xvj AND OF SEA URCHINS 665 



in the shell, and, hke so many long cables, moor the animal to 

 the ground. They constitute a symmetrical system of forces, 

 with one resultant downwards, in the direction of gravity, and 

 another outwards in a radial direction; and if we look upon the 

 shell as originally spherical, both will tend to depress the sphere 

 into a flattened cake. We need not consider the radial component, 

 but may treat the case as that of a spherical shell symmetrically 

 depressed under the influence of gravity. This is precisely the 

 condition which we have to deal with in a drop of liquid lying on 

 a plate; the form of which is determined by its own -uniform 

 surface-tension, plus gravity, acting against the uniform internal 

 hydrostatic pressure. Simple as this system is, the full mathe- 

 matical investigation of the form of a drop is not easy, and we 

 can scarcely hope that the systematic study of the Echinodermata 

 will ever be conducted by methods based on Laplace's differential 

 equation * ; but we have no 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 gravity. We can represent the phenomenon by 

 using india-rubber balls filled with water, of different sizes ; the 

 little 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 w^hen we let drops of 

 heavy oil (such as the orthotoluidene spoken of on p. 219), 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. 328). In a very few cases, 

 such as the fossil Palaeechinus, we have an approximately spherical 



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



