TRANSACTIONS OF SECTION A. 601 



small vortex rings. Lord Kelvin' at the Mancliester lueetino- discussed the 

 question uuicli more thorouwlily and satisfactorily, and deduced that the velocity 

 of propagation was \/-/-j times tbe velocity of mean square of the turbulent 

 motion. We can make little further progress until we know something of the 

 arrangement of the small motions which confer the quasi-rigidity. This may be 

 completely irregular and unsteady, or arranged in some definite order of steady 

 motions. I am inclined to the view that the latter is nearer the truth. In this 

 ease we should expect a regular structure of small cells iu which the motions are 

 all similar. 15y the word cell I do not mean a small vessel bounded by walls, but a 

 portion of the iluid in which the motion is a complete system in itself. ISuch a 

 theory might be called a cell theory of the elher. The simplest type perhaps is to 

 suppose the medium spaced into rectangular boxes, in each of whicb the motion 

 may be specified as follows. Holding the box with one set of faces horizontal 

 the fluid streams up in the centre of the box, then turns round, flows down tbe 

 sides and up the centre again. In fact it behaves like a Hill's vortex squeezed 

 from a spherical into a box form. Each box has thus rotational circulation 

 complete in itself. The six adjoining compartments have their motion the same in 

 kind but in the reverse direction, and so on. In this way we get continuous and 

 energetic small motions throughout the medium, and the state is a stable one. If 

 there is a shear, so that each cell becomes slightly rhomboidal, tbe rotational 

 motions inside tend to prevent it, and thus propagate the disturbance, but the cells 

 produce no efl'ect on the general irrotational motion of the fluid, at least when the- 

 irrotatlonal velocities are small compared with fhose of the propagation of light. 

 In this case the rate at which the cells adjust themselves to an equilibrium position 

 is far quicker than the rate at which this equilibrium distribution is disturbed by 

 the gross motions. The linear dimensions of the cells must be small compared 

 ■with the wave lengths of light. They must probably be small also compared with 

 the atoms of gross matter, which are themselves small compared with the same 

 standard. 



"We may regard each cell as a dynamical system by itself, into which we pour 

 or take away energy. This added energy will depend only on the shape into 

 which the box is deformed. AVe may then, for our convenience in considering the 

 gross motions of the medium as a whole, i.e. our secondary medium, regard these 

 as interlocked systems, neglect the direct consideration of the motions inside them, 

 but regard the energy which they absorb as a potential function for the general 

 motion. This potential function will contain terms of two kinds, one involving the 

 shear of the cells, and this shear will be the same as that of the rotational deforma- 

 tion in the secondary medium. The second will depend on alterations iu tbe ratios 

 of the edges of the cells.'- The former will give rise to waves of transversal displace- 

 ments. The second cannot be transmitted as waves, but may produce local ett'ects. 

 If a continuous solid be placed in such a medium, the cells will rearrange 

 themselves so as to keep the continuity of their motions. The cells will become 

 distorted (but without resultant shear), and a static stress will be set up. AVe have 

 then to deal with the primary stuft' itself, whose rotation gives a structure to the 

 ether, and the structural ether itself. The former we may call the primary medium. 

 The ether which can transmit transversal disturbances, and which is built up out of 

 the first, we may call the secondary medium. "Whether an atom of matter is to 

 be considered as a vortical mass of the primary or of the secondary medium 

 is a matter to be left open in the present state of the theory. 



At the Bath meeting of this Association, I sketched out atheory of the electrical 

 action of a fluid ether in which electrical lines of force were vortex filaments 

 combined with an equivalent number of hollow vortices of the same vortical 

 strength.^ An electaic charge on a body depended on the number of ends of fila- 

 ments abutting on it, the sign being determined by the direction of rotation of 

 the filament looked at from the body. This theory gave a complete account of 



' 'On the "Vortex Theory of the Luminiferous Ether,' Brit. Assoc. Repmis, 1887, 

 p. 486, also Phil. Mag., October 1887, p. 342. 



- Including other changes of form involving no rotations. 



' 'A Vortex Analogue of Static Electricity,' Brit. Assoc. Rep., 1888, p. 577. 



