418 



Mr. F. W. Dyson. 



[May 5, 



differing materially from the rest of the series. The purple alloy of 

 gold and aluminium M, AuAl 2 , is almost certainly a true chemical 

 compound, the solidified mass being as nearly uniform in composition 

 as may be. The uniformity of the alloy (J) of platinum with 10 per 

 cent, of rhodium is of much interest, in view of the important part 

 which the alloy is playing in pyrometric work. 



Conducting the experiments, the results of which are embodied in 

 the present paper, has been very laborious, and although, as already 

 stated, no complete series of the alloys of any two metals has been 

 examined, quite sufficient data have been collected to afford valuable 

 guidance to the metallurgist, who will now know what behaviour 

 may be expected from the other members of the groups of the alloys 

 in question. The gold-platinum series of alloys are of industrial im- 

 portance, as native gold is so often associated with platinum, and it 

 is somewhat surprising to find that assays made on pieces of metal 

 cut from the exterior of an ingot cannot be trusted to represent the 

 composition of the mass. The aim of the investigation has been to 

 show, that notwithstanding the great difficulty which attends the 

 preparation of alloys of metals with very high melting points, it is 

 possible to elicit from them the same kind of information which has 

 proved to be so useful in the case of the more ordinary and tractable 

 alloys. 



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

 Fellow of Trinity College, Cambridge. Communicated by 

 Professor J. J. Thomson, F.R.S. Received March 19, 1892. 



(Abstract.) 



If r, 0, be the coordinates of any point outside an anchor ring, 

 whose central circle is of radius c, then 



f 



Jo 



ddj 



o <v/(?* 2 + c 2 — 2 cr sin cos 0) 

 , , f *" cos deb 



and COS - n . „ ;tt 



J y/ir' + c*— 2cr sin # cos 0) 



are solutions of Laplace's equation, which are finite at all external 

 points and vanish at infinity. 

 Let these be called I and J. 



Then dljdz and dJ/dz are also solutions of Laplace's equation. 



Four sets of solutions are obtained by differentiating these integrals 

 any number of times with respect to c. 



Thus, I, dljdc, d 2 Ijdc 2 , &c, are all solutions of Laplace's equation, 

 finite at ail external points and vanishing at infinity. 



