140 



NA TURE 



[December 12, 1901 



not think it necessary that strict malhematical proofs should be 

 given for everything. An engineer learned physical constants, 

 and physical data might be taken for granted. He believed 

 that the education of the engineer in mathematics would gain 

 and not lose if instead of strict proof there was more of illus- 

 tration. Prof. Barr gave the calculus an important position, 

 but expressed his desire for the portable formula: advocated by 

 Prof. Perry. Dr. II. S. Carslaw, in the course of some 

 remarks, said if teachers in schools would anticipate the 

 teachers in the colleges by using graphical methods they 

 would not hear mathematics spoken of as killing thought and 

 destroying education. At present Euclid is given far too pro- 

 minent a position in school work, with the result that algebra 

 and trigonometry suffer. I'rof. G. A. Gibson expressed general 

 agreement with the views of Prof. Barr. He would not, how- 

 ever, insist too much on doing away with logical demonstra- 

 tion. The foundation for the teaching of mathematics should 

 be laid at school, and he complained that two years of a school- 

 boy's life -were worse than wasted by the enormous amount of 

 rules which he had to commit to memory, which were of no 

 intellectual interest and which he was almost certain to forget. 



The Education Committee of the General Medical Council 

 presented a second report on the steps to be taken for the 

 improvement of preliminary examinations at the meeting of the 

 Council last week. Sir John Batty Tuke, chairman of the 

 , Committee, in presenting the report explained that in November, 

 189S, the Education Committee was asked to report when, in its 

 opinion, it would be practicable to raise preliminary examina- 

 tion to the senior and higher standards. In June, 1S99, the 

 Committee reported, after consultation with a large number of 

 educational authorities, that it would be better if educational 

 experts were appointed to review the circumstances of all 

 examinations. Experts were appointed, and in December, 

 iSgg, the Committee submitted a report, along with a report 

 of the experts, who held that it was impossible to raise the 

 standard to the senior or higher grade in the present condition 

 of secondary education in Great Britain. Thereupon the 

 experts were asked to state reasons for the belief. In March, 

 19CX3, they gave these reasons, and the Committee was then 

 enabled to work upon certain fixed principles. The principal 

 difficulty met with was how to produce a rise in the character 

 of examinations in reality, a real bonA-fidc rise. It was easy to 

 make an examination look more serious on paper than it really 

 was. The Committee had not asked for this to be done, but 

 had made representations to the various examining bodies, 

 asking them to raise the standard of the pass-marks rather than 

 increase the difficulty of an examination. Feeling that the 

 Council had the true interests of education at heart, the various 

 examining bodies had met the Committee in the most con- 

 ciliatory spirit and had, wherever neces.sary, provided examina- 

 tions in order to bring about a common good. The Committee 

 expressed the opinion that it would not be practicable to raise 

 the standard of the examinations until the state of secondary 

 education in the country was in a less chaotic condition than it 

 is now. The responsibility lay with the country, and it was 

 sincerely to be hoped that the Government during the next 

 se.ssion would bring forward a strong measure by which this 

 important object might be attained. After some discussion, 

 the Council adopted the motion " That the report of the Edu- 

 cation Committee on the steps taken for the improvement of 

 preliminary examinations be appmvcrl." 



SCIENTIFIC SERIAL. 



Bulletin of the American Mathematical Society, November. — 

 On wron,skians of functions of a real variable, by Prof. Bocher, 

 has for its object the settling certain questions connected with 

 the subject so as to clear the way for further investigations — 

 such as whether the roots of wron.skians of sets of linearly 

 independent solutions can have an infinite number of roots in a 

 given interval, and also the question to what extent the theory 

 of the adjoint (adjungirte) differential ei)uation remains valid 

 when the coefficients of the dilTerenlial equation are not assumed 

 to be analytic but merely continuous functions. To do this he 

 considers the slightly more general subject of linear families of 

 which the solutions of a homogeneous linear differential equation 

 form a special case. The paper was coinmunicated at the 

 August meeting of the .Society, as also was the following, on the 

 configurations of the 27 lines on a cubic surface and the 28 



NO, 1676, VOL. 65] 



bitangents to a quartic curve, by Prof. L. E. Dickson, .\fter 

 determining four systems of simple groups in an arbitrary domain 

 of rationality which include the four systems of .simple con- 

 tinuous groups of Lie, the author was led to consider the 

 analogous problem for the five isolated simple continuous 

 groups of 14, 52, 78, 133 and 248 parameters. The groups of 

 78 and 133 parameters are related to certain interesting forms 

 of the third and fourth degrees respectively (Cartan's theses), and 

 these suggest certain forms discussed in the paper. — Dr. G. A. 

