MY CLASS IN GEOMETRY. 41 



truths set forth in the lines and figures I had conned as a "boy ; ex- 

 amples which, had they been presented at school, would certainly 

 have somewhat diminished Euclid's unpopularity. In fullness of 

 time it fell to my lot to be concerned in the instruction of three 

 k y S _ on e of fourteen, the second twelve, the third a few months 

 younger. In thinking over how I might make attractive what had 

 once been my best-enjoyed lessons, I took up my ink-stained Eu- 

 clid Playfair's edition. A glance at its pages dispossessed me of 

 all notion of going systematically through the propositions they 

 took on at that moment a particularly rigid look, as if their con- 

 nection with the world of fact and life was of the remotest. Why, 

 I thought, not take a hint from the new mode of studying physics 

 and chemistry ? If a boy gets a better idea of a wheel and axle 

 from a real wheel and axle than from a picture, or more clearly 

 understands the chief characteristic of oxygen when he sees wood 

 and iron burned in it than when he only hears about its combus- 

 tive energy, why not give him geometry embodied in a fact before 

 stating it in abstract principle ? Deciding to try what could be 

 done in putting book and blackboard last instead of first, I made 

 a beginning. Taking the boys for a walk, I drew their attention 

 to the shape of the lot on which their house stood. Its depth was 

 nearly thrice its width, and a low fence surrounded it. As we 

 went along the road, a suburban one near Montreal, we noticed 

 the shapes of other fenced lots and fields. Counting our paces 

 and noting their number, we walked around two of the latter. 

 This established the fact that both fields were square, and that 

 while the area of one was an acre and a half, that of the other 

 was ten. When we returned home the boys were asked to make 

 drawings of the house-lot and of the two square fields, showing 

 to a scale how they differed in size. This task accomplished, they 

 drew a diagram of the house-lot as it would be if square instead 

 of oblong. With a foot-rule passed around the diagram it was 

 soon clear to them that, if the four sides of the lot were equal, some 

 fencing could be saved. The next question was whether any other 

 form of lot having straight sides could be inclosed with as little 

 fence as a square. Rectangles, triangles, and polygons were drawn 

 in considerable variety and number and their areas calculated, 

 only to confirm a suspicion the boys had entertained from the first 

 that of lots of practicable form square ones need least fencing. 

 In comparing their notes of the number of paces taken in walking 

 around the two square fields, a fact of some interest came out. 

 While the larger field contained nearly seven times as much land 

 as the other, it only needed about two and a half times the length 

 of fencing to surround it. Taking a drawing of the larger inclos- 

 ure, I divided it into four equal parts by two lines drawn at right 

 angles to each other. It only needed a moment for the boys to 



