“‘THIS IS THE TACHYPOMP. DOES IT JUSTIFY THE NAME?’”]
“Number VIII runs a quarter of a mile in fifteen seconds, and reaches the end of number VII. Meanwhile number VII has run a quarter of a mile in the same time, and reached the end of number VI; number VI, a quarter of a mile in fifteen seconds, and reached the end of number V; number V, the end of number IV; number IV, of number III; number III, of number II; number II, of number I. And number I, in fifteen seconds, has gone its quarter of a mile along the ground track, and has reached station B. All this has been done in fifteen seconds. Wherefore, numbers I, II, III, IV, V, VI, VII, and VIII come to rest against the bumping-post at B, at precisely the same second. We, in number VIII, reach B just when number I reaches it. In other words, we accomplish two miles in fifteen seconds. Each of the eight cars, moving at the rate of a mile a minute, has contributed a quarter of a mile to our journey, and has done its work in fifteen seconds. All the eight did their work at once, during the same fifteen seconds. Consequently we have been whizzed through the air at the somewhat startling speed of seven and a half seconds to the mile. This is the Tachypomp. Does it justify the name?”
“IN FRONT OF ME STOOD PROFESSOR SURD HIMSELF, LOOKING DOWN WITH A NOT UNPLEASANT SMILE”]
Although a little bewildered by the complexity of cars, I apprehended the general principle of the machine. I made a diagram, and understood it much better. “You have merely improved on the idea of my moving faster than the train when I was going to the smoking-car?” I said.
“Precisely. So far we have kept within the bounds of the practicable. To satisfy the professor, you can theorize in something after this fashion: if we double the number of cars, thus decreasing by one half the distance which each has to go, we shall attain twice the speed. Each of the sixteen cars will have but one eighth of a mile to go. At the uniform rate we have adopted, the two miles can be done in seven and a half instead of fifteen seconds. With thirty-two cars, and a sixteenth of a mile, or twenty rods difference in their length, we arrive at the speed of a mile in less than two seconds; with sixty-four cars, each traveling but ten rods, a mile under the second. More than sixty miles a minute! If this isn’t rapid enough for the professor, tell him to go on increasing the number of his cars and diminishing the distance each one has to run. If sixty-four cars yield a speed of a mile inside the second, let him fancy a Tachypomp of six hundred and forty cars, and amuse himself calculating the rate of car number 640. Just whisper to him that when he has an infinite number of cars with an infinitesimal difference in their lengths, he will have obtained that infinite speed for which he seems to yearn. Then demand Abscissa.”