174 SCIENCE PROGRESS 



of this after the plane course, with a discussion of particular 

 solids, the use of the globes and a little descriptive geometry. 

 The difficulty of the mensuration of solids is vanquished by 

 the magic touch of integration. 



Now that geometry has become numerical and mathematical 

 tables no longer a luxury, trigonometry cannot be kept out 

 of the non-specialist course. The step is easy from measuring 

 angles on paper to measuring angles with a simple instrument 

 of the theodolite species ; there are some who would say that 

 the step should be reversed. But real people do not go about 

 measuring elevations without a purpose; why then should school- 

 boys ? If they take an elevation, let them get something out 

 of it-— the height of some object in which they are interested. 

 To do this by drawing teaches, first, what a good weapon 

 drawing is ; secondly, the nature of similar figures ; the word 

 " similar " should be heard of here or hereabouts. Now drawing 

 is a method which no one need be too proud to use at any age 

 but after the earlier stages of secondary school life its use 

 should be merely incidental ; when a boy has mathematical 

 tables and has taken elevations, it is very arbitrary to with- 

 hold from him the proper way of reckoning the height by the 

 tangent of the angle. Further than this, it is needed by the 

 physics teacher with his inclined planes and tangent galvano- 

 meters. Trigonometry therefore cannot be excluded from the 

 non-specialist course. I am not one of those who regret that 

 boys find it an easy subject; there is no fear that mathematics 

 will ever be too easy. And with trigonometry we begin to get 

 the " outlook " which is the text of the present article. For 

 a boy can now be brought within sight of a long row of 

 applications to various matters of general interest and import- 

 ance. This arises from the fact that the mathematical tables 

 we teach him to use represent a vast source of energy, the 

 stored-up brainwork of former generations, a source of energy 

 too that does not waste as it is used. In learning trigonometry 

 he is learning how to tap this source. 



Trigonometry is liable to just the same educational misuse 

 as algebra. The trigonometry taught in all schools twenty 

 years ago and taught no doubt in many to-day, consisted 

 mainly of algebraic manipulation. Teachers had altogether lost 

 sight of the utilitarian motive to which we must appeal if we 

 want to have the natural boy with us rather than against us. 



