HERMANN VON HELMHOLTZ 



and the second, , will become narrower, and suffer 

 acceleration, b ultimately overtaking a, and, under 

 favourable conditions, passing through it. Then they 

 will separate and again follow each other, but b will 

 widen, and a contract, until a will pass through b. 

 Thus the vortex rings will pass alternately through 

 each other. On the other hand, if the coaxial rings 

 have equal radii and equal rotational movements, but 

 in opposite senses, they will approach each other 

 and suffer distension, and this mutual approach and 

 simultaneous spreading out will go on indefinitely 

 until the rings are infinitely close and infinitely 

 wide. 



In an incompressible frictionless fluid rotatory 

 movements can neither originate nor disappear ; the 

 vorticity, or product of any section of the ring and 

 the speed of rotation, then is an unchangeable 

 quantity. As they move in the surrounding fluid 

 they are always composed of the same particles. 

 Thus the vortex rings have perpetuity. They may 

 jostle against each other and undergo endless 

 changes of form, but they cannot be broken or 

 dissolved. They have the indestructibility which is 

 believed to belong to the ultimate constituents of 

 matter. Lord Kelvin made Helmholtz's investi- 

 gation the basis of the splendid hypothesis, that the 

 atoms of matter are composed of minute vortex 

 rings in the ether, and he worked out in detail 

 the analogy between such rotational movements and 

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