18810 



Vibrations of a Vortex Ring, §c. 



145 



Percentage of iodide of silver in Temperature at which con- 



the copper-silver iodide alloys. traction on heat commences. 



38-2232 284° C. 



55-3066 233 



64-9884 214 



71-2225 199 



88-1304 153 



Tims while 66*206 per cent, of iodide of lead lowered the point of 

 change 18° C, the presence of 61*7767 per cent, of iodide of copper 

 raised it 142° C. 



9. The possible causes of these results are discussed. 



10. The lead-silver iodide alloy is compared with the copper-silver 

 iodide alloy, as to structure, properties, &c. 



11. The results of the microscopic examinations of these alloys is 

 given, and shown by drawings. 



12. The special properties of each alloy are described. 



Erratum. — " Proc. Roy. Soc," vol. 32, p. 550, 16 lines from 

 bottom of page : for " more than twenty times," read " nearly 

 four times." 



X. " On the Vibrations of a Vortex Ring, and the Action of 

 Two Vortex Rings upon each other.' 7 By J. J. THOMSON, 

 B.A., Fellow of Trinity College, Cambridge. Communi- 

 cated by Lord Ratleigh, F.R.S. Received November 16, 

 1881. 



(Abstract.) 



In the first part of the paper it is shown that if the circular axis of 

 a vortex ring be displaced so as to be represented by the equations — 



p = a + a il cos nd, 



z = /3 K cos nd. 



when p is the distance of a point on the circular axis from the 

 straight axis, and z the distance of a point on the circular axis from 

 its mean plane, then — 



a,i — A cos log — n V ' ri l — 1 . t + b\ 



\ 2a" e J 



/»,= A V ^~ 1 sin f-^log =£» v/^=l . t+B), 

 n \2a 2 e J 



when w is the angular velocity of molecular rotation, e the radias 

 of the cross section of the vortex core, and a the radius of the aper- 



