i66 



NATURE 



[December 15, 1904 



barium nitrate, the latter finally also being decomposed 

 into baryta. — Metallic derivatives of nitrogen iodide and 

 their bearing on its constitution : O. Silberrad. Guyard's 

 supposed copper derivative of nitrogen iodide is shown to 

 be a cuprosamine periodide. The silver derivative de- 

 scribed by Szuhay is found to be a true nitrogen iodide 

 derivative of the formula NI^.NH.Ag. — Synthesis of 

 I : i-dimethylhexahydrobenzene : A. W. Crossley and 

 Nora Renouf. — The formation and reactions of imino- 

 conipounds, (i.) condensation of ethyl cyanoacetate with its 

 sodium derivative : H. Baron, F. G. P. Remfry, and J. F. 

 Thorpe. This is a preliminary communication regarding 

 the properties of compounds containing the group 

 — C(=NH) — , which in some respects closely resembles the 

 =CO group in reaction. — The affinity constants of aniline 

 and its derivatives : R. C. Farmer and F. J. Warth. 

 These constants are best measured in such cases bv deter- 

 mining the distribution of the salts between two immiscible 

 .solvents applied simultaneously. The following substituents 

 exert a decreasing electronegative action, in the order in 

 which thev are given, on the affinitv constant of aniline : — 

 NO,,COdH,— N = NPh,Br,CI,Me,dMe. — The attractive 

 force of crystals for like molecules in saturated solutions : 

 E. Sonstadt. Crystals of a salt were placed in saturated 

 solutions of the same salt, and the amount of the latter 

 withdrawn from the solution by the attractive force of the 

 crystals was determined periodically. — The Grignard re- 

 action applied to the esters of hydroxy-acids : P. F. 

 Frankland and D. F. Twiss. A substance which is prob- 

 ably ao55-tetraphenylerythritol W'as obtained by the action 

 of magnesium phenyl bromide on dimethyltartrate. — Note 

 on the addition of hydrogen cyanide to unsaturated com- 

 pounds : A. Lapworth. It is shown that in spite of 

 Knoevenagel's assertion to the contrary, there is no experi- 

 mental evidence that mesityl oxide unites directly with 

 hydrogen cyanide except in the presence of alkalis. The' 

 author is now engaged in the examination of a number 

 of products obtained by the interaction of aldehydes with 

 chloroacetates in presence of potassium cyanide. 



Mathematical Society, December 8. — Prof. Forsyth, 

 president, in the chair. — The following papers were com- 

 municated : — On a deficient multinomial expansion : Major 

 MacMahon. A generalisation of the binomial theorem, 

 made by .\bel and restated by Cayley, leads to the consider- 

 ation of the series that is obtained from an ordinary multi- 

 nomial expansion by restricting the indices of the terms 

 to obey certain Diophantine inequalities. The paper con- 

 tains investigations of the number of terms in such a series, 

 the sum of the coefficients, and a syzygetic theory of the 

 distinct terms. — The application of basic numbers to 

 Bessel's and Legendre's functions : Rev. F. H. Jackson. 

 The author generalises various functions that are expressed 

 by power series by replacing n in the coefficient of .•«" by 

 (/" — !)(/>— i). Two generalisations are obtained of 

 Bessel's functions, one being derived from the other by in- 

 version of the " base " />. In the present paper the author 

 shows that these two functions are connected by a relation 

 containing basic exponential functions. He obtains also 

 generalisations of a number of results which bear on the 

 relations between Legendre's functions and Bessel's func- 

 tions, and ,he connects the theory of the generalised 

 Legendre's functions with that of the Theta functions. — 

 On groups of order p'^<fi ■ Prof. W. Burnside. In a 

 previous paper the author had proved that these groups are 

 soluble. In the present paper it is shown that, subject to 

 certain specified exceptions when the order is even, a group 

 of the specified order in which f^x;^ must have a character- 

 istic subgroup of order /", where a is such that fis greater 

 than f^T^- — On the failure of convergence of Fourier's 

 series : Ur. E. W. Hobson. Fourier's series formed for a 

 continuous function may not converge at a point, and then 

 it does not represent the function at the point. In the 

 paper attention is directed to a class of series which fail to 

 converge, but can be made to converge to any assigned 

 value by enclosing suitable sets of terms in brackets and 

 treating the terms in a bracket as a single term. No 

 example has ever been found of a non-convergent Fourier's 

 series which cannot be included in this class. The nature 

 of the set of points in the periodic interval at which a 

 Fourier's series fails to converge is discussed, and it is 



NO. 1833, VOL. 71] 



shown that, when the function to be represented by the 

 series is continuous, this set has the " measure " zero. — 

 An extension of Borel's exponential method of summation 

 of divergent series applied to linear differential equations : 

 E. Cunningham. The object of the paper is to make 

 more precise the connection between Laplace's solution of 

 linear differential equations in terms of definite integrals 

 and the asymptotic expansion of the solution as the product 

 of an exponential function and a descending power series. 

