176 SCIENCE PROGRESS 



The more mathematical teaching looks outwards the better will 

 it be for schools; the place for self-centred mathematics is the 

 university. 



The main reason for turning over to the mathematician the 

 elementary instruction in mechanics is this, that in any case 

 mechanics is taught by the mathematical staff to the top classes 

 in connection with scholarship work. In the past there have 

 been two separate and unrelated systems of mechanics-teaching 

 within each school : the elements taught inductively by the 

 physicist to the middle classes and the whole subject taught 

 again, deductively, by the mathematician to the top classes. 

 There might have been something to be said for this double 

 system if the two courses were deliberately designed to fit in 

 with one another but the number of schools in which this 

 occurred must have been small. I imagine that pretty often 

 the mathematician did not know that any other system of 

 mechanics-teaching existed in the school : there is frequently 

 in schools a lack of touch between departments which would 

 do credit to a Government office. It is the business of the 

 headmaster to see that such things do not occur ; but not many 

 classical headmasters are competent to exercise general super- 

 vision over the mathematics and science of their schools and 

 the ignorance of headmasters is itself a result and an evidence 

 of the failure of mathematical teaching in the past. 



When mathematicians do take over the whole teaching of 

 mechanics they will have to struggle consciously against the 

 temptation to turn it into a set of mathematical problems. 

 Mechanics will be valuable to the average boy in so far as 

 it creates in him a vivid perception of laws of physical 

 phenomena ; the niceties of analytical elegance tend to distract 

 his attention from the fundamental principles and even to 

 cultivate wrong impressions through such abstract conceptions 

 as the perfectly rough insect, the small elephant whose weight 

 may be neglected and so forth. It is true that this fauna is 

 almost extinct but we still hear too much of the frictionless 

 machine and too little of the efficiency of actual machines ; the 

 influence of the Cambridge school of applied mathematics in 

 its decadence is still dominant. 



The case for statics in the non-specialist course is quite 

 clear ; when we come to speak of dynamics there is much 

 difference of opinion. In these days of electric motors, auto- 



