A.—­It is.

19. Q.—­Therefore during the first second of falling as much impelling power will be given by the force of gravity as during every succeeding second?

A.—­Undoubtedly.

20. Q.—­How comes it, then, that while the body falls 64-4/12 feet in two seconds, it falls only 16-1/12 feet in one second; or why, since it falls only 16-1/12 feet in one second, should it fall more than twice 16-1/12 feet in two?

A.—­Because 16-1/12 feet is the average and not the maximum velocity during the first second.  The velocity acquired at the end of the 1st second is not 16-1/12, but 32-1/6 feet per second, and at the end of the 2d second a velocity of 32-1/6 feet has to be added; so that the total velocity at the end of the 2d second becomes 64-2/6 feet; at the end of the 3d, the velocity becomes 96-3/6 feet, at the end of the 4th, 128-4/6 feet, and so on.  These numbers proceed in the progression 1, 2, 3, 4, &c., so that it appears that the velocities acquired by a falling body at different points, are simply as the times of falling.  But if the velocities be as the times, and the total space passed through be as the squares of the times, then the total space passed through must be as the squares of the velocity; and as the vis viva or mechanical power inherent in a falling body, of any given weight, is measurable by the height through which it descends, it follows that the vis viva is proportionate to the square of the velocity.  Of two balls therefore, of equal weight, but one moving twice as fast as the other, the faster ball has four times the energy or mechanical force accumulated in it that the slower ball has.  If the speed of a fly-wheel be doubled, it has four times the vis viva it possessed before—­vis viva being measurable by a reference to the height through which a body must have fallen, to acquire the velocity given.

21. Q.—­By what considerations is the vis viva or mechanical energy proper for the fly-wheel of an engine determined?

A.—­By a reference to the power produced every half-stroke of the engine, joined to the consideration of what relation the energy of the fly-wheel rim must have thereto, to keep the irregularities of motion within the limits which are admissible.  It is found in practice, that when the power resident in the fly-wheel rim, when the engine moves at its average speed, is from two and a half to four times greater than the power generated by the engine in one half-stroke—­the variation, depending on the energy inherent in the machinery the engine has to drive and the equability of motion required—­the engine will work with sufficient regularity for most ordinary purposes, but where great equability of motion is required, it will be advisable to make the power resident in the fly-wheel equal to six times the power generated by the engine in one half-stroke.