power of his balloon would gain on its surface were its dimensions increased one thousand or ten thousand fold—step by step approaching the conclusion that, if air-ships are ever to be manageable in the face of adverse winds, they must be made vastly larger than any balloons as yet put together.
Not far from home stood a large store, displaying a miscellaneous stock of groceries, fruits, dry goods, shoes, and so on. As we cast our eyes about its shelves, counters, and floor, we saw many kinds of packages—cans of fish, marmalade, and oil, glass jars of preserves and olives, boxes of rice and starch, large paper sacks of flour. Outside the door stood half a dozen empty barrels and packing-cases. It certainly seemed as if the cost of paper, glass, tin, and lumber for packages must be an important item in retailing. One after another the boys discovered that the store was giving them their old lesson in a new form. They saw that the larger a jar or box the less material it needed. On their return home they were gradually led up to finding that form as well as size is an element in economy. Just as farms square in shape need least fence, they found that a cubical package needs least material to make it, and that tins of cylindrical form require least metal when of equal breadth and height.
Our next lesson was one for lack of which not a few inventors and designers have wasted time and money. Taking the trio to Victoria Bridge, we asked its custodian the length of its central span. His reply was, three hundred and fifty-two feet. When I asked the boys how matters would be changed if the span were twice as large, they soon perceived that, while increased in strength by breadth and thickness, it would be heavier by added length as well. On our return we compared two boards differing in each of their three dimensions as one and two, serving to make manifest why it often happens that a design for a bridge or roof, admirable as a model, fails in the large dimensions of practical construction.
One day a roofer had to be called in to make needful repairs. We went with him to the roof, and found the gutter choked with mud. How had it got there? A glance at the roof, an iron one, showed it covered with dust which the next shower would add to the deposit in the gutter. Dust-particles are extremely small and fine, and did not this explain how the wind had been able to take hold of them and carry them far up into the air? Although the boys had considerably less pocket-money than they liked, they had still enough to enable them to observe that the smallest coins were most worn. When they came to think it over, they readily hit on the reason why.
Our next lessons were intended to bring out the relations which subsist between several of the principal forms of solids. Two series of models in wood were accordingly made. The first consisted