1893.] 



The Potential of an Anchor Ring. 



375 



8 c 



12loff 15 , 



VcV ^-* T2 \e) J * 



32 \c 

 &c. 



The results agree with those obtained by Mr. Hicks, via toroidal 

 functions. The Anted oscillations are very briefly discussed. 



6. The motion of a number of fine vortex rings on the same axis is 

 discussed. Equations are obtained giving the forward velocity and 

 the rate of increase of the radius for each ring. Let m x be the 

 strength, Ci the mean radius, a x the radius of the cross- section, z x the 

 distance of the centre of the ring along the axis of z. 



It is shown that the kinetic energy of the system is given by 



= 82 | 



COS clcjy 



-f- mim-i 



o Z \)'* + Ci— 2 dc 2 cos + c 3 2 } 



The equations of motion are 



i 3t .i 3t 



m x c Y z x = — • — . —m x c x Cx = — • 



The integral expressing the constancy of momentum takes the 

 simple form 



^(niiCi) = const. 



The following particular cases are worked out in detail : — 



1. The motion of a ring following another of equal strength. 



2. The direct approach of a ring to a fixed plane. 



3. The motion of a ring over a spherical obstacle. 



IV. "Analogy of Sound and Colour. — Comparison of the Seven 

 Colours of the Rainbow with the Seven Notes of the 

 Musical Scale, as determined by the Monochord, and of the 

 Wave-lengths of Colour and Sound." By J. D. MACDOXALD, 

 M.D., F.R.S. Received March 13, 1893. 



