this point of view, such a series as the following (Fig. 454). In 

 a very few cases, such as the fossil Paheechinus, we have an 

 approximately spherical shell, that is to say a shell so strong that 

 the influence of gravity becomes negligible as a cause of deformation, 

 just as (to compare small things with great) the surface tension of 

 mercury is so high that small drops of it seem perfectly spherical {. 

 The ordinary species of Echinus begin to display a pronounced 

 depression, and this reaches its maximum in such soft-shelled flexible 

 forms as Phormosoma. On the general question I took the oppor- 



♦ Cf. Bashforth and Adams, Theoretical Forms of Drops, etc., Cambridge, 1883. 



t The drops must be spherical, or very nearly so, to produce a rainbow. But the 

 bow is said to be always better defined near the top than down below; which seems 

 to shew that the lower and larger raindrops are the less perfect spheres. (Cf. 

 T. W. Backhouse, Symons's M. Met. Mag. 1879, p. 25.) For the small round 

 droplets in the cloud tend to cannon off one another, and remain small and spherical. 

 But when there comes a diflference of potential between cloud and cloud, or be- 

 tween earth and sky, then the spherules become distorted, one droplet coalesces 

 with another, and the big drops begin to fall. 



X Cf. A. Ferguson, On the theoretical shape of large bubbles and drops, Phil. Mag. 

 (6), XXV, pp. 507-520, 1913. 



