Researches in Vortex Motion. 



335 



not yet been investigated. If the energy be increased sufficiently 

 the aperture becomes large compared with the thickness of the core 

 and approximate calculation is applicable. The differential equa- 

 tion for y in terms of toroidal co-ordinates is given, but the fuH 

 development is left for a future occasion. 



In the paper itself the problem is treated purely as a question of 

 hydrodynamics, and the results simply as the properties of certain 

 possible fluid motions. It may not, however, be out of place here to 

 offer a few remarks, of a more speculative kind, on the bearing of the 

 results on physical theories. 



In the first place, gyrostatic motion of the kind here considered is 

 not confined to aggregates, which are symmetrical about an axis. 

 Although the theory is very complicated, it is easy to see that they 

 must exist. In the address to Section A, at the Ipswich meeting of 

 the British Association, a vortex cell theory of the ether was indi- 

 cated. The ether consisted of closely packed elements, each element 

 being a vortex aggregate. To fix ideas, the case of elements of the 

 shape of a rectangular box was taken, although this particular shape 

 is not essential. The vortical motion there considered was not 

 gyrostatic, but it i-s clear that a gyrostatic modification is possible. 

 The primary rotations must be arranged in opposite directions in 

 alternate cells. This is, however, not necessarily the case with the 

 secondary gyrostatic motion. They may either be or not be in the 

 same direction, although conditions of stability might decide this 

 question. If the common direction is not a necessity,- it is easy to 

 conceive that certain operations on boundaries immersed in the ether 

 might make them so, and in this way produce the same effect as 

 vortex filaments stretching between them. Such a theory would not 

 necessitate return vortex filaments such as are required in any 

 theory which attempts to explain electrical actions by such filaments. 

 It is very conceivable that they would produce the stresses along and 

 perpendicular to tubes of force which are required in an electric 

 field. If a cell, such as that of the X 2 aggregates in this paper, were 

 possible, the necessity that the primary rotations should be alter- 

 nately directed would not exist, at least so far as continuity of motion 

 had to decide. 



In the second place, does the new theory throw any light on a 

 vortex atom theory of matter? In this respect two remarks should 

 be made. The first is, that if vortex atoms are realities the exact 

 quantitative theory developed in this paper cannot accord with actual 

 facts, because it is developed with reference to a surrounding irrota- 

 tional ether, which cannot be the case in nature. IsTeverthe^ss, many 

 of the general properties would doubtless be similar, and possibly 

 the same for aggregates of the X 2 family. 



The second remark is, that the results of the paper refer only to 



