a corn-fan, or any machine that has a rotatory motion; he will be entertained with his new employment; he will compare the velocities of different machines; the meaning of this word will be easily added to his vocabulary.
"Does that part of the arms of the wind-mill which is near the axle-tree, or centre, I mean that part which has no cloth or sail upon it, go as fast as the ends of the arms that are the farthest from the centre?"
"No, not near so fast."
"But that part goes as often round in a minute as the rest of the sail."
"Yes, but it does not go as fast."
"How so?"
"It does not go so far round."
"No, it does not. The extremities of the sails go through more space in the same time than the part near the centre."
By conversations like these, the technical meaning of the word velocity may be made quite familiar to a child much younger than what has been mentioned; he may not only comprehend that velocity means time and space considered together, but if he is sufficiently advanced in arithmetic, he may be readily taught how to express and compare in numbers velocities composed of certain portions of time and space. He will not inquire about the abstract meaning of the word space; he has seen space measured on paper, on timber, on the water, in the air, and he perceives distinctly that it is a term equally applicable to all distances that can exist between objects of any sort, or that he can see, feel, or imagine.
Momentum, a less common word, the meaning of which is not quite so easy to convey to a child, may, by degrees, be explained to him: at every instant he feels the effect of momentum in his own motions, and in the motions of every thing that strikes against him; his feelings and experience require only proper terms to become the subject of his conversation. When he begins to inquire, it is the proper time to instruct him. For instance, a boy of ten years old, who had acquired the meaning of some other terms in science, this morning asked the meaning of the word momentum; he was desired to explain what he thought it meant.
He answered, "Force."
"What do you mean by force?"
"Effort."
"Of what?"
"Of gravity."
"Do you mean that force by which a body is drawn down to the earth?"
"No."
"Would a feather, if it were moving with the greatest conceivable swiftness or velocity, throw down a castle?"
"No."21
"Would a mountain torn up by the roots, as fabled in Milton, if it moved with the least conceivable velocity, throw down a castle?"
"Yes, I think it would."
The difference between an uniform, and an uniformly accelerated motion, the measure of the velocity of falling bodies, the composition of motions communicated to the same body in different directions at the same time, and the cause of the curvilinear track of projectiles, seem, at first, intricate subjects, and above the capacity of boys of ten or twelve years old; but by short and well-timed lessons, they may be explained without confounding or fatiguing their attention. We tried another experiment whilst this chapter was writing, to determine whether we had asserted too much upon this subject. After a conversation between two boys upon the descent of bodies towards the earth, and upon the measure of the increasing velocity with which they fall, they were desired, with a view to ascertain whether they understood what was said, to invent a machine which should show the difference between an uniform and an accelerated velocity, and in particular to show, by occular demonstration, "that if one body moves in a given time through a given space, with an uniform motion, and if another body moves through the same space in the same time with an uniformly accelerated motion, the uniform motion of the one will be equal to half the accelerated motion of the other." The eldest boy, H – , thirteen years old, invented and executed the following machine for this purpose:
Plate I, Fig. 3. b is a bracket 9 inches by 5, consisting of a back and two sides of hard wood: two inches from the back two slits are made in the sides of the bracket half an inch deep, and an eighth of an inch wide, to receive the two wire pivots of a roller; which roller is composed of a cylinder, three inches long and half an inch diameter; and a cone three inches long and one inch diameter in its largest part or base. The cylinder and cone are not separate, but are turned out of one piece; a string is fastened to the cone at its base a, with a bullet or any other small weight at the other end of it; and another string and weight are fastened to the cylinder at c; the pivot p of wire is bent into the form of a handle; if the handle is turned either way, the strings will be respectively wound up upon the cone and cylinder; their lengths should now be adjusted, so that when the string on the cone is wound up as far as the cone will permit, the two weights may be at an equal distance from the bottom of the bracket, which bottom we suppose to be parallel with the pivots; the bracket should now be fastened against a wall, at such a height as to let the weights lightly touch the floor when the strings are unwound: silk or bobbin is a proper kind of string for this purpose, as it is woven or plaited, and therefore is not liable to twist. When the strings are wound up to their greatest heights, if the handle be suddenly let go, both the weights will begin to fall at the same moment; but the weight 1, will descend at first but slowly, and will pass through but small space compared with the weight 2. As they descend further, No. 2 still continues to get before No. 1; but after some time, No. 1 begins to overtake No. 2, and at last they come to the ground together. If this machine is required to show exactly the space that a falling body would describe in given times, the cone and cylinder must have grooves cut spirally upon their circumference, to direct the string with precision. To describe these spiral lines, became a new subject of inquiry. The young mechanics were again eager to exert their powers of invention; the eldest invented a machine upon the same principle as that which is used by the best workmen for cutting clock fusees; and it is described in Berthoud. The youngest invented the engine delineated, Plate 1, Fig. 4.
The roller or cone (or both together) which it is required to cut spirally, must be furnished with a handle, and a toothed wheel w, which turns a smaller wheel or pinion w. This pinion carries with it a screw s, which draws forward the puppet p, in which the graver of chisel g slides without shake. This graver has a point or edge shaped properly to form the spiral groove, with a shoulder to regulate the depth of the groove. The iron rod r, which is firmly fastened in the puppet, slides through mortices at mm, and guides the puppet in a straight line.
Plate 1.
The rest of the machine is intelligible from the drawing.
A simple method of showing the nature of compound forces was thought of at the same time. An ivory ball was placed at the corner of a board sixteen inches broad, and two feet long; two other similar balls were let fall down inclined troughs against the first ball in different directions, but at the same time. One fell in a direction parallel to the length of the board; the other ball fell back in a direction parallel to its breadth. By raising the troughs, such a force was communicated to each of the falling balls, as was sufficient to drive the ball that was at rest to that side or end of the board which was opposite, or at right angles, to the line of its motion.
When both balls were let fall together, they drove the ball that was at rest diagonally, so as to reach the opposite corner. If the same board were placed as an inclined plane, at an angle of five or six degrees, a ball placed at one of its uppermost corners, would fall with an accelerated motion in a direct line; but if another ball
When this question was sometime afterwards repeated to S – , he observed, that the feather would throw down the castle, if its swiftness were so great as to make up for its want of weight.
