TRANSACTIONS OF SECTION A. 



577 



Liveing and Dewar give 3 Angstrom's units as their probable error. Accord- 

 ing to that the formula might be absolutely correct. However, our other 

 formulas do not agree quite so well with the observations. They contain series 

 of liues in the spectra of thallium, potassium, sodium, tin, zinc, and magnesium. 

 As the spectrum defines an element, so the constants of the formula may be said 

 to define the element. Possibly they will be found to be in some connection -with 

 the atomic weight. 



5. A Vortex Analogue of Static Electricity. 

 By Professor W. M. Hicks, M.A., F.B.S. 



Consider two bodies in contact placed in an infinite fluid, and with a vortex 

 filament the ends of which are one on one surface, the other on the other. If 

 now the surfaces be separated from one another, there will be formed at the 

 point where they separate a hollow vortex filament stretching from one to the 

 other, with rotation equal and opposite to that of the original filament. As the 

 bodies are moved apart these filaments will not in general take up a position 

 of rest. If the strength of the original filament be very great, or if there be 

 several of them, the resulting hollow vortex wiU, through instability, split up into 

 a number of smaller ones. 



If the resulting number be very large they -will idtimately take up some 

 position of stable equilibrium. "What the distribution in this jcase will be I cannot 

 say, but the following is one state of equilibrium and probably, although I have 

 not proved it, a stable one. The two sets of filaments -will be mixed up A^ath each 

 other, and each -will distribute itself according to the same law as the distribu- 

 tion of lines of force between the two bodies supposed equally and oppositely 

 electrified. 



In the case of the original filaments, as the surfaces are further and further 

 separated, their sections become smaller and smaller. This is, however, not the 

 case with the hollow filaments. Their section depends only on the pressure of the 

 fluid and their circulation, and as these remain constant the areas of their section 

 also remain so. In such a hollow^ vortex the pressure inside sinks to zero. Con- 

 sequently the portion of the surface on which it abuts experiences a diminution of 

 pressure, a diminution which is the same at all distances. The two bodies are 

 therefore attracted. Moreover, as the two bodies separate further, the distribution 

 of the filaments being the same as that of electrical lines of force, and the dimi- 

 nution of pressure for each line being constant, it follows that the force between 

 the two bodies follows precisely the same laws as the force between the two bodies 

 supposed equally and oppositely electrified. It can be shown that the effect of the 

 original filaments is similar, the diminution of pressure being half as large again 

 as for the hollow vortices. 



If another surface be brought into the presence of the others, some of the 

 1888. p p 



