of Moving Vortex-rings. 69 



drawn, the vortex-velocity at centre is only a trifle greater 

 than the translational velocity. This plate also represents 

 the lines of magnetic force due to a circular current with a 

 repellent pole on its axis, at a point 2*518 diameters away 

 from the plane of ihe circle. The dots on the curves indicate 

 the distribution of the crossing-points which guide the drawing. 

 Plate IV. shows the attempt of a ring to advance in an 

 oblique direction, not normal to its plane. It is supposed to 

 have been knocked out of a hole by a slant impulse. There 

 is evidently a good deal of vibration, both of ihe ring as a 

 whole and of its cross section ; and it looks as though a very 

 little would suffice to break it up altogether. The resultant 

 velocity at the centre of the ring happens, in the particular 

 case here chosen, to be about zero. 



In cases of oblique progression a tendency to a bodily shifting 

 of the uniform flow-lines, parallel to themselves, as they pass 

 from before to behind the ring, is noticeable, and is exhibited 

 in rig. 1. Perhaps this means a heaving or sinuous path of 

 motion for the ring. The right mode of joining up the 

 guiding-points is however in this case by no means obvious ; 

 and fig. 2 (Plate IV.) is just as likely to be correct as fig. 1. 

 In fig. 2 no shifting of distant stream-lines occurs, but then 

 it hardly seems a real case of vortex-motion : at least it looks 

 only like a ring shaking itself to pieces ; while fig. 1 suggests 

 an attempt of the same ring to pull itself together. 



I have a number of other diagrams drawn in the rough, in- 

 dicating various features of the clash or chase of vortex-rings. 

 The direct clash of two equal opposite rings, or the impact 

 of one against a looking-glass, is of course very easy. The 

 clash of two rings of different strength is more complex — one 

 appears to be opened out over the other. 



The chase of two unequal rings, and the penetration of the 

 front one by its pursuer, are well shown ; but if the rings are 

 of equal strength they refuse to penetrate, and seem to amal- 

 gamate or pair, no matter at what different speeds they may 

 be going. 



The deflection of one ring by another whose path is inclined 

 to it, as calculated by Prof. J. J. Thomson in his * Adams 

 Essay,' * can also be illustrated, together with what I think 

 corresponds to vibrations of the core about the circular form. 

 But all these diagrams I propose to publish in a more 

 complete form later. This " experimental " method of investi- 

 gation, by diagrams based on simple superposition of velocities, 

 seems capable of great extension, because one is limited by no 

 approximations or conditions : the only difficulty is the inter- 

 pretation of results. 



* See also Phil. Trans, ii. 1882. 



