March 27, 1913] 



NATURE 



95 



Mr. F. E. Baxandall (Proc. Roy. Soc, vol. lxxiv., 

 pp. 54S-550, 1905), when many lines in the emission 

 spectrum of M Centauri (also an Orion star with 

 bright hydrogen lines) were found to agree in wave- 

 length with enhanced iron lines. 



What Becomes of the Light of the Stars? — This 

 question Prof. Very, of the Westwood Observatory, 

 Mass., U.S.A., places before the readers of The Popu- 

 lar Science Monthly, and proceeds to give an interest- 

 ing answer in an essay, highly speculative in char- 

 acter, developed in eighteen pages of the March num- 

 ber. The author ably marshals a useful body of 

 evidence tending to establish that there is a general 

 absorption of light by the ether. In this transforma- 

 tion of energy he sees the genesis of matter, and 

 in meteorites he finds the " appointed instruments " 

 whereby the nascent dust is collected " into the germs 

 of future worlds." By atomic disintegration like that 

 accompanying the degradation of radio-active elements 

 the cosmogonic process is made reversible. 



It may be mentioned that in reference to the 

 "transient nebulosity," which appeared around Nova 

 Persei, the author states : " It was an electric pheno- 

 menon, an exhibition of canal rays, or positive ions, 

 on a grand scale," and that to explain the high tem- 

 perature of the helium stars, he makes the hypothesis 

 that they "contain an exceptional amount of pecu- 

 liarly unstable elements." 



Publications of the Strassburg University Ob- 

 servatory. — The second part of vol. iv. of the Annalen 

 der Kaiserlichen Universitats-Sterniuartc in Strass- 

 burg, published under the direction of Dr. Bausch- 

 inger, contains a large number of observations of 

 double stars, planets, satellites, and nebula?. The 

 double stars were observed with a 49-cm. refractor 

 by Dr. VVirtz between 1902 and 19 10, and the results 

 are compared with those obtained by other observers 

 and with the ephemerides. The same observer is 

 also responsible for the measures of the major planets 

 and their discussion, in which are given the diameters 

 and other measures, such as the dimensions of the 

 Martian snowcaps, and the positions of the streifen 

 on Jupiter ; for the polar and equatorial diameters of 

 the latter planet he finds the values 35-986" +0-028" 

 and 38-254" ±0-030" respectively. 



Tide Tables. — From the Government Astronomer of 

 New Zealand, Mr. C. E. Adams, we have received a 

 report of the tide observations made at Auckland since 

 December 1, 1908. These have now been harmonic- 

 ally analysed, and the results are given. There is 

 also an interesting description of a new tide gauge 

 designed by Mr. W. Ferguson, in which the recording 

 pencil is moved by a clock and the paper on which 

 the record is made is moved by the tide. The gauge 

 has been running some months, and has given great 

 satisfaction. 



From the Government Printing Bureau at Ottawa 

 we have received copies of the tide tables for the 

 Canadian coast for 1913. The accompanying letter- 

 press contains many interesting facts concerning the 

 tides on the Pacific coast. 



Stars with Variable Radial Velocities. — Mr. 

 J. H. Moore, of the D. C. Mills Expedition's Observa- 

 tory, Santiago, Chile, gives a list (L.O. Bulletin 224) 

 of nine stars of about 5-0 magnitude, having variable 

 radial velocities. In the same bulletin Prof. W. W. 

 Campbell gives observations showing that the radial 

 velocities of 8 Andromeda? and f- Cephei respectively 

 vary between — 1-8 km. and — io-S km., and +156 

 and +29-4. The latter also makes a correction re- 

 garding the radial velocity of i Capricorni. In L.O. 

 Bulletin 97 this was stated to be variable. The 

 removal of some errors of reduction leaves the velocity 

 apparently constant at + 12 km. per second. 

 NO. 2265, VOL. 91] 



THE TEACHING OF MATHEMATICS. 1 

 r PHE papers enumerated below complete those 

 J- written for the recent International Congress of 

 Mathematicians. They deal with secondary schools, 

 girls' school, preparatory schools, the training of 

 teachers, technical institutes, and universities. Earlier 

 papers in the same series were described in Nature of 

 March 14, 1912 (p. 44), and of May 23 (p. 305). 



