October 29, 1908] 



iVA 7 URE 



665 



When this serius pi-ocf-tds to infinity tlie terms contain- 

 ing X, under certain conditions, vanisli. So also they 

 vanish if any proximate number is substituted for x in 

 them. We are thus left with .v, on the left side, equated 

 to a series containing only k and the coefficients a, b, 

 <:.... This explains why we may start the process 

 described at the beginning of this paper with any number 

 (under certain limitations) for .Vj, because, whatever that 

 number may be, it is gradually rendered negligible by 

 the successive operations. 



The series has been already studied to some extent in 

 the paper referred to, and has been used for solving equa- 

 tions. Its coefficients are simply those of the multinomial 

 theorem with some modifications. .\s it has n values de- 

 pending on the I! values of v'-", we may suppose that these 

 values are the n roots of the original equation, though 

 we may not be able yet to evaluate all of them. This 

 has been proved in the previous paper to be the case, 

 because the sums of the products of the values talcen one, 

 two, three . . . times together are equal to the successive 

 coefficients of the original equation with the proper signs. 

 Hence there are some reasons for thinking that the series 

 theoretically constitutes the general trausccndcutal solution 

 of the equatiap of the nth degree. How far this is really 

 the case must be discussed more fully on another occasion, 

 together with details and developments of the method out- 

 lined above. 



The method is not the same as the methods of approxi- 

 mation of Xcwton, Lagrange, and Horner. The well- 

 known ascending power series for the reversion of a func- 

 tion, and cases in which certain repeated operations (such 

 as continued fractions) converge to a root of an equation, 

 thus solving certain functional and difference equations, 

 arc only particular instances of the above theorem. 



RoN.iLD Ross. 



The Nature of X-Rays. 



In a letter to N.«UKE of July 30 Prof. Bragg tries to 

 show that his neutral-pair theory of X-rays may form the 

 basis of an explanation of the secondary X-ray phenomena 

 which I 'briefly summarised in an earlier letter (May 7). 

 He, however, neglects the consideration of so much 

 important evidence that I cannot attempt to reply In detail. 

 In reply to his discussion of statements (3), (6), and (5), I 

 need only state that he has confused two distinct types of 

 secondary X-radiatlon, and that his statement of Mr. 

 Crowther's results is inaccurate when applied, as he 

 applies it, to the scattered radiation alone. (May I also 

 be permitted, in passing, to point out that both the general 

 results attributed to Mr. Crowther had been published 

 by the writer previous to the publication of Mr. Crowther's 

 paper ?) 



.\gain. Prof. Bragg has evidently overlooked the work 

 to which I referred in statements (7), (8), and (9). The 

 evidence which I put forward for consideration was not 

 the older work of M. Sagnac, Dr. Walter, and Mr. Adams 

 which Prof. Bragg discusses, but the results of experi- 

 ments by Mr. Sadler and myself on homogeneous beams 

 of X-rays, which have not yet been published in full, 

 though preliminary notices had appeared in Nature. The 

 paper giving an account of this work was read before the 

 London Physical Society on June 12. Prof. Bragg, as a 

 consequence, docs not discuss the points with full Icnow- 

 ledge of experimental facts. 



Of the three remaining points, one — the polarisation of 

 .1 t^iiinary beam (i) — is not discussed, because Prof. Haga 

 has been unable to verify it by a much cruder method than 

 (hat originally eniploved. It is nevertheless a phvsical 

 fact. 



Finally, two results — the polarisation in scattered radia- 

 tion (4) and the equality in the penetrating powers of 

 primary and secondary (scattered) rays (2) — which appear 

 possible to Prof. Bragg on the neutral-pair theory, require 

 assumptions which, to my mind, are extremely doubtful. 

 On the other hand, many of these results were foretold on 

 the ether pulse theory, and, indeed, they all find an easy 

 explanation on this theory, as I believe Prof. Bragg will 

 readily admit when he has become fully acquainted with 



XO. 2035, VOL. 78] 



the experiments. For a fuller discussion I can, unfor- 

 tunately, only refer to two unpublished papers, botli of 

 which, however, are In the press. These are the one 

 already referred to and one which will appear in the 

 forthcoming number of the " Jahrbuch der Radioaktivitat 

 und Elektronik." 



In reply to Prof. Bragg's contention, may I add that 

 the phenomena involving radiation of only one kind — 

 X-radiation — to me appeared simpler than those involving 

 two — X and 3 radiations? 



Liverpool, .August 8. Charles G. B.4RKLA. 



It is, of course, true that my letter (dated June 5) to 

 which Dr. Barkla refers was written before I had had 

 the opportunity of studying Dr. Barkla 's latest results. 

 .'\ portion of my argument was based on his earlier worlc, 

 and may need a little alteration in consequence. I have 

 myself found by recent experiment that his older state- 

 ments needed amendment. For example, the emergence 

 and Incidence secondary Rontgen radiations differ both in 

 quality and quantity ; the former is sometimes far greater 

 than the latter. 



May I take this opportunity of correcting a statement 

 In a letter of mine which appeared in N.ature of July 23? 

 .\s pointed out in an addendum to a recent paper con- 

 tributed by Dr. Laub to the Annalen der Physik, I have 

 been wrong in supposing that Dr. Wien still maintains 

 that the energy of the secondary kathode ray is drawn 

 from the energy of the atom. Had I understood Dr. 

 Wlon correctly, I should certainly not have taken so much 

 pains to disprove a theory which he had already 

 abandoned. W. H. Bragg. 



The L^niversltv of .Adelaide. September 17. 



The Supposed Inheritance of Acquired Characters. 



Dr. Francis Darwin, in his presidential address before 

 the British Association, writes as follows : — 



" Fischer showed that when chrysalids of Arclia cnja 

 are subjected to a low temperature a certain number of 

 them produce dark-coloured insects ; and further that these 

 moths mated together yield dark-coloured offspring. This 

 has been held to prove somatic inheritance, but Weismann 

 points out that it is explicable ty the low temperature 

 having an Identical effect on the colour-determinants e.xist- 

 Ing In the wing-rudiments of the pupa, and on the same 

 determinants occurring in the germ-cells." 



It occurs to me that still another explanation is possible 

 to cover at least some such cases. In discussing various 

 types of latency. Dr. Shull (^American Naturalist, July) 

 has recently defined as " latency due to fluctuation " those 

 cases (of which manv are known) in which the special 

 characters of a race do not appear except under suitable 

 conditions. Following this idea, it is possible to think of 

 the dark Arctia caja appearing after exposure to cold as 

 representing a variation which possessed an inherent 

 tendency to darkness not exhibited under more ordinary 

 conditions. Indeed, this must have been the case, since 

 only " a certain number " were affected. Given such a 

 variation, it is not unreasonable to suppose that when 

 examples were mated together the tendency would be so 

 emphasised as to appear under normal temperatures, thus 

 producing an apparent case of the inheritance of acquired 

 characters. T. D. A. Cockerell. 



University of Colorado, October 7. 



Determination of Sex : a Correction. 



May I correct a slip In your report of " Zoology at the 

 British .Association" (Nature, October 22, p. 647)? The 

 cinnamon canaries resulting from the mating green hen X 

 cinnamon cock are all females, not males, as there 

 accidentally stated. The point Is critical in the Interpreta- 

 tion of that curious case. W. B.\teson. 



October 26. 



