308 



Dr. W. Ramsay and Mr. S. Young. [June 21, 



tangent from the centre to the ring, and is therefore equal to R for 

 small rings — and j* is the cyclic constant. For a solid ring, with the 

 same notation, 



V=^-(log 4 ~2\ 



Tn the steady motion considered, the fluid carried forward with the 

 ring forms a single mass without aperture, even for extremely small 

 cores, though not for infinitely small ones. For values of R/r>10 3 

 there will be no aperture, whilst for less values the fluid carried for- 

 ward will be ring-shaped. To a first approximation the energy due 

 to the cyclic motion is the most important, and is the same as for a 

 rigid ring at rest of the same size, it does not depend on the velocity 

 of translation, except in so far as this determines the size of the 

 aperture ; as entering in this way the principal term varies inversely 

 as the velocity of translation, and thus increases with diminished 

 translatory motion, a result obtained by Sir W. Thomson* from 

 general reasoning. The terms obtained by the second approximation 

 arise from the translatory motion. 



Lastly, the times of vibration in classes (2) and (4) above are 

 determined, when the ring moves steadily. In class (2), or for fluted 

 vibrations, the time of vibration for small rings is given very 

 approximately by /adj (2p */n), d being the density, andp the pressure 

 of the fluid at a great distance, whilst n is the number of crimpings 

 in a section. This is the proof of the statement made above as to 

 the independence of the temperature. In class (4) the time of pul- 

 sation is (fid/2p) v / (log4/7£). As h depends on the size of the ring, 

 and therefore on the energy, this time is not independent of the 

 latter, but varies slowly with it. The times here given must be 

 understood as applying to rings moving steadily ; when a ring is 

 changing its size they must be modified. The investigation of this 

 case, and of that in which there is a core of denser matter than the 

 surrounding fluid, I hope shortly to take up. 



III. " Influence of Pressure on the Temperature of Volatilization 

 of Solids." By William Ramsay, Ph.D., and Sydney 

 Young, B.Sc. Communicated by Sir Andrew Ramsay, 

 LL.D., F.R.S. Received June 5, 1883. 



(Abstract.) 



The experiments described in the paper were undertaken in order 

 to ascertain whether solids have definite volatilizing points, under 

 * " Vortex Atoms," " Proc. Roy. Soc. Edin.," yi j " Phil. Mag.," (4), 34. 



