December 14, 191 1] 



NATURE 



227 



present our teaching involves a large amount of disciplinary 

 drill in subjects like algebra, which affords no outlook 

 beyond that afforded by the examination value of the 

 subject. 



Mr. Godfrey finds that, whatever may be the real educa- 

 tional value of this training, we have no definite proof that 

 it confers advantages which could not be at least equally 

 f-lTiciently derived from other studies. On the other hand, 

 we have certainly failed in one thing : broadly speaking, we 

 have failed to make mathematical thought enter as a main 

 element into the life of the educated classes. More and 

 more the affairs of life are being made amenable to mathe- 

 matical treatment, and as it has turned out the development 

 has been on lines divergent from the lines of schoolwork. 

 In these developments, the study of the calculus has been 

 the fundamental form in which mathematics is applied to 

 the affairs of modern life. This study, however, does not 

 grow out of the summit of school mathematics, but branches 

 off low down the stem, and it is independent of formal 

 geometry ; a vigorous pruning of school algebra and arith- 

 metic would in no wise prejudice the growth we want to 

 encourage. 



Mr. Godfrey, referring to the requirements of the non- 

 mathematical schoolboy, compares the drudgery and drill 

 of multiplying and dividing long algebraic expressions to 

 the technique of piano-playing, which may be useful for the 

 professional musician, but conspicuously fails to stimulate 

 a taste for music in the average pupil. He finds that the 

 tiine saved from»this drill would amply suffice not only for 

 the teaching of the calculus when its fundamental prin- 

 ciples are divested of the unnecessary complications intro- 

 duced by the consideration of transcendental functions, but 

 that a stimulating course in mechanics can quite well be 

 fitted into the curriculum which the mathematical as distinct 

 from the science master can provide for the non-specialist 

 schoolboy. 



As regards statics the position is clear, provided that 

 (experimental methods receive due prominence. The case for 

 dynamics is not so clear, and Mr. Godfrey's difficulties may 

 perhaps receive confirmation from the disagreement which 

 still exists among teachers regarding mass and weight, 

 poundals and slugs. He would therefore propose to restrict 

 the study to kinematics, which, as he points out, is really 

 nothing more than geometry with the introduction of a time 

 element. Many of Mr. Godfrey's suggestions have been 

 under the consideration of the committees appointed by the 

 Mathematical Association to inquire into the teaching of 

 school mathematics, and the feasibility of the proposals to 

 which he directs attention is proved by the fact that, in the 

 French lyc^cs for classical specialists, the proposed training 

 in analysis is reached with a far shorter number of hours 

 of schoolwork than is given to mathematics in England. 



The views indicated very imperfectly in this abstract will 

 doubtless be read with regret by disciples of the old school. 

 But England's neglect of mathematics requires us to face 

 many hard and unpleasant truths, and it is probably no 

 exaggeration to say that at the present time a plea for the 

 study of classics, even Latin and Greek grammar, would 

 receive a favourable reception at the hands of a large 

 section of the British public which would turn a deaf ear to 

 any corresponding claim of the mathematician. 



G. H. B. 



lUE JIEALTII OF THE X. IT ION. 

 'T'HE sixth annual meeting of the National League for 

 Physical Education and Improvement was held at the 

 Mansion House on December 8, the Lord Mayor presiding. 

 Letters of regret were read from the Archbishop of York, 

 Lord Haldane, the Lord Chief Justice, and others. The 

 first speaker was Sir Archibald Geikie, president of the 

 Royal .Society. He greatly approved of the objects of the 

 league, which are to stimulate public interest in the 

 physical improvement of the people, to lessen waste by 

 coordinating agencies already established for this purpose, 

 and starting them where none at present exist, to make 

 better known the local powers already possessed bv public 

 authorities, and to promote fresh legislation where neces- 

 sary. In a short, telling speech he pointed out that while 

 the league was to be congratulated on the very rapid and 



NO. 2198, VOL. 88] 



excellent progress it had made during the six years in 

 which it has been in existence, it has been, and still is, 

 hampered by want of funds, a want which it is to be hoped 

 will be remedied in the coming year by the aid of all. 

 those who have the health of the nation at heart. 



