January 19, 191 1] 



NATURE 



385 



three-prism spectrographs, which would separate the lines 



d enable better elements to be derived. 



In No. 8 Mr. F. C. Jordan discusses the orbit of 

 Tt ,'\ndromed3e from measures of iii plates taken with 

 the Mellon spectrograph between August, 1907, and 

 October, 1909, and derives a period of 143-67 days. A 

 point of special interest is that this binary is a helium 

 star with a long period, and it has been shown that heliutn 

 binaries are sharply divided into long and short periods. 

 The latter are generally less than one month, whilst the 

 shortest of the former class is 116 days. The increase of 

 eccentricity with period is also notable, the mean periods 

 for the two groups being 838 and 147-1 dajs, whilst the 

 corresponding mean eccentricities are 0-19 and 0-41 re- 

 spectively. T Andromedae is a notable example, the 



entricity of its orbit being 0-58. The point is a very 



iking one, but the data are, as yet, too meagre to 

 arrant speculation concerning its possible significance. 



The Discovery of Kepler's Laws. — The historj- of 

 Kepler's labours in working out his three laws of planetary 

 motions is interestingly told by M. Bigourdan in No. 23 

 of the Revue generale des Sciences. Refused as a divine, 

 Kepler pursued his study of mathematics, and was 

 appointed professor at Gratz in 1594, then being twenty- 

 three years of age. But in 1599 he was, as a Protestant, 

 expelled from Styria, and accepted a post under Tycho 

 Brahe. For a number of years he endeavoured to fit 

 Tycho Brahe 's wonderfully accurate observations into the 

 geocentric system which the latter upheld, but without 

 success, for there was always a residual error in latitude 

 of 8' or 9', and this amount Kepler believed to be 

 impossible in such careful observations. Then, after the 

 master's death, he worked away at the heliocentric idea, 

 and succeeded, eventually, in discovering the laws which 

 are the basis of our knowledge of orbital motions. In his 

 paper M. Bigourdan introduces many other points of 

 interest concerning Kepler's life and methods. 



Bright Bolides. — The apparitions of several bright 

 bolides during the latter part of 19 10 are recorded in 

 Nos. 37—38 of the Gazette astronomique bv M. Birken- 

 stock, director of the Bureau Central M^t6orique. One, 

 recorded by several observers at different stations, appeared 

 about 8.45 (C.E.T.) on August 19, and, as seen at Novi, 

 was about three-quarters the size of the full moon ; it then 

 split into two parts, each half the size of the moon, and, 

 leaving a train, disappeared after a flight which lasted 

 fbree seconds. Other bolides were recorded on September 



and 23, and October 8. 



The Astrographic Catalogue, Catania Zones. — We 

 have received part i., vol. vii., of the Catania astro- 

 graphic catalogue, giving the positions of 8855 stars. 

 These have been determined from fifteen plates covering 

 the region oh. to 3h. in R..A., and +52° to +54° in 

 declination ; excluding repetitions, the net number of new 

 positions is 7872. Tables for the geometrical corrections 

 for zone +53°, with their arguments, and ten-year pre- 

 cession constants up to the year 2000, are also given. 



CONFERENCES OF MATHEMATICAL 



TEACHERS AND OF PUBLIC SCHOOL 



SCIENCE MASTERS. 



T^HE annual meeting of the Mathematical Association 

 was held at the London Day Training College on 

 January 11, and the science masters met in the same 

 building on January 11 and 12. The officials of the 

 college and of the respective associations made admirable 

 arrangements, which conduced to the success of the 

 gatherings both from the working and the social aspects. 



Prof. H. H. Turner presided at the mathematical meet- 

 ings, and in his address gave a historical resume of the 

 recent advance of " the astronomical regiment " under 

 the leadership of Pickering, Stratton, Perrine, Melotte, 

 and Cowell. He described the discoveries of the new 

 satellites of Saturn and Jupiter, and the revelations into 

 the past of planets which resulted from an examination 

 of the orbits of these satellites. The members present, 

 rnostly teachers in schools, were greatlv interested in the 

 " news from the front " of the mathernatical armv. The 



xNO. 2 15 I, VOL. 85] 



annual report showed a large increase in membership and 

 an expansion of the Mathematical Gazette. 



