Geological Society, 283 



of the actually existing elements will be finite and perfectly 

 determinate. The question is often'asked, " Why do there exist 

 only elements of a few definite atomic weights ? " From our 

 point of view the question is similar to the one, " Why can a 

 string give only definite notes ?" 



From the above considerations it appears to result clearly 

 that an analytical expression for e -F(jy) is more complicated 

 than is the case for the simple cotangent : an expression of 

 the form 



£=acos7r— — ( A + cotan ir „ J 



might suit better. But since the periods of the elements turn 

 out to be unequal (0 to ?, ? to 36, 36 to 84, 84 to 132, 

 132 to'168 ?, 168 to 216, 216 to 264 ?) the constants b, c, d,f, 

 A would be themselves independent of p. In such cases 

 trigonometrical functions offer no special advantage. It 

 might perhaps be simpler to take 



Ai Ao A? 



e— — + — — + — +... 



P~Pi P~P2 P-Pz 



or e = B (p-p f ) (p-p")(p-p" f )... 



where pi, p 2 , p% . . . denote the roots of the equation - = 0, 



p', p", p f// , . . . the roots of the equation <? = 0, and A 1? A 2 , 

 A 3 , . . . and B denote constants. 



XXIX. Proceedings of Learned Societies. 

 GEOLOGICAL SOCIETY. 



[Continued from p. 207.] 



May 13th, 1896.— Dr. Henry Hicks, F.R.S., President, 

 in the Chair. 



THE following communications were read : — 

 1. ' An Account of a Head or Gateway driven into the Eastern 

 Boundary-fault of the South Staffordshire Coal Field.' By William 

 Earnworth, Esq., F.G.S. 



The author describes certain peculiarities observed during the 

 driving of a head towards the fault separating the Coal Measures 

 and Permian rocks, from a pit situated 4 miles east of Walsall, at 

 the southern extremity of the Cannock Chase Coal Field. 



2. ' On the Geographical Evolution of Jamaica/ By J. W, 

 Spencer, M.A., Ph.D., E.G.S. 



The object of the paper is to set forth the physical and geological 



