20 



Sir William Thomson on Vortex Atoms, 



as its plane passes through the position of his eye, a convex* 

 outline of an atmosphere of smoke in front of the ring. This 



convex outline indicates the bounding surface between the quan- 

 tity of smoke which is carried forward with the ring in its mo- 

 tion, and the surrounding air which yields to let it pass. It is 

 not so easy to distinguish the corresponding convex outline be- 

 hind the ring, because a confused trail of smoke is generally left 

 in the rear. In a perfect fluid the bounding surface of the por- 

 tion carried forward would necessarily be quite symmetrical on the 

 anterior and posterior sides of the middle plane of the ring. The 

 motion of the surrounding fluid must be precisely the same as it 

 would be if the space within this surface were occupied by a 

 smooth solid ; but in reality the air within it is in a state of 



* The diagram represents precisely the convex outline referred to, and 

 the lines of motion of the interior fluid carried along by the vortex, for the 

 case of a double vortex consisting of two infinitely long, parallel, straight 

 vortices of equal rotations in opposite directions. The curves have been 

 drawn by Mr. D. M'Farlane, from calculations which he has performed by 

 means of the equation of the system of curves., which is 



2/ 2 _ 2# 

 a a 



N+l 

 N-l 



('+?)> 



where log e N= 



x+b 



The proof will be given in the mathematical paper which the author intends 

 to communicate in a short time to the Royal Society of Edinburgh. 