Mr. G. Goodwill read a paper on the teaching of 

 elementary mechanics, in which he recommended that 

 dynamics should precede statics, and that the idea of 

 change of velocity should be treated as a basal concept 

 necessary for a proper approach to the subject. He 

 showed an extremely simple ballistic pendulum used for 

 measurements of change of momentum. By abandoning 

 the usual uniplanar arrangement, he has at once simplified 

 the exercises and tangibly increased their didactic v^lue. 



Canon J. M. Wilson described two fragments of ancient 

 geometrical treatises found in the Worcester Cathedral 

 Library. The first was written by Gerbert, who became 

 Pope Sylvester H. in 979. At that time Euclid was known 

 only to the Moors, and Gerbert failed in his attempt to 

 enter the University of Granada. The second fragment 

 dated from the early part of the twelfth century, and was 

 written by a monk of Bath named Adelhard or .-Ethelhard. 

 He succeeded in learning Arabic and entering the Uni- 

 versities of Granada, Cordova, and Seville by professing 

 to be a Mohammedan. The fragment discovered by Canon 

 Wilson proved to be part of a translation of Euclid from 

 the Arabic into Latin. This translation was used in all 

 the schools of Europe until 1583, when Euclid's own Greek 

 text became known. 



Mr. A. W. Siddons presented an important report by 

 the Mathematical Association Committee " On the Teach- 

 ing of Algebra and Trigonometry " (published by Bell 

 and Sons, price 3d.). The report dealt with the function 

 of algebra in the school curriculum for boys who were 

 not likely to specialise in mathematics, and aimed particu- 

 larly at giving teachers opportunit>- to develop with their 

 pupils mathematical ideas of great educational value — 

 ideas drawn from mechanics, mensuration, solid geo- 

 metry, infinitesimal calculus, and more especially from 

 numerical trigonometry. Mr. F. W. Dobbs (Eton) 

 thought the recommendations went too far, whereas Mr. 

 Barnard said that the Rugby masters thought the sug- 

 gested syllabus was inadequate. Other speakers supported 

 the views of the authors, and the general effect of the 

 discussion was to strengthen the hands of the committee 

 and to endorse their conclusions. The meeting referred to 

 the committee a paper read by Mr. C. \'. Durell. who 

 urged that much commercial arithmetic should be omitted 

 in order to find time for work more productive of mathe- 

 matical intelligence. 



.Among interesting exhibits were a projection of the 

 earth's surface on a cube, shown by Prof. Turner, a 

 celestial cylinder by Dr. T. P. Nunn, and apparatus illus- 

 trating Mr. Goodwill's paper. Prof. E. W. Hobson has 

 accepted the office of president for the coming year. 



Sir E. Ray Lankester opened the science masters' meet- 

 ing with an address upon " Compulsory Science z'ersus 

 Compulsory Greek." The main question he desired to 

 raise was whether the right choice of subjects for study 

 was made in our public schools, and whether it was right 

 and proper, as he should suggest, to cease altc^ether the 

 cumbrous efforts to teach the Greek language to school- 

 boys and to substitute for it as a regular and necessarv 

 part of the curriculum a well-considered, duly adapted, 

 and skilfully designed course of instruction in natural 

 science — using that term in the most comprehensive sense. 

 The results of education were not transmitted by physio- 

 logical heredity. Every individual born had to begin its 

 education on a blank sheet. But man had created for 

 himself a gigantic and overpowering possession, a sort of 

 physical envelope of customs, taboos, traditions, laws and 

 knowledge, which, though not transmitted to new in- 

 dividuals at birth as part of their structure, was yet a 

 heritage by which man was educated. This heritage was 

 put into his jjossession by gesture ; by word spoken, 

 written, or printed ; by law ; by the training given in 

 the nursery and school : and by the experience of life. 

 Individuals did not start equal, and it was the business 

 of the educator to ascertain the various degrees of educa- 

 bilitv- in the young and to adapt the course of education 

 administered to them to their varying aptitudes. The 

 well-educated man was he who had been enabled most 

 fully to benefit by the accumulated inheritance of human 

 knowledge and experience, and to enter on manhood as 

 the heir of all the ages. The true Greek spirit was 



