428 



Mr. L. N. G. Filon. On the Resistance 



6. The amount of absorption produced by a given thickness of a 



solution of a metallic salt is not proportional to the amount of 

 salt in solution, but appears to follow approximately a loga- 

 rithmic law. 



7. The amount of absorption varies logarithmically with the thickness 



of the solution traversed by the rays. The percentage absorp- 

 tion may be represented by an equation of the form r = log 

 (Xt + /x) where X is a constant depending on the nature of the 

 solution, and on the penetrative power of the X rays, and t is 

 the thickness of the solution traversed. 



It is to be noticed that all the above tables and conclusions are based 

 on measurements made with solutions containing the equivalent weight 

 of the salts, in grams per litre, so that the molecular absorption of the 

 salts with divalent or trivalent bases is greater than that indicated in 

 the tables. 



The conclusions 1, 5, and 7, given above, are in exact agreement 

 with those stated by Dr. Gladstone and Mr. Hibbert in their articles 

 in the ' Chemical News ' (loc. cit.). 



Numerous references have been made throughout this paper to their 

 articles and reports before the British Association, though it was not 

 until the above investigations were nearly completed that attention 

 was drawn to the work that had been done by them. 



" On the Eesistance to Torsion of certain Forms of Shafting, with 

 special Eeference to the Effect of Key ways." By L. N. G. 

 Filon, M.A., Besearch Student of King's College, Cambridge, 

 Fellow of University College, London, 1851 Exhibition 

 Science Besearch Scholar. Communicated by Professor M. 

 J. M. Hill. Beceived June 1, — Bead June 15, 1899. 



(Abstract.) 



The object of the present paper is to obtain solutions of the problem 

 of Torsion for certain cylinders, whose cross-sections are bounded by 

 confocal conies. It is mainly an extension of de Saint- Venant's in- 

 vestigations, and is based upon his general equations of torsion. 



The method employed depends upon the use of conjugate functions 

 £ and rj, such that £ = const, represents confocal ellipses and = const, 

 confocal hyperbolas. 



The use of conjugate functions for the torsion problem has been 

 suggested by Thomson and Tait,* by Clebsch,f and by Boussinesq4 



* ' Natural Philosophy.' 



f ' Theorie cler Elasticitat fester Korper,' §§ 33 — 35. 



X ' Journal de Mathematiques,' pp. 177 — 186, serie 3, vol. 6. 



