470 



ATOM. 



quantity which in unit of time flows through any section of the same vort.-x 

 tube niuat be the same. Hence, at any section of a vortex tube the product 

 of the an* of the section into the mean velocity of rotation is the same. 

 Thia quantity is called the ftrrnyth of the vortex tube. 



A vortex tube cannot begin or end within the fluid; for, if it did, the 

 imaginary fluid, whose velocity components are a, /?, y, would be generated from 

 nothing at the beginning of the tube, and reduced to nothing at the end of it. 

 fTnnm if the tube has a beginning and an end, they must lie on the surface 

 of the fluid mass. If the fluid is infinite the vortex tube must be infinite, or 

 else it must return into itself. 



We have thus arrived at the following remarkable theorems relating to a 

 finite vortex tube in an infinite fluid: (1) It returns into itself, forming a 

 ring. We may therefore describe it as a vortex ring. (2) It always 

 of the same portion of the fluid. Hence its volume is invariable. (3) 



Its strength remains always the same. Hence the velocity of rotation at any 

 section varies inversely as the area of that section, and that of any segment 

 varies directly as the length of that segment. (4) No part of the fluid which 

 is not originally in a state of rotational motion can ever enter into that state, 

 and no part of the fluid whose motion is rotational can ever cease to move 

 rotationally. (5) No vortex tube can ever pass through any other vortex tube, 

 or through any of its own convolutions. Hence, if two vortex tubes are linked 

 together, they can never be separated, and if a single vortex tube is knotted 

 "ii itself, it can never become untied. (G) The motion at any instant of every 

 part of the fluid, including the vortex rings themselves, may be accurately 

 represented by conceiving an electric current to occupy the place of each vortex 

 ring, the strength of the current being proportional to that of the ring. The 

 magnetic force at any point of space will then represent in direction and mag- 

 nitude the velocity of the fluid at the corresponding point of the fluid. 



These properties of vortex rings suggested to Sir William Thomson* the 

 possibility of founding on them a new form of the atomic theory. The con- 

 ditions which must be satisfied by an atom are permanence in magnitude, 

 capability of internal motion or vibration, and a sufficient amount of possible 

 characteristics to account for the difference between atoms of different kinds. 



The small hard body imagined by Lucretius, and adopted by Newton, was 

 invented for the express purpose of accounting for the permanence of the pro- 



"On Vortex Atoms," Proc. Hoy. Soc. Edin., 18th February, 1867. 