Bishop Boyd Carpenter described more in detail the work 

 of the league during the past year. The three subjects on 

 which it had been particularly engaged were the need for 

 a clean milk supply, organised physical recreation, and 

 the dangers arising from the use of inflammable makes of 

 flannelette. He showed that the league's work was not 

 of a purely philanthropic nature — it was an effort at self- 

 protection on the part of a great nation. It tried to protect 

 children in their upgrowth and to prevent them, in various 

 ways, from becoming a source of weakness to the com- 

 munity. 



Prof. Bostock Hill, medical officer of health for 

 Warwickshire, suggested that a national health week be 

 instituted, culminating in a Health Sunday, when the 

 churches might bring home to the nation the gospel of 

 hygiene. Communal sanitation has resulted in a very 

 considerable reduction in the death-rate of this country ; 

 but he pointed out that more than communal effort was 

 now required, and that this could only be brought about by 

 giving to the people individually a knowledge of what 

 hygiene could do for them, and at the same time co- 

 ordinating the services of all societies, private and public, 

 towards this end. People must be brought to understand 

 that hygiene consists in the spread of cleanliness, applied 

 to air, food, earth, and the dwelling. 



Lady St. Davids brought forward several practical 

 suggestions, such as the formation of tooth clubs for tooth- 

 less people, instead of boot clubs for bootless children, 

 since the former were in more danger of injuring their 

 constitution than the latter. She also pleaded for the 

 closer cooperation of the nursing profession with all who 

 were concerned in the promotion of the health of the 

 nation. 



THE ANALYSIS OF SPECIES."^ 



'T*HE author of the paper referred to below has made an 

 -^ important pioneer contribution to the study ot 

 heredity in crosses between plants of widely divergent 

 phylogeny, viz. reputed species of Linum, and has com- 

 pared the results obtained from such species-hybrids with 

 those obtained from the simpler varietal crosses. Statis- 

 tical methods have been utilised for the expression of the 

 characters examined, as in the work of Johanssen. 



The general trend of the results is to show that even in 

 cases where the composition of F, appears to present 

 perfectly smooth variation between the two parental 

 extremes, the behaviour in F3 shows that the inheritance 

 is in reality factorial, and can be most easily explained on 

 Mendelian principles. The frequency with which the 

 parental forms reappear is least in crosses of reputed 

 species, and becomes more common with closer crosses 

 until simple mono-hybrids are reached. The methods by 

 which the data were obtained appear to have been above 

 suspicion, both experimentally and statistically, while the 

 important error from vicinism is said to have been 

 excluded. 



One possibility has perhaps been overlooked, namely, 

 that while the inheritance of such a character as length of 

 seed is probably determined by several allelomorphic pairs, 

 yet the ultimate dimensions of the seed of any given plant, 

 fluctuation having been evaluated, may be influenced 

 through correlation with other similarly inherited 

 characters, notably the dimensions of the fruit. The posi- 

 tion of any plant in the frequency curve for a family is 

 thus, apart from fluctuation, firstly determined by the 

 factors which it carries, and secondarily by a deflection of 

 the expression of those factors from the normal by somatic 

 correlation. 



The characters studied were the length and breadth of 

 the seed, the length and breadth of the petals, and the 



1 " Dm Verhalren flukiiiierend variiender Merkmale bei der Battard- 

 ierung." Von Tine Tammes. «iu« dem Boianirehen I^boraiorium der 

 UnivrrsitJit Groninifen. Extrait du Recueil des Travaux botaniques Nrfer- 

 land.-ii«, vol. viii., Livr. 3, 1911. 



