470 



NATURE 



[October 14, 1909 



fiom the centre of the cluster; the second one is moving 

 towards the centre. Several others in the cluster appear 

 to have a slight motion. 



On Friday, August 27, owing to the large number of 

 papers presented to the section, it was divided into three 

 departments, which met concurrently. In the mathematical 

 department. Prof. E. H. Moore dealt with fundamental 

 analogies existing in diverse branches of mathematics, and 

 proposed a method for unifying these branches in a more 

 general theory embracing all such analogous branches. 

 Further information with regard to Prof. Moore's theory 

 will be found in a paper by him on a form of general 

 analysis with applications to linear differential and integral 

 equations {_Alii del IV. Congrcsso Internationale del 

 Mathematici, vol. ii.. pp. 98-114), and in a memoir 

 t'ntitled " Introduction to a Form of General Analysis," 

 which will shortly be published by the Vale University 

 Press. Prof. E. H. Hobson, in a paper on the present 

 state of the theory of aggregates, considered a number of 

 points in connection with the theory, and indicated the 

 ■desirability of a new and more adequate definition of an 

 aggregate of a more restricted character than the one due 

 I0 G. Cantor, and of sucli a character that no difficulties 

 ■would arise from the ascription of a cardinal number to 

 each such aggregate, and also of an ordinal type in case 

 the aggregate is an ordered one. Prof. G. A. Miller, in 

 a paper on generalisations of the icosahedral group, con- 

 sidered the group the two generating operators of which 

 satisfy one of the following three sets of conditions : — 

 t^' = l„\ (>,/.,):' = (/.,/,)=; 



Amongst otiier theorems. Prof. Miller proves the follow- 

 ing : — There is an infinite number of groups each of whicii 

 may be generated by two operators satisfying one of these 

 conditions. Each of the possible groups generated by f,(. 

 ■contains either the icosahedral group or the group of 

 order 120, which is insoluble and does not contain a sub- 

 group of order 60, and it must have one of these groups 

 for its commutator subgroup. Prof. G. A. Bliss foUo-sved 

 with a new proof of a theorem of Weierstrass concerning 

 the factorisation of power series which states that any 

 convergent series in ^+1 variables, F(.v,, x,, .\-j, . . . x, y^) 

 in which the lowest term in y alone is of degree n, can be 

 expressed as a product 



(>" + (7,J'"-1t . . . +a„_,jj'-(-a„1 * (jr, . . . x,„ y), 

 •where a^,a, . . . a„are convergent series in -v,, .v, . . . x^, 

 which vanish with these arguments, while * is a con- 

 vergent series in all ^+1 variables with a constant term 

 different from zero. The author also gave formulae by 

 which the coefificients in the different series may be com- 

 puted. Mr. J. H. Grace read a paper in which a treat- 

 ment was given of ideals in a quadratic field, and Prof. 

 \V. H. Metzler one on a continuant of order n+i which 

 is expressible as the product of n+i factors. Prof. Ellery 

 W. Davis gave a complete representation of the elements 

 of the central conic the axes of which are non-similar 

 •complex quantities. In a paper on the invention of the 

 slide rule, Prof. F. Cajori sifted the evidence in connec- 

 •tion with this subject bearing on the rival claims of 

 Gunter, Oughtred, and Wingate. His conclusion is that 

 the slide rule was undoubtedly invented by William 

 Oughtred in 1832. Papers by Major P. A. MacMahon 

 on a correspondence in the theory of the partition of 

 numbers, and by Mr. J. W. Nicholson on the asymptotic 

 expansion of Legendre's functions, were read in title only 

 in the absence of the authors. The like fate overtook 

 the report of the committee on the further tabulation of 

 Bessel functions. This committee has made further pro- 

 gress during the year. Using the notation of previous re- 

 ports, values of Q,(.v) have been calculated for integral 

 values of n from n=i to n = 6. From these the values of 

 sin-'(Q'R) have been computed for the same values of 

 n, and the values for )! = 5, i|, . . . 6i have been added. 

 From the tables of the present report and those of the 

 iqo7 report, the values of J„(.v) for values of n from o to 

 ^h at intervals of |, and for values of x greater than 10, 

 can be computed to six places without sensible error. 

 The Neumann function Y„(.v1 can be calculated from the 

 same data. 



KG. 2085, VOL. 81] 



Meanwhile, the department of general physics was hold- 

 ing a joint meeting with Section B (Chemistry). The 

 papers of more particularly chemical interest will be re- 

 ferred to in the report of the proceedings of that section. 

