AND THE ACTION OF TWO VORTICES IN A PERFECT FLUID. 
Case 1,—Vortices moving in the same direction. 
Fig 4. 
1. When the positions of the vortices when nearest together are as represented 
in fig. 4. 
The way in which their paths are deflected is indicated by the dotted lines. 
The vortex C D increases in radius and energy and its velocity is decreased. 
Case II.—Vortices moving in opposite directions. 
The position of the vortices when nearest together is represented in fig. 5. 
The way their paths are deflected is indicated by the dotted lines in the figure. 
The vortex C D decreases in radius and energy and its velocity is increased. 
The vortex A B increases in radius and energy and its velocity is decreased. 
These results may be summed up in the following rule. The vortex which first 
passes through the point of intersection of the directions of motion of the vortices 
is deflected towards the direction of motion of the other : it increases in radius 
and energy and its velocity is decreased; the other vortex is deflected in the same 
direction : it decreases in radius and energy and its velocity is increased. 
(Note added March 21st, 1882.) 
Sir William Thomson has pointed out to me that when n is very great the time 
of vibration of the single vortex which for this case is (equation 23) 
/cr27T 3 e 3 . nl 
7 re 
when l is the wave-length 27 ra/n, does not agree infinitely nearly as it ought with the 
value obtained by him for the rapidity of the transverse vibrations of a straight 
