On the RadioactiviUi of Metals generaUf/, 343 



after Gauss, beoins his later paper {Leipziger Berichte, 

 vol. vii, (1855)) by stating- that he had recently become con- 

 vinced that the chief proi)erties of a system of lenses can be 

 tlednced by a purely oeometric method much more easily 

 than by continued fractions. But in the actual working out 

 of his method, he uses continued fractions after all. To 

 mention more recent writers, Herman in his lately published 

 Treatise bases his treatment on the well-known optical theorem 

 of Cotes ; but the symbolic expressions involved in that 

 theorem seem quite as complicated as continued fractions. 

 And Chrystal, in his paper in the Proceedings of the Edin- 

 burgh Mathematical Society, vol. xiv. (1895), gives a very 

 concise and complete summary of the theory, avoiding inter- 

 mediate calculations, but purely algebraic in its character. 



I may mention that I had worked out the foregoing method 

 in all its main features and in its chief details when my 

 acquaintance with the theory of the cardinal points was 

 derived solely from the treatises of Heath and of Herman, 

 and the paper by Chrystal. On looking up the literature 

 bearing on the subject that was accessible to me^ I found 

 that, so far as details are concerned, very much had been 

 anticipated by previous Avriters, amongst whom I might 

 specially mention Bravais (A7in. de Chimie et de Physique, 

 3rd ser. vol. xxxiii. (1851)) who points out the existence of 

 what I have called the vertex for a point ; and A. Martin 

 {ibid. -Ith ser. vol. x. (1867)) who develops the ideas of Gauss, 

 Bravais, Yerdet, and Listing, and who points out the existence 

 of what I have called the base-plane for an axial point {plan 

 refracteur) ; as well as Mobius and Clerk Maxwell, already 

 mentioned. 



But I did not find any anticipation of my fundamental idea 

 of method ; and the very considerable simplification I have 

 been able to introduce into the geometric treatment of the 

 subject seems to me to justify publication. 



XLII. On the Radioactivity of Metols generally. By J. C. 

 McLexxax and E. F. Burton, University of Toronto"^. 



Introduction. 



IN a former paper by the authors t on the conductivity of 

 a mass of ordinary air confined within a large metallic 

 receiver, it was shown that about 37 per cent, of the con- 

 ductivity was due to an exceedingly penetrating radiation 



* Communicated bv the Authors : read before the Eoval Society of 

 Canada, May 18, 1903. 



t Phvs. Eeview, vol. xvi. No. 3, p. 184 (1903). 