Secondary Schools. 



No. 20 is a judicial discussion of "The Calculus 

 as a School Subject." Mr. Jackson states impartially 

 the questions involved, some of which can only 

 be settled by greater experience than we now possess. 

 Some questions are already settled, e.g. that if the 

 calculus is to be introduced time must be found by 

 a reduction in the drill which now prevails in algebra 

 and trigonometry, by a frank recognition that tangents 

 to curves and varying velocities involve the ideas of 

 the calculus with some knowledge of the concrete 

 ment that follows from this recognition. It is also 

 desirable that the pupil should come to the study of 

 the calculus, and by giving these subjects the treat- 

 matters to which its methods arc applicable. Mr. 

 Jackson appears to be unaware that it is useless to 

 point out an imperfection of proof to pupils who 

 cannot discover the imperfection for themselves ; but 

 his pedagogy is in general so good that we feel sure 

 he does himself injustice in this apparent ignorance. 



Mr. Barnard (No. 22) frankly disapproves of the 

 methods of teaching which have resulted from Prof. 

 Perry's movement. He is all for thoroughness, and 

 most of his article is taken up with a list of the 

 blunders of text-books. We gather that he attributes 

 these blunders to the new methods, a surprising view 

 when we consider how few men educated in the new 

 methods are old enough to write books. 



Our conclusion is different. Writers of text-books 

 are on the whole picked men, such as university 

 professors and the ablest schoolmasters, and they are 

 at present men trained on the old "thorough" 

 methods ; and if such blunders are possible for these 

 picked men, it is indeed few of the schoolboys who 

 are fit to profit by that training. 



1 The Teaching of Mathematics in the United Kingdom. Special 

 Reports on Education Subjects. 



No. 18. " Mathematics in the Education of Girls and Women." By Miss 

 E. R. Gwatkin, Miss Sara A. Burstall and Mrs. Henry Sidgwick. Price 



"No. rg. "Mathematics in Scotch Schools." By Prof. G. A. Gibson. 

 Price 3d. 



No. 20. "The Calculus as a School Subject." By Mr. C. S. Jackson. 

 Price rW. . „,.,.. 



No. 2t. "The Relation of Mathematics to Engineering at Cambridge. 

 Ev Prof. B. Hopkinson. Price iM 



No. 22. "The Teaching of Algebra in Schools." Ey Mr. S. Barnard. 

 Price lid. . . 



No. 23. "Research and Advance Study as a Training for Mathematical 

 Teachers." Ey Prof. G. H. Bryan. Price lid. 



No. 24. "The Teaching of Mathematics in Erening Technical Institu- 

 tions." By Dr. W. E. Sumpner. Price id. 



No. 25. " The Undergraduate Course in Pass Mathematics, generally, 

 and in relation to Economics and Statistics." By Prof. A. L. Bowley. 

 P,ice lid. 



No. 26. "The Preliminary Mathematical Training of Technical 

 Students." By Mr. P. Abbott. Price iW. 



No. 27. "The Training of Teachers of Mathematics." By Dr. T. P. 

 Nunn. Price ili 



No. 28. " Recent Changes 

 By Mr. A. Berry- Price iM 



No. 29. "Mathematics in the Preparatory School.' By Mr. E. 

 Kitchener. Price ijrf. 



No. 30. " Course in Mathematics for Municipal Secondary Schools. 

 By Mr. L. M. Jones. Price rjrf. 



No. 31. "Examinations for Mathematical Scholarships at Oxford and 

 Cambridge." Ey Mr. A. E. Jolliffe and Mr. G. H. Hardy. Price 2d. 



No. 32. "Parallel Straight Lines and the Method of Direction." By 

 Mr. T. James Garstang. Price id. 



No. 33 " Practical Mathematics at Public Schools." By Prof. H. H. 

 Turner, Mr. R..C Fawdry, Mr. A. W. Siddons, Mr. F. W. Sanderson, and 

 Mr. G. M. Bell. Price id. 



No. 34. " Mathematical Examinations at Oxford." Ey Mr. A. L. Dixon. 



the Mathematical Tripos at Cambridge 



Price 6d. 



(London : Wyman and So 

 Dublin ; E. Ponsonby, Ltd.) 



Lt Edinburgh : Oli' 



nd Boyd ; 