 The latter series, with the exponential factor omitted, is 

 shown to be " summable " in a sense analogous to that of 

 Borel's theory; and it is proved that the fundamental 

 properties of summable divergent series, such as differenti- 

 ation term by term, addition and multiplication term by 

 term, are valid for the series in question. — On the linear 

 differential equation of the second order : Prof. A. C. 

 Dixon. 



C.IMERIDGE. 



Philosophical Society, November 14. — Prof. iMai.'-hall 

 Ward, president, in the chair. — The charge of the o rays 

 from polonium : Prof. Thomson, F.R.S. A bismuth disc 

 covered with polonium (or radio-tellurium), as supplied by 

 Sthamer, was mounted on pivots in a vacuum tube. In 

 front of the disc and about 3 cm. from it was a very care- 

 fully insulated gold-leaf electroscope which could be charged 

 with either positive or negative electricity. The vacuum 

 tube was exhausted by first pumping out as much air as 

 possible by a mercury pump, and then using Dewar's 

 method of e.xtracting the remainder of the air by dense 

 charcoal cooled by liquid air. In this way vacua w^ere 

 obtained very much superior to those got by pumping alone. 

 It was found that at these very low vacua the electroscope 

 in front of the polonium if negatively charged leaks so 

 slowly that it is hardly possible to measure the leak with 

 accuracy ; while if the electroscope is positively charged its 

 leak is very rapid, certainly more than too times the leak 

 when charged negatively. Thus the polonium gives out 

 large quantities of negative electricity, but not enough 

 positive to be detected ; this is very remarkable, as polonium 

 is generally supposed to give out nothing but a rays. In 

 order to see that the positive electricity had not been 

 swamped by the negative the instrument was placed in a 

 strong magnetic field ; this stopped the negative corpuscles 

 coming out of the polonium from reaching the electroscope, 

 and it was found that now the latter no longer leaked when 

 charged with positive electricity ; but though the negative 

 particles had been stopped no positive ones could be detected, 

 for there was no leak from the electroscope when negatively 

 electrified. The author was never able to be sure of any 

 increase in the charge of a negatively electrified body placed 

 near the polonium ; this he thinks is due to the negative 

 particles from the polonium moving so slowly that they 

 are unable to make headway against the repulsion exerted 

 by a negatively electrified body. The a rays of polonium 

 are deflected by a magnet, hence they must be positively 

 charged at some part, at any rate, of their course, yet no 

 trace can be found of this charge when the rays strike 

 against an electroscope. The question is discussed whether 

 the o particles lose their charge when they pass through 

 the cloud of negative ones near the polonium, or whether 

 they are alternately charged and discharged, the time during 

 which they are uncharged being much longer than the time 

 they are charged. — On the dynamical significance of Kundt's 

 law of selective dispersion in connection with the trans- 

 mission of the energy of trains of dispersive waves : Prof. 

 Larmor, F.R.S. — The chlorination of a picoline : W. J. 

 Sell, F.R.S. — An attempted synthesis of uric acid : H. J. H. 

 Fcnton, F.R.S. — The diffusion of hydrogen through 

 palladium : O. W. Richardson. The paper is chiefly a 

 criticism of the conclusions drawn by Mr. G. N. St. Schmidt 

 (Drudc's Antt., vol. xiii. p. 747) from his experiments on 

 this subject. The author shows that the known facts can 

 be explained on the hypothesis that the hydrogen inside the 

 metal is dissociated, in the same way as for platinum. — 

 Optically active nitrogen compounds : Miss M. B. Thomas 

 and H. O. Jones. The work was undertaken in order to 

 find out what connection exists between the constitution 

 of optically active nitrogen compounds and the numerical 

 value of their rotatory power. The rotation for a basic 

 ion may be determined by preparing the salt with an acid 

 of known rotatory power, and subtracting the rotation due 