 Miller gives an account of the mathematical work done at the 

 fiftieth annual general meeting of the American Association for 

 the Advancement cf Science. There are given the titles, with 

 abstracts, of twenty-five papers. — Prof. J. S. Ames reviews " Die 

 partiellen Differentialgleichungen der mathematischen I'hysik" 

 (nach Kiemann's Vorlesungen in vierter Auflage neu bearbeitet 

 von Heinrich Weber, erster bd. 1900, zweiter bd. 1901). — 

 Amongst the notes are included the Cambridge mathematical 

 courses for the current academic year. — New publications as 

 usual. 



SOCIETIES AND ACADEMIES. 



Lo.VDON. 

 Royal Society, November 21. — "On the Properties of the 

 Arterial and Venous Walls." By John A. Mac William, M.D., 

 Regius Professor of Physiology in the University of Aberdeen. 

 Communicated by Sir Michael Foster, K.C.B., Sec. R.S. 



November 28. — "A Comparative Study of the Spectra, 

 Densities and Melting Points of some Groups of Elements, and 

 of the Relation of Properties to Atomic Mass." By Hugh 

 Ramage, B..\., A.R.C.Sc.L, St. John's College, Cambridge. 

 Communicated by Prof. Liveing, F. R.S. 



It has been usual for investigators to rest satisfied when the 

 properties of the elements were shown to be "a periodic 

 function of the atomic mass." Diagrams drawn by the method 

 employed in this paper will show in what degree the properties 

 vary with the atomic mass, and will make it easier to establish 

 the exact quantitative relations. 



The work and results presented by the author make it clearer 

 that the properties of the elements are fundamentally due to the 

 structure, as revealed by their spectra, of the atoms rather than 

 to the quantity of matter in them. It is inconceivable, for 

 instance, that the change from calcium to strontium proceeded 

 through the intermediate elements when we consider that the 

 strontium molecules must have a similar structure to those of 

 calcium. This structure is so simple that the fundamental 

 (Bunsen flame) spectrum of each of these elements contains only 

 one line attributed to the element. The anomaly, according to 

 Mendeleetrs law, in the atomic masses of tellurium and iodine 

 is further evidence of this. The properties of these elements 

 may have nothing whatever to do with each other. They are, 

 however, clo.sely related to and in correct order with those of the 

 elements of their respective groups. The genesis was not in the 

 direction of tellurium to iodine, but from, or perhaps through, 

 oxygen and fluorine respectively. So also is this the case with 

 the other groups. 



It is more probable that in the genesis of the elements the 

 properties of certain fundamental matter are modified by suc- 

 cessive additions of matter to them, or by causes of which this 

 is to us the apparent result. The regularity in the changes in 

 the properties of lithium, beryllium, boron and carbon, as seen 

 in the diagrams, is very remarkable. It is, furthermore, very 

 suggestive, for the changes in properties are approximately pro- 

 portional to the quantity of matter in the atom in excess of a 

 constant quantity (which is about 6), as if it were the same 

 matter that is added in each case. 



Geological Society, November 20. — Mr. J. J. H. Teall, 

 V.P.R.S., president, in the chair. — Dr. Vaughan Cornish ex- 

 hibited photographs of waves and ripples in water, cloud, 

 sand and snow. — Notes on the Genus Lichas, by Mr. 

 F. R. C. Reed. The Lichadida; are divided into two great 

 groups: (l) that with a p.iir of bi-composite lateral lobes to 

 the glabella and a more or less definite fourth pair of lateral 

 lobes ; and {2) a group with a pair of tri-composite lateral 

 lobes, through the fusion of the fourth pair with the bi-com- 

 posite pair of the preceding group. Names are proposed for 

 each group, and also, where necessary, for the eight sections, of 

 subgeneric value, into which each group is subdivided. The 



