316 SCIENCE PROGRESS. 



carries him easily over the initial difficulties ; he is not frightened by the drudgery 

 which accompanies the early stages of every serious study. To a boy of con- 

 siderable scientific talent, it probably makes little difference whether he be taught 

 well or badly. But sound teaching is of paramount importance to the great 

 number whose only chance of a little science comes during their school life. 

 There is no doubt in my mind that the teaching ought principally to be addressed 

 to them. Those who believe that science can convey an inspiring message to 

 everyone will agree that the infusion of a scientific spirit is of greater importance 

 than the knowledge of scientific facts. 



But we must insist that all science depends on strict and clear reasoning. 

 Leaving proof out of the question, the value of scientific evidence centres in the 

 agreement between the conclusion drawn from certain premises and the observed 

 facts. That agreement to be perfect has to be quantitative as well as qualitative, 

 and measurement therefore lies at its root. To express it in different words, 

 mechanics, as Leonardo da Vinci has pointed out, is the foundation of all science. 

 Mechanics implies a certain amount of mathematics, with a moderate facility in 

 the manipulation of numbers, and here we meet with the difficulty that the study 

 of mathematics is unsympathetic to a considerable section of the community. 

 Are we, then, to draw a line even at an early stage of the teaching, separating 

 those who have an aptitude for mathematics from those who have not? It seems 

 that we must either exclude a number of scholars from scientific teaching, or force 

 a distasteful subject on them. I have suffered too much myself from the latter 

 alternative to advocate it without qualification, but I should not assume that what 

 may be only a superficial aversion has any deep-seated cause in the constitution 

 of a boy's brain. Maxwell, in his own trenchant manner, once said to me : " All 

 men are mathematicians, only some know it and some don't." It is here that the 

 skilful teacher has his chance, and may stir the imagination of the pupil to a point 

 at which the aversion is overcome. A member of my own family furnishes an 

 example which may serve to illustrate my meaning. As a boy he made no 

 progress in his mathematical lessons ; he disliked the subject so much that he 

 went to the headmaster of the school, declared his inability to master its elements, 

 and asked to be excused from further attendance, declaring himself willing to 

 spend the time on any other subject that might be assigned to him. The head- 

 master, being a reasonable man, talked to him sympathetically (he was probably 

 no mathematician himself). " Try another six months," he said, " and if at the 

 end of that time you come to me with the same request, I will agree to it." 

 Whether it was the feeling of freedom from compulsion, or whether he was put 

 under another teacher who succeeded in appealing to his imagination in the right 

 way, these six months altered his whole outlook. He stuck to his mathematics, 

 went to the University, and ultimately became a mathematician of some repute. 

 He had to lead the life of an invalid, and I remember him an old man lying 

 on his couch, finding his chief consolation in mathematical work, which leading 

 journals found sufficiently important to publish. 



Exciting the imagination is one of the most powerful methods of mastering 

 difficulties by overcoming the distaste for the initial drudgery of work which only 

 becomes interesting when these difficulties have been surmounted. It is specially 

 important in illustrating numerical relationships, and allowing the mind to grasp 

 the meaning of large figures. 



Astronomy will furnish a number of suitable examples. The distance from the 

 sun to the earth is about 92,000,000 miles, a number which perhaps in itself does 

 not convey much, but if we use an illustration due to the late Professor Young 



