372 



Mr. F. W. Dyson. 



[Apr. 20, 



advance towards the more refrangible parts of the spectrum in the 

 inverse order of their atomic weights.* The correlation of the 

 spectral reactions of thallium, indium, and gallium with the other 

 properties of these elements is of further interest from the fact that 

 their arc spectra (below the ultra-violet) are represented by homo- 

 logous pairs of lines in the order of their atomic weights. Tl = 204 ; 

 X6560, 5349. In = 113-4 ; A, 4510, 4101. Ga = 70 ; \ 41 70, 4031. The 

 intervals of space between each homologous pair of lines, as will be 

 seen, increase in the same order. These relations are further repre- 

 sented in the subjoined diagram, reduced from the scale of 

 Angstrom's normal spectrum. 



It would be interesting to know if the arc spectrum of scandium 

 is represented by a similar pair of lines in the ultra-violet, as I have 

 already suggested in the paper referred to before this elementary 

 substance was discovered. 



III. " The Potential of an Anchor Ring." By F. W. Dyson, 

 M.A., Fellow of Trinity College, Cambridge, Isaac Newton 

 Student in the University of Cambridge. Communicated 

 by Professor J. J. Thomson, F.R.S. Received March 16, 

 1893. 



(Abstract.) 



1. This paper is a continuation of some researches on rings published 

 in the ' Phil. Trans./ 1893. In that paper the potential of an anchor 

 ring was found at all external points ; here it is determined for 

 internal points. The annular form of rotating gravitating fluid was 

 considered ; the stability of such a ring is investigated here. In 

 addition, the potential of a ring of elliptic cross-section, being of 

 interest in connexion with Saturn, is obtained. Besides this, the 

 similarity of the methods and of the analysis employed has led 

 me to put in this paper also the determination of the steady motion 

 of a single vortex ring of finite cross-section and the motion of 

 several fine vortex rings on the same axis. 



2. Let the figure represent a section through the axis Oz of an 

 anchor ring. O is the centre of the ring, C the centre of the cross- 

 section, P any point inside the ring. 



Let OC = c, CA = a, CP =11, z ACP = X - 



Then it is shown that 



* c Proceedings and Memoirs of the Manchester Lit. and Phil. Society,' 1878— 

 1886. 



