1. Two Kinds of Impossibles.—On the very threshold of my subject I am met by the objection that" many things far more wonderful, and, before their realization, seemingly far more impossible, than flying-machines, have, nevertheless, actually come to pass. Then why not this also? He is a bold man that declares anything impossible in this age of rapid progress and startling inventions." I answer: True enough, many wonderful and apparently impossible things have indeed come to pass; and that, too, in spite of the adverse predictions of some rash scientists. But there are two kinds of impossibles—the seeming and the real. The seeming impossibles we believe to be impossible, only because we do not yet understand the principles involved in the problem, and therefore can not conceive the conditions necessary for their successful application. Such are all the cases which most readily occur to the mind as triumphs of science—such, for example, as the locomotive, the telegraph, the telephone, etc. The real impossibles, on the contrary, we know to be such, because we see clearly through all the principles involved in the problem and the limits of their possible application. Of this kind are the problem of a perpetual-motion machine, and of a self-supporting arch of indefinite length. Now observe—that, of these two kinds of impossibles, to the unreflecting the seeming are far the more impossible and wonderful. In fact, to most people the real impossibles do not seem impossible, or wonderful, or even difficult at all. Hence, in every age and country we find men who waste their lives in vain attempts to make perpetual-motion machines. So, also, in regard to the indefinite arch. Most people do not see at once why an arch of any length should not support itself if only it be big and strong in proportion to its length.
Let me stop a moment to illustrate this by an anecdote, I remember many years ago meeting a traveling agent of a Remington bridge (a wooden suspension-bridge), who had with him for exhibition a small model which, when set up, was about twenty feet long, and had stringers about as big as my finger. This little model not only sustained itself, but, in addition, the weight of a stout looker-on—"a fat and greasy citizen"—twenty times as heavy as the bridge itself. "Now," said the plausible agent," if you increase the size and strength of the stringers in proportion as you increase the length of your bridge, it is evident that a bridge of this pattern, of any length, will not only sustain itself, but twenty times its own weight in the form of loaded wagons," Most of those who heard it accepted his reasoning as irrefutable. Of course, every engineer knows that this is not true. For, while the weight of the bridge increases as the cube of the diameter of all its parts, the strength of the stringers increases only as the square of their diameter. In increasing the size in