MATHEMATICS IN ENGLISH SCHOOLS 177 



mobiles and aeroplanes it would seem that every one should 

 be allowed to gain clear notions about energy and force ; but 

 my own experience (not more recent than six years ago) is 

 that it is very difficult to give clear notions. Perhaps there is 

 something in the contention that boys are becoming increasingly 

 familiar with machines and power in various forms, that all 

 this is a very modern development and that what was difficult 

 ten years ago may be found much easier to-day. I should not 

 like to deny the force of this but still I should hesitate to count 

 dynamics in the non-specialist mathematics course. General 

 notions about work and energy should enter into statics, via 

 the efficiency of machines ; but precise quantitative knowledge 

 concerning mass, force, momentum and kinetic energy has 

 been attained slowly in the growth of civilisation and appears 

 to be essentially difficult. 



If we restrict dynamics to be study of motion — velocity and 

 acceleration — we are easing the burden very appreciably. Ideas 

 of velocity and acceleration are within the range of geometry. 

 It is an obsolete dictum that motion — that is space, plus time — 

 is excluded from the scope of geometry. One of the chief 

 tendencies of geometry teaching is to use every opportunity 

 of presenting continuous change of configuration. If we may 

 for the occasion use the words statical and dynamical in the 

 popular sense of at rest and in motion, we may say that the 

 tendency is to make mathematics dynamical instead of statical. 

 Mathematics was statical when it dealt entirely with things 

 in stato quo quiescendi. Everything was fixed and immovable : 

 determination of roots of equations, study of fixed geometrical 

 figures. But now we regard algebra as concerned less with 

 the determination of values than with the study of relations 

 between variables. The idea of function is hovering over 

 school mathematics ; the graphing of functions has already 

 found admittance and this is but the first glimpse of a profound 

 change which is coming on. We are beginning to realise the 

 meaning of the iravra pel of our schooldays ; the Greek philo- 

 sopher's discovery was brought within the range of mathematics 

 by Newton's fluxious and now after twenty-four centuries it 

 has filtered down to the schools. 



When once it is granted that geometry is to tell us not 

 only how figures stand but also how they move and change, 

 it is a short step to the space-time diagram and the idea of velocity 



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