Practical Education, Volume II. Edgeworth Maria
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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 were made (by descending through an inclined trough) to strike the first ball at right angles to the line of its former descent, at the moment when it began to descend, it would not, as in the former experiment, move diagonally, but would describe a curve.
The reason why it describes a curve, and why that curve is not circular, was easily understood. Children who are thus induced to invent machines or apparatus for explaining and demonstrating the laws of mechanism, not only fix indelibly those laws in their own minds, but enlarge their powers of invention, and preserve a certain originality of thought, which leads to new discoveries.
We therefore strongly recommend it to teachers, to use as few precepts as possible in the rudiments of science, and to encourage their pupils to use their own understandings as they advance. In mechanism, a general view of the powers and uses of engines is all that need be taught; where more is necessary, such a foundation, with the assistance of good books, and the examination of good machinery, will perfect the knowledge of theory and facilitate practice.
At first we should not encumber our pupils with accurate demonstration. The application of mathematics to mechanics is undoubtedly of the highest use, and has opened a source of ingenious and important inquiry. Archimedes, the greatest name amongst mechanic philosophers, scorned the mere practical application of his sublime discoveries, and at the moment when the most stupendous effects were producing by his engines, he was so deeply absorbed in abstract speculation as to be insensible to the fear of death. We do not mean, therefore, to undervalue either the application of strict demonstration to problems in mechanics, or the exhibition of the most accurate machinery in philosophical lectures; but we wish to point out a method of giving a general notion of the mechanical organs to our pupils, which shall be immediately obvious to their comprehension, and which may serve as a sure foundation for future improvement. We are told by a vulgar proverb, that though we believe what we see, we have yet a higher belief in what we feel. This adage is particularly applicable to mechanics. When a person perceives the effect of his own bodily exertions with different engines, and when he can compare in a rough manner their relative advantages, he is not disposed to reject their assistance, or expect more than is reasonable from their application. The young theorist in mechanics thinks he can produce a perpetual motion! When he has been accustomed to refer to the plain dictates of common sense and experience, on this, as well as on every other subject, he will not easily be led astray by visionary theories.
Plate 2.
To bring the sense of feeling to our assistance in teaching the uses of the mechanic powers, the following apparatus was constructed, to which we have given the name Panorganon.
It is composed of two principal parts: a frame to contain the moving machinery; and a capstan or windlass, which is erected on a sill or plank, that is sunk a few inches into the ground: the frame is by this means, and by six braces or props, rendered steady. The cross rail, or transom, is strengthened by braces and a king-post to make it lighter and cheaper. The capstan consists of an upright shaft, upon which are fixed two drums; about which a rope may be wound up, and two levers or arms by which it may be turned round. There is also a screw of iron coiled round the lower part of the shaft, to show the properties of the screw as a mechanic power. The rope which goes round the drum passes over one of the pulleys near to the top of the frame, and under another pulley near the bottom of the frame. As two drums of different sizes are employed, it is necessary to have an upright roller to conduct the rope in a proper direction to the pulleys, when either of the drums is used. Near the frame, and in the direction in which the rope runs, is laid a platform or road of deal boards, one board in breadth,