Page:Popular Science Monthly Volume 38.djvu/53

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43
MY CLASS IN GEOMETRY.

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 separate 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 underwent 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 remained 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 comparatively large surface retarded its motion through the water. The next day we visited Montreal's wharves, and, pacing alongside several 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 proportionately to power much larger moving surfaces to be retarded by friction than those we had seen a few minutes before. On being 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 identical 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 confident that there was no Euclid in that plaything. It proved otherwise. That evening he calculated how much the lifting