TRANSACTIONS OF SECTION G. 719 



Thanks mainly to the efforts of a British Association Committee, really good 

 teaching of experimental science is now being iutroduced into all public schools, 

 in spite of most persistent opposition wearing an appearance of friendliness. In 

 consequence, too, of the appointment of a British Association 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 100-3 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 compelled 

 to attempt any abstract reasoning about things of which he knows nothing; he 

 will be versed in experimental mathematics, which he may or may not call mensura- 

 tion ; 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 mathe- 

 matics.' Four years ago it was an unorthodox subject called 'practical mathe- 

 matics,' but it is establishing itself in every polytechnic and technical college 

 and evening or day science school in the coimtry. Several times I have been 

 informed that on starting an evening class, when 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 for ever ; a class in practical mathematics maintains 

 its large numbers to the end of the winter.- 



Hitherto the average boy has been taught mathematics and mechanics as if he 

 were going to be a Newton or a Laplace ; he learnt nothing and became stupid. I 

 am sorry to say that the teaching of mechanics and mechanical engineering through 

 experiment is comparatively unknown. Cambridge writers and other writers of 

 books on experimental mechanics are unfortunately ignorant of engineering. Univer- 

 sity courses on engineering — with one splendid exception, under Professor Ewing 

 at Cambridge — assume that undergraduates are taught their mechanics as a logical 

 development of one or two axioms ; whereas in many technical schools under the 

 Science and Art Department apprentices go through a wonderfully good laboratory 

 course in mechanical engineering. We really want to give only a few fundamental 

 ideas about momentum and the transformations of energy and the properties of 

 materials, and to give them from so many points of view that they become part of 

 a student's mental machinery, so that he uses them continually. Instead of giving 

 a hundred labour-saving rules which must be forgotten, we ought to give the one 

 or two ideas which a man's common-sense will enable him to apply to any problem 

 whatsoever and which cannot be forgotten. A boy of good mathematical attain- 

 ments msij build on this experimental knowledge afterwards a superstructure 

 more elaborate than liankine or Kelvin or Maxwell ever dreamt of as being 

 possible. Every boy will build some superstructure of his own. 



I must not dwell any longer on the three essential parts of a good general 

 education which lead to the three powers which all boys of fifteen ought to 

 possess ; power to use books and to enjoy reading ; power to use mathematics and 

 to enjoy its use ; power to study Nature sympathetically. English Board School 

 boys who go to evening classes in many technical schools after they become 

 apprentices are really obtaining this kind of education. The Scotch Education 

 Board is trying to give it to all boys in primary and secondary schools. It will, 

 I fear, be some time before the sons of well-to-do parents in England have a 

 chance of obtaining it. 



When a boy or man of any age or any kind of experience enters an engineering 



' Discussion last year and report of Committee, published by Macmillan. 



= To many men it will seem absurd that a real working knowledge of what is 

 usually called higher mathematics, accompanied by mental training, 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 everybody. These general beliefs of 

 ours are very wonderful. 



