January 25, 191 2] 



NATURE 



425 



a. Ascending arm of Lockyer^s curve. 



1. Rigelian stars ¥2"= +2*3 km. 3 stars 



2. Taurian ,, =+8'8 ,, 4 ,, 



3. Crucian ,, =+37 m 3^ ,, 



/3. Maximum of Lockyer's curve. 



1. Ainitaniian stars V2''=-0'4km. 5 stars 



2. Argonian ,, — o „ 



y. Descending arm of Lockyer's curve. 



1. Acherriian stars Vo''^ -5'4km. il stars 



2. Algolian „ = -37 ,, 10 „ 



Grouping them further, and taking general means for 

 ach of the groups a, 0, and 7, we get : — 



It is obvious that the /3 group is so small, and its mean 

 error so much greater than the mean value of the veloci- 

 ties, that it is negligible, and Dr. Ludendorff considers 

 only the o and y groups ; the difference bet%veen these is 

 + 87 km., with a mean error of +2-0 km. 



Further analysis shows that, of the forty-five stars in 

 group a, thirty-one have V, positive, with a maximum of 

 + 25 km., and fourteen negative, with a maximum 

 negative value —7 km., while the mean of the + values 

 is +7-2, and that of the negative values —2-8. 



Analysing similarly the 7 group, the mean — V^ is 

 8-8 km., and the mean +¥, is -I- 3-9 km., so there can 

 remain no reasonable doubt as to the reality of the con- 

 nection between + values and " ascending " stars and 

 — values and " descending " stars. 



Taking these same seventy-one stars and arranging 

 them under the Harvard equivalents of the Lockyer 

 classes is rather a hazardous proceeding on account of the 

 generical differences of the two classifications with their 

 consequent overlappings ; but Dr. Ludendorff has done it 

 systematically, and finds that the mean velocity difference 

 between the analogues of the a and 7 groups employed 

 above is +36 km., with a probable error of ±2-41 km. 

 It is evident that the systematic difference so obvious in 

 the previous tables is somewhat obscured, and it becomes 

 more so when the whole of Campbell's 224 stars are 

 arranged under the Harvard equivalents of the Lockyer 

 classes. Dr. Ludendorff therefore concludes the com- 

 parisons with the statement that when one arranges the 

 helium stars of Campbell's catalogue under the Lockyer 

 classification, there appears in the mean values of the 

 absolute radial velocities of the several classes a distinct 

 systematic difference. When one arranges the stars under 

 the Harvard, or the Miss Maury, classifications, this 

 systematic difference is not so clear as under the Lockyer 

 arrangement. 



Arising out of the question as to the reality of the 

 observed difference, several suggestions as to its origin are 

 made. The question of systematic error in the actual 

 measuring is dismissed, and the evidence of streaming, 

 disclosed by arranging the stars in four R.A. groups, is 

 very small. 



Dr. Ludendorff concludes with the suggestion that the 

 wave-lengths in the spectra of helium stars vary with the 

 condition of the star, and that this variation of condition 

 may also be a function of Lockyer's arrangement of the 

 stellar classes. Further, he makes the important sugges- 

 tion that, as the Lockyer classification discloses this 

 systematic difference, while the Harvard classifications 

 do not show it so clearly, in the future discussion of 

 a definite classification of ttie stars the classification which 

 discloses this difference, possibly dependent upon spectral 

 evolution, should receive most careful consideration. The 

 elements of the spectral change, as shown in this dis- 

 cussion of the helium stars, are already incorporated in 

 the classification, which by further natural development, 

 and maybe slight modifications, may be made still more 

 to portray the development of a star as it grows older. 



William E. Rolston. 



NO. 2204, VOL. 88] 



EDUCATIONAL CONFERENCES 



CONSIDERED IN RELATION TO SCIENCE IX 



PUBLIC SCHOOLS.' 



U. 



Laboratory Work in Schools and in Examinations. 

 J N our previous article we gave an account of those dis- 

 cussions at the annual meeting of the Public School 

 Science Masters' Association which dealt with the sequence 

 of studies. The remaining discussions were concerned 

 with the position of qualitative analysis and the relation 

 between laboratory work in schools and the practical 

 examinations of public examining bodies. Dr. E. B. 

 Ludlam (Clifton) found the position of the teacher difficult, 

 as he thought that modern methods were better than those 

 in which qualitative analysis had figured so largely, but 

 was obliged by the scholarship examinations and those for 

 the higher certificate to retain too much of the older 

 methods. At the same time, he found that boys were 

 stimulated by exercises in the identification of substances, 

 a process which enlarged a boy's chemical experience and 

 gave scope to his individuality. He therefore advocated a 

 study of " comparative chemistry," with early attention to 

 metals and the periodic classification ; in connection there- 

 with, the boys should work out their own methods of 

 identification. From the discussion on examinations, 

 opened by Mr. G. F. Daniell, it appeared that there was 

 a desire for more alternative questions, i.e. more options, 

 in the practical tests, and xMr. H. Richardson suggested a 

 number of useful variants from the ordinary type of ques- 

 tion. In practical chemistry, the use of the blow-pipe and 

 some work with unknown substances should be retained ; 

 but there had been too much refinement of anal.vtical work, 

 both qualitative and volumetric. Problems, accompanied 

 by fairly full working instructions, would bring the 

 examination work more into line with the work in the 

 school laboratory. The opener, and several subsequent 

 speakers, advocated closer relations between teachers and 

 examiners, and agreed that it was important that the 

 examiner should .be present during the laboratory 

 examination. 



Mathematical Teaching. 



It is usually Unprofitable to deal with papers on mathe- 

 matical subjects by means of short abstracts. We there- 

 fore give the programme of the meeting of the Mathe- 

 matical Association, and attempt to review the present 

 position in the light of the discussions. 



The president's address, by Prof. E. W. Hobson. 

 appeared in Nature of January 18. Mr. C. Godfrey gave 

 some account of the work of the International Commission 

 on Mathematical Teaching. Mr. G. St. L. Carson read a 

 paper on some unrealised possibilities in mathematical 

 education, and there was a discussion on the introduction 

 of the calculus, in which Mr. C. V. Durcll, Mr. A. W. 

 Siddons, Dr. T. P. Nunn, and others took part. 



Broadly stated, the papers threw light upon (i) the 

 democratisation of mathematics ; (2) the relation between 

 the instrumental and the philosophical elements in mathe- 

 matical teaching. Prof. Hobson 's address makes clear 

 what we wish to convey by (i), and we observed that the 

 idea influenced most of the speakers. Prof. Perry and the 

 Board of Education use the term " practical mathematics " 

 in the sense of vocational mathematics, and Prof. Hobson 

 had apparently the same idea in his references to " prac- 

 tical life." VVhere the president spoke of the " practical 

 side " being overdeveloped he had in view laboratorv 

 exercises. By " instrumental " mathematics we mean t' 

 method of teaching which uses the utilitarian motive 

 order to lead the pupil to mathematical concepts. We put 

 it that Prof. Hobson recognises the democratisation of 

 mathematics as a welcome fact, believes that this justifies 

 some, but not exclusive, use of the instrumental method, 

 and lays stress on the necessity for combining with the 

 latter considerable philosophical and deductive training. 

 Mr. Godfrey told us that Italy had, more than any other 

 country, continued to demand a philosophical treatment of 

 geometry from young beginners, employing methods moi** 

 rigorou'; than those of Euclid. Germany, on the other 

 hand, hnd gore farther than any other nation in develop- 

 ' Cominu"d from p. -ot. 



