770 



SCIENCE. 



[N. S. Vol. XVI. No. 411. 



of the British Empire, ought in future to 

 hold the first place in the examination and 

 to be exacted from all candidates.' The 

 italics are mine. It will be noticed that 

 they say nothing about the practical im- 

 possibility of obtaining teachers. As to 

 mathematics, the committee say : "It is of 

 almost equal importance that every officer 

 should have a thorough grounding in the 

 elementary part of mathematics. But they 

 think that elementary mechanics and geo- 

 metrical drawing, which under the name . 

 of practical geometry is now often used 

 as an introduction to theoretical instruc- 

 tion, should be added to this part of the ex- 

 amination so as to insure that at this stage 

 of instruction the practical application of 

 mathematics may not be left out of sight. ' ' 

 As Sir Hugh Evans would have said, 'It 

 is a very discretion answer — the meaning 

 is good'; but I would that the committee 

 had condemned abstract mathematics for 

 these army candidates altogether. 



This report appears in good time. It 

 would be well if committees would sit and 

 take evidence as to the education of men in 

 the other professions entered by our aver- 

 age boys. It is likely that when an au- 

 thoritative report is prepared on the want 

 of education of clergymen, for example, 

 exactly the same statements will be made 

 in regard to the general education which 

 ought to precede the technical training; 

 but perhaps a reference may be made in the 

 report to the importance of a study of 

 geology and biology, as well as physical 

 science. Think of the clergyman being 

 able to meet his scientific enemies in the 

 gate ! 



Thanlis mainly to the efforts of a British 

 Association Committee, really good teach- 

 ing of experimental science is now being in- 

 troduced into all public schools, in spite of 

 most persistent opposition wearing an ap- 

 pearance of friendliness. In consequence, 

 too, of the appointment of a British Asso- 



ciation Committee last year, at what might 

 be called the psychological moment, a great 

 reform has already begun in the teaching 

 of mathematics.* Even in the regulations 

 for the Oxford Locals for 1903 Euclid is 

 repudiated. It seems probable that at the 

 end of another five years no average boy 

 of fifteen years of age will have been com- 

 pelled to attempt any abstract reasoning 

 about things of which he knows nothing; 

 he will be versed in experimental mathe- 

 matics, which he may or may not call men- 

 suration; he will use logarithms, and mere 

 multiplication and division will be a joy 

 to him ; he will have a working power with 

 algebra and sines and cosines; he will be 

 able to tackle at once any curious new 

 problem which can be solved by squared 

 paper; and he will have no fear of the 

 symbols of the infinitesimal calculus. 

 When I insist that a boy ought to be able to 

 compute, this is the sort of computation 

 that I mean. Five years hence it will be 

 called 'elementary mathematics.' Four 

 years ago it was an unorthodox subject 

 called 'practical mathematics,' but it is 

 establishing itself in every polytechnic and 

 technical college and evening or day sci- 

 ence school in the country. Several times 

 I have been informed that on starting an 

 evening class, Avhen plans have been made 

 for a possible attendance of ten or twenty 

 students, the actual attendance has been 

 200 to 300. Pupils may come for one or 

 two nights to a class on academic mathe- 

 matics, but then stay away forever; a class 

 in practical mathematics maintains its 

 large numbers to the end of the winter, f 



* Discussion last year ttnd report of committee, 

 published by Macmillan. 



t To many men it will seem absurd that a real 

 working knowledge of what is usually called 

 higher mathematics, accompanied by mental train- 

 ing, can be given to the average boy. In the same 

 way it seemed absurd 500 years ago that power to 

 read and write and cipher could be given to every- 

 body. These general beliefs of ours are very 

 wonderful. 



