42 THE POPULAR SCIENCE MONTHLY. 



perceive how these lines of division, representing as they did so 

 much new fencing, explained why the small field had proportion- 

 ately to area so much longer a boundary than the large one. 



A chess-board served as another illustration. Taking each of 

 its sixty-four squares to represent a farm duly inclosed, it was 

 easy to see how a farmer rich enough to buy the whole number, 

 were he to combine them in one stretch of land, could dispense 

 with an immense quantity of lumber or wire fencing. During a 

 journey from Montreal to Quebec the boys had their attention 

 directed to the disadvantageous way in which many of the farms 

 had been divided into strips long and narrow. " Just like a row 

 of chess squares run together," said one of the lads. 



When a good many examples had impressed the lesson on their 

 minds pretty thoroughly, I had them write under their drawings, 

 taking care that the terms used were understood : " Like plane 

 figures vary in boundary as their like linear dimensions ; they 

 vary in area as the square of their like linear dimensions." It 

 proved, however, that while the boys knew this to be true of 

 squares, they could not at first comprehend that it was equally 

 true of other forms. They drew equilateral and other triangles 

 and ascertained that they conformed to the rule, but I was taken 

 aback a little when the eldest boy said, " It isn't so with circles, is 

 it ?" His doubt was duly removed, but the remark showed how 

 easy it is to make words outrun ideas ; how hard it is for a young 

 mind to recognize new cases of a general law with which in other 

 examples it is quite familiar. 



One chilly evening the sitting-room in which my pupils and I 

 sat was warmed by a grate-fire. Shaking out some small live 

 coals, I bade the boys observe which of them turned black soonest. 

 They were quick to see that the smallest did, but they were un- 

 able to tell why. They were reminded of the rule they had com- 

 mitted to paper, but to no purpose, until I broke a large glowing 

 coal into a score of fragments which became black almost at once. 

 Then one of them cried, " Why, smashing that coal gave it more 

 surface ! " This young fellow was studying the elements of astron- 

 omy at school, so I had him give us some account of how the 

 planets differ from one another in size, how the moon compares 

 with the earth in mass, and how vastly larger than any of its 

 worlds is the sun. Explaining to him the theory of the solar sys- 

 tem's fiery origin, I shall not soon forget his keen delight in 

 which the others presently shared when it burst upon him that 

 because the moon is much smaller than the earth it must be much 

 colder ; that, indeed, it is like a small cinder compared with a large 

 one. It was easy to advance from this to understanding why 

 Jupiter, with eleven times the diameter of the earth, still glows 

 faintly in the sky ; and then to note that the sun pours out its 



