A force, for instance the pressure of the finger or the hand, equal to one pound against a body free to move, will, we will say, move that body in one second of time through a space of ten feet, and at the end of that second the body will have a velocity of twenty feet. It is manifest that at the end of the second the velocity will be twenty feet per second for its initial velocity is zero, and its average velocity ten feet per second, the acceleration being, of course, presumed uniform. Now, it is _not_ true as the Perpetual Motion worker had assumed that the same energy--i. e., the same work that is required to increase the velocity from zero to ten feet per second will increase the velocity from ten feet per second to twenty feet per second, and _in that assumption_ lay the fallacy of our friends who were thus seeking Perpetual Motion. The greater the velocity, the more energy is required to impart a given acceleration. To increase the velocity from ten feet per second to twenty feet per second, the applied force must continue through one second of time, and more energy is required to follow a rapidly moving body, and continue to apply to it a given force for one second than would be required to follow and maintain the application of the same force to a body moving more slowly--the _distance_ traveled is greater in one case than in the other. It must be plain that if the moving body have a velocity at the end of the first second of twenty feet per second, it will, at the end of the second second, with the same pressure (force) continued against the same resistance, have a velocity of forty feet per second, and at the end of three seconds have a velocity of sixty feet, and at the end of four seconds a velocity of eighty feet, and so on. Now, at the beginning of the second second it had a velocity of twenty feet, and at the end of that second a velocity of forty feet. It therefore, traveled through that second with an average velocity of thirty feet and, of course, during the second second traveled exactly thirty feet. It traveled ten feet the first second, and if it traveled thirty feet the second, then in the two seconds it traveled forty feet--four times as far as it traveled the first second. At the beginning of the third second it had a velocity of forty feet, and at the end of the third second a velocity of sixty feet. The average velocity then for the third second would be one-half the sum of forty feet and plus sixty feet--that is to say, it would be fifty feet, and that would be the distance traveled during the third second. The first second it traveled ten feet, the second second thirty feet, and the third second fifty feet, making a total in three seconds of ninety feet--that is to say, in three seconds it traveled nine times as far as in one second.