THE TEACHING OF MECHANICS 101 



assumptions, the truth of which is intuitional, but 

 does not follow from his scheme of axioms and 

 postulates. 



Of late years much has been done to check the 

 undue expenditure of time and energy, in the 

 customary treatment of Algebra, upon the acquire- 

 ment of skill in the manipulation of artificially 

 complicated algebraical expressions. Indeed no 

 subject has suffered more from its own technique 

 than Algebra ; much effort which should have been 

 directed towards the acquirement of really fruitful 

 ideas has been wasted upon an often vain effort 

 to acquire an almost mechanical dexterity in 

 dealing with symbols out of relation with the 

 concrete. The time gained by the restriction of 

 this kind of work to the necessary minimum has, 

 in the hands of -the best teachers, been employed, 

 to the lasting advantage of the pupils, in giving 

 them some comprehension of the use of the subject 

 in dealing with actualities, and in extending their 

 mental vision by means of an appropriately simple 

 introduction to the principles of the Calculus. 



Both in Schools and Universities the teaching 

 of Mechanics has suffered from the undue separa- 

 tion of the Mathematical and the Experimental 

 teaching of the subject. Neither treatment of the 

 subject can be satisfactory without at least some 

 admixture of the other. Although, in a teaching 

 course, the precise relation between the two sides of 

 the subject must largely depend upon the ultimate 



