194 SCIENCE PROGRESS 



alertness of brain. It is true that interest must be aroused 

 before detailed study is commenced but if the scientific method 

 be pursued, interest continues and increases during investi- 

 gation or verification so that progress may be made from the 

 simple to the complex, from the indefinite to the definite, from 

 the concrete to the abstract, from the empirical to the rational. 



To the remarks on the importance of mechanics and its value 

 as an educational medium, no exception can be taken. " The 

 wise teacher will lead his boys readily from experimental fact 

 to deduced principle and from deduced principle to simple 

 calculations, which can again be verified by experiment." But 

 this reads like a piece of special pleading for the heuristic 

 method and certainly reflects its spirit admirably, though the 

 carping critic might inquire if there be not a danger of system- 

 atising the rediscovery of principles, if not of facts, in the 

 teaching of experimental mechanics. 



Prof. Thompson also dealt with the recent reforms in mathe- 

 matical teaching. He appeared to deplore the disappearance 

 of Euclid, gave it as his deliberate opinion that boys are less 

 capable of following a sustained train of thought nowadays 

 than they used to be and stated his belief that their failure was 

 partly due to the new methods used in teaching Geometry. 

 If this be the case, it may perhaps be referred to the fact that 

 we are in the transition stage in which opinion is deliquescent; 

 but as the plan now generally adopted is that of inquiry, the 

 above remarks on the heuristic method apply here and it is 

 hardly necessary to repeat the arguments which have led to the 

 downfall of Euclid. There is no doubt that many capable boys 

 are being trained to think precisely and to express their thoughts 

 clearly, so that some discipline equivalent to that claimed for 

 Euclid's presentation of the facts of Geometry as a chain of 

 connected thought has been found. Since the abstract method 

 formerly pursued — a method designed to lead to a fixed result 

 on a rigidly defined syllabus with a definite unalterable 

 sequence — has given place to concrete treatment leading up 

 to abstract reasoning, the freedom gained is desirable on every 

 educational ground ; but this freedom is no valid reason for the 

 neglect of a logical coherent sequence, so that as much, if not 

 more, training in precision of expression can accompany the 

 course in Geometry as has ever been the case. It is all a 

 question of method, of presentation and development combined 