 Prof. E. Goldstein led off the physical papers witli one 

 on the three-fold emission spectra of solid organic com- 

 pounds, which the council has ordered to be printed 

 ill extcnso. Prof. Goldstein finds that aromatic substances 

 solidified by liquid air can emit three discontinuous spectra, 

 which are quite different from one another, when they 

 are exposed to kathode rays. First, the initial spectra are 

 observed at the beginning of the luminescence ; when these 

 become fainter the chiej spectra, which are very character- 

 istic for each substance, appear ; the solution spectra are 

 observed when the aromatic substance is dissolved in 

 another medium and the frozen mixture is exposed to 

 kathode rays. .\\\ three spectra commence in the red ; the 

 initial spectra extend to tiie ultra-violet ; the chief spectra 

 are shorter. Very characteristic solution spectra are given 

 by naphthalene and its derivatives. The solution spectrum ' 

 varies with the solvent medium. Very small quantities of 

 aromatic bodies are sufficient to give marked solution 

 spectra ; on the other hand, the phenomenon gives a very 

 sensitive method of detecting slight impurities. In this 

 way it may be stated that until now no aromatic sub- 

 stance has been prepared in a really pure state. In the 

 consequent discussion Sir J. ]. Thomson pointed out that 

 the results w^ould have been clearer if kathodic rays of 

 only one velocity had been employed. Changes come in 

 very abruptly as the energy of the rays passes a certain 

 value. Experiments are in progress in the Cavendish 

 Laboratory upon lithium chloride. With ordinary kathode 

 ravs (t'=io' to 6x10') the chloride exhibits a steely-blue 

 appearance, and gives a continuous spectrum ; but with 

 positive ions the spectrum shows the lithium red line and 

 very little continuous background. As to the origin of 

 these phosphorescent spectra, he emphasi%;d the fact that 

 phosphorescence is not so much a question of ionisation 

 as of the breaking up of complex aggregates, e.g. iodine 

 vapour phosphoresces without showing any sign of ionisa- 

 tion. You can freeze out the phosphorescence, thereby 

 making these complexes stable. Prof. H. E. Armstrong 

 raised the point as to whether something of the same sort 

 as Goldstein had brought forward goes on in a Welsbach 

 mantle. Experiment shows that you can obtain phos- 

 phorescent spectra by inserting traces of rare earths. The 

 next paper was by !\Ir. E. F. Burton, on the influence of 

 electrolytes on colloidal ferric oxide solutions. .\ commercial 

 ferric oxide solution was dialysed in conductivity water, and 

 the velocitv with which the particles moved in a unit 

 electric field was observed from time to time. -As the 

 purification continued the velocity at first increased, but 

 afterwards decreased in almost linear relation with the 

 amount of chlorine found. A comparison of the coagu- 

 lating powers of monovalent, divalent, and trivalent ions 

 on the colloidal particles indicates that the Linder-Picton- 

 Hardv law holds good. This paper was followed by one 

 by Dr. Otto Hahn, on methods of separation of radio- 

 active products. These methods are based on the working 

 hvDothesis that sincle radio-active products emit onlv one 

 tvpe of radiation, either homogeneous a narticles or homo- 

 geneous j3 particles. This hypothesis requires that 

 tlioi-ium C and actinium B be complex. Also, radium C 

 must be complex, and consist of three products, one emitting 

 a particles and two emitting different 6 particles. Experi- 

 ments using a " recoil " method seem to supoort these 

 conclusions. The author also has found that radium itself 

 emits 6 as well as a particles ; it also must be complex ; 

 and experiment seems to show th.at the B particles come 

 from r.adium itself, the w^ell-known ct particles being due 

 to a new body, radium X. Prof. Rutherford, in comment- 

 ing upon the paoer, oressed the bearing of the results 

 upon the supnosed purity of ordinary " chemically pure " 

 bodies. Sir J. Larmor asked for an explanation of the 

 well-known difFicultv in connection with the emanation 

 being positively charged aftpr emitting a oositively charged 

 bodv, and in renlv Dr. Hahn expressed his belief that 

 S particles are simultaneously expelled. In answer to a 

 question of Prof. Bumstead's. Dr. Hahn replied that he 

 bad not made any magnetic exoeriments to test the homo- 

 geneity of his various rays. Prof. J. C. McLennan then 



