MY CLASS IN GEOMETRY. 43 



wealth of heat and light because the immensity of its bulk has, 

 comparatively speaking, so little surface to radiate from. 



To make the law concerned in all this definite and clear, I took 

 eight blocks, each an inch cube, and had the boys tell me how 

 much surface each had six square inches. Building the eight 

 blocks into one cube, they then counted the square inches of its 

 surface twenty-four ; four times as many as that of each sepa- 

 rate cube. With twenty-seven blocks built into a cube, they 

 found that structure to have a surface of fifty-four square inches, 

 nine times that of each component block. As the blocks under- 

 went the building process, a portion of their surfaces came into 

 contact, and thus hidden could not count in the outer surfaces of 

 the large cubes: Observation and comparison brought the boys 

 to the rule which told exactly what proportion of surface re- 

 mained exposed. They wrote, " Like solids vary in surface as the 

 square, and in contents as the cube of their like dimensions." 

 They were glad to note that the first half of their new rule was 

 nothing but their old one of the farms and fields over again. 



As the law at which we had now arrived is one of the most 

 important in geometry, I took pains to illustrate it in a variety of 

 ways. Taking a long, narrow vial of clear glass, nearly filled 

 with water and corked, I passed it around, requesting each of the 

 boys to shake it smartly, hold it upright, and observe which of 

 the bubbles came to the surface first. All three declared that the 

 biggest did, but it was a little while before they could be made to 

 discern why. They had to be reminded of the cinders and the 

 building-blocks before they saw that a small bubble's compara- 

 tively large surface retarded its motion through the water. The 

 next day we visited Montreal's wharves, and, pacing alongside sev- 

 eral vessels, jotted down their length. In response to questions, the 

 boys showed their mastery of the principle which decides that the 

 larger a ship the less is its surface in proportion to tonnage. Going 

 aboard an Allan liner, of five thousand tons burden, we descended 

 to the engine-room ; we next visited a steamer of somewhat less than 

 one thousand tons, and inspected her engines engines having pro- 

 portionately to power much larger moving surfaces to be retarded 

 by friction than those we had seen a few minutes before. On be- 

 ing reminded of their experiments with the vial, the boys were 

 pleasantly surprised to find that the largest bubble and the ocean 

 racer come first to their respective ports by virtue of their identi- 

 cal quality of bigness, by reason of the economies which dwell 

 with size. As we walked homeward, the youngest of our party 

 espied a street-vender with a supply of gaudy toy -balloons. One 

 of them bought, I dare say the little fellow's mind was pretty con- 

 fident that there was no Euclid in that plaything. It proved 

 otherwise. That evening he calculated how much the lifting 



