294 Professor A. M. Worthington [May 18, 



complete circle after all is over, for there is generally some slight 

 disturbing lateral velocity which causes many to mingle again with 

 the central drop, or with each other. But even if only half or a 

 quarter of the circle is left, it is easy to estimate how many drops, 

 and therefore how many arms there have been. It may be mentioned 

 that sometimes the surface of the central lake of liquid, Figs. 14, 15, 

 16, 17, was seen to be covered with beautiful concentric ripples, not 

 shown in the figures. 



The question now naturally presents itself, why should the drop 

 behave in this manner? In seeking the answer it will be useful to 

 ask ourselves another question. What should we have expected the 

 drop to do ? Well, to this I suppose most people would be inclined, 

 arguing from analogy with a solid, to reply that it would be reason- 

 able to expect the drop to flatten itself, and even very considerably 

 flatten itself, and then, collecting itself together again, to rebound, 

 perhaps as a column such as we have seen, but not to form this 

 regular system of rays and arms and subordinate drops. 



Now this argument from analogy with a solid is rather mislead- 

 ing, for the forces that operate in the case of a solid sphere that 

 flattens itself and rebounds, are due to the bodily elasticity which 

 enables it not only to resist, but also to recover from any distortion 

 of shape or shearing of its internal parts past each other. But a 

 liquid has no power of recovering from such internal shear, and the 

 only force that checks the spread, and ultimately causes the recovery 

 of shape is the surface tension, which arises from the fact that the 

 surface layers are always in a state of extension and always en- 

 deavouring to contract. Thus we are at liberty when dealing 

 with the motions of the drop to think of the interior liquid as 

 not coherent, provided we furnish it with a suitable elastic skin. 

 Where the surface skin is sharply curved outwards, as it is at 

 the sharp edge of the flattened disc, there the interior liquid will 

 be strongly pressed back. In fact the process of flattening and 

 recoil is one in which energy of motion is first expended in creating 

 fresh liquid surface, and subsequently recovered as the surface con- 

 tracts. The transformation is, however, at all moments accompanied 

 by a great loss of energy as heat. Moreover, it must be remembered 

 that the energy expended in creating the surface of the satellite drops 

 is not restored if these remain permanently separate. Thus the sur- 

 face tension explains the recoil, and it is also closely connected with 

 the formation of the subordinate rays and arms. To explain this it 

 is only necessary to remind you that a liquid cylinder is an unstable 

 configuration. As you know, any fine jet becomes beaded and breaks 

 into drops, but it is not necessary that there should be any flow of 

 liquid along the jet ; if, for example, we could realise a rod of liquid 

 of the shape and size of this ruler and liberate it in the air, it would 

 not retain its cylindrical shape, but would segment or divide itself 

 up into a row of drops regularly disposed according to a definite 

 and very simple numerical law, viz. that the distances between the 



