Royal Society. 465 



collected, and the remaining ore would bring a much higher 

 price than it does at present. 



Other methods have been tried with success, so far as the fact 

 of ca])ability goes, to arrange the furnace, the draught, the heat, 

 and the mixture of ores, so as to convert the copper into the 

 state of a soluble sulphate ; the ore is afterwards boiled in water, 

 to which, after passing from the ore, is added metallic iron, 

 which precipitates the copper in the metallic state ; but no method 

 has yet surpassed in point of oeconomy the ordinary single bed 

 calciner. However, we must not forget the fact, that at least 

 30,000 tons of sulphur of the value of about .€300,000 pass 

 into the atmosphere every year in the compass of a few miles, 

 which somewhat reflects upon our character as practical men 

 desirous of turning all things to account. 

 [To be continued.] 



LXXIV. Pfoceedinffs of Learned Societies. 



ROYAL SOCIETY. 

 [Continued from p. 393.] 

 May 27 " A NALYTICAL Researches connected with Steiner's 

 1852. -ty. ExtensionofMalfatti's Problem." By Arthur Cay- 

 ley, M.A., Fellow of Trinity College, Cambridge. Communicated 

 by J. J. Sylvester, Esq., F.R.S, 



The problem, in a triangle to describe three circles each of them 

 touching the two others and also two sides of the triangle, has been 

 termed after the Italian geometer, by whom it was proposed and 

 solved, Malfatti's Problem. The problem to which the author refers 

 as Steiner's extension of Malfatti's Problem, is as follows : " To de- 

 termine three sections of a surface of the second order, each of them 

 touching the two others, and also two of three given sections of the 

 surface of the second order," a problem proposed in Steiner's me- 

 moir ' Einige Geometrische Betrachtungen,' Crelle, t. i. The geome- 

 trical construction of the problem in question is readily deduced 

 from that given in the memoir just mentioned for a somewhat less 

 general problem, viz. that in which the surface of the second order 

 is replaced by a sphere ; it is for the sake of the analytical develop- 

 ments to which the problem gives rise that the author proposes to 

 resume here the discussion of the problem. The following is an 

 analysis of the present memoir : — 



§ 1. Contains a lemma which appears to the author to constitute 

 the foundation of the analytical theory of the sections of a surface of 

 the second order. 



§ 2. Contains a statement of the geometrical construction of 

 Steiner's extension of Malfatti's problem. 



§ 3. Is a verification, founded on a particular choice of co-ordi- 

 nates, of the construction in question. 



Phil. May. S. K Vol. 4. No. 27. Dec, 1853. 3 II 



