Edgeworth Maria
Practical Education, Volume II
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, and twenty or thirty feet long, upon which a small sledge loaded with different weights may be drawn. Plate 2. Fig. 1.
F. F. The frame.
b. b. Braces to keep the frame steady.
a. a. a. Angular braces to strengthen the transom; and also a king-post.
S. A round, taper shaft, strengthened above and below the mortises with iron hoops.
L L. Two arms, or levers, by which the shaft, &c. are to be moved round.
D D. The drum, which has two rims of different circumferences.
R. The roller to conduct the rope.
P. The pulley, round which the rope passes to the larger drum.
P 2. Another pulley to answer to the smaller drum.
P 3. A pulley through which the rope passes when experiments are tried with levers, &c.
P 4. Another pulley through which the rope passes when the sledge is used.
Ro. The road of deal boards for the sledge to move on.
Sl. The sledge, with pieces of hard wood attached to it, to guide it on the road.
Uses of the Panorganon
As this machine is to be moved by the force of men or children, and as their force varies not only with the strength and weight of each individual, but also according to the different manner in which that strength or weight is applied; it is, in the first place, requisite to establish one determinate mode of applying human force to the machine; and also a method of determining the relative force of each individual whose strength is applied to it.
To estimate the force with which a person can draw horizontally by a rope over his shoulder
EXPERIMENT I
Hang a common long scale-beam (without scales or chains) from the top or transom of the frame, so as that one end of it may come within an inch of one side or post of the machine. Tie a rope to the hook of the scale-beam, where the chains of the scale are usually hung, and pass it through the pulley P 3, which is about four feet from the ground; let the person pull this rope from 1 towards 2, turning his back to the machine, and pulling the rope over his shoulder – Pl. 2. Fig. 6. As the pulley may be either too high or too low to permit the rope to be horizontal, the person who pulls it should be placed ten or fifteen feet from the machine, which will lessen the angular direction of the cord, and the inaccuracy of the experiment. Hang weights to the other end of the scale-beam, until the person who pulls can but just walk forward, pulling fairly without propping his feet against any thing. This weight will estimate the force with which he can draw horizontally by a rope over his shoulder.22 Let a child who tries this, walk on the board with dry shoes; let him afterwards chalk his shoes, and afterwards try it with his shoes soaped: he will find that he can pull with different degrees of force in these different circumstances; but when he tries the following experiments, let his shoes be always dry, that his force may be always the same.
To show the power of the three different sorts of levers
EXPERIMENT II
Instead of putting the cord that comes from the scale-beam, as in the last experiment, over the shoulder of the boy, hook it to the end 1 of the lever L, Fig. 2. Plate 2. This lever is passed through a socket – Plate 2. Fig. 3. – in which it can be shifted from one of its ends towards the other, and can be fastened at any place by the screw of the socket. This socket has two gudgeons, upon which it, and the lever which it contains, can turn. This socket and its gudgeons can be lifted out of the holes in which it plays, between the rail R R, Plate 2. Fig. 2. and may be put into other holes at R R, Fig. 5. Loop another rope to the other end of this lever, and let the boy pull as before. Perhaps it should be pointed out, that the boy must walk in a direction contrary to that in which he walked before, viz. from 1 towards 3. The height to which the weight ascends, and the distance to which the boy advances, should be carefully marked and measured; and it will be found, that he can raise the weight to the same height, advancing through the same space as in the former experiment. In this case, as both ends of the lever moved through equal spaces, the lever only changed the direction of the motion, and added no mechanical power to the direct strength of the boy.
EXPERIMENT III
Shift the lever to its extremity in the socket; the middle of the lever will be now opposite to the pulley, Pl. 2. Fig. 4. – hook to it the rope that goes through the pulley P 3, and fasten to the other end of the lever the rope by which the boy is to pull. This will be a lever of the second kind, as it is called in books of mechanics; in using which, the resistance is placed between the centre of motion or fulcrum, and the moving power. He will now raise double the weight that he did in Experiment II, and he will advance through double the space.
EXPERIMENT IV
Shift the lever, and the socket which forms the axis (without shifting the lever from the place in which it was in the socket in the last experiment) to the holes that are prepared for it at R R, Plate 2. Fig. 5. The free end of the lever E will now be opposite to the rope, and to the pulley (over which the rope comes from the scale-beam.) Hook this rope to it, and hook the rope by which the boy pulls, to the middle of the lever. The effect will now be different from what it was in the two last experiments; the boy will advance only half as far, and will raise only half as much weight as before. This is called a lever of the third sort. The first and second kinds of levers are used in quarrying; and the operations of many tools may be referred to them. The third kind of lever is employed but seldom, but its properties may be observed with advantage whilst a long ladder is raised, as the man who raises it, is obliged to exert an increasing force until the ladder is nearly perpendicular. When this lever is used, it is obvious, from what has been said, that the power must always pass through less space than the thing which is to be moved; it can never, therefore, be of service in gaining power. But the object of some machines, is to increase velocity, instead of obtaining power, as in a sledge-hammer moved by mill-work. (V. the plates in Emerson's Mechanics, No. 236.)
The experiments upon levers may be varied at pleasure, increasing or diminishing the mechanical advantage, so as to balance the power and the resistance, to accustom the learners to calculate the relation between the power and the effect in different circumstances; always pointing out, that whatever excess there is in the power,23 or in the resistance, is always compensated by the difference of space through which the inferiour passes.
The experiments which we have mentioned, are sufficiently satisfactory to a pupil, as to the immediate relation between the power and the resistance; but the different spaces through which the power and the resistance move when one exceeds the other, cannot be obvious, without they pass through much larger spaces than levers will permit.
EXPERIMENT V
Place the sledge on the farthest end of the wooden road – Plate 2. Fig. 1. – fasten a rope to the sledge, and conduct it through the lowest pulley P 4, and through the pulley P 3, so as that the boy may be enabled to draw it by the rope passed over his shoulder. The sledge must now be loaded, until the boy can but just advance with short steps steadily upon the wooden road; this must be done with care, as there will be but just room for him beside the rope. He will meet the sledge exactly on the middle of the road, from which he must step aside to pass the sledge. Let the time of this experiment be noted. It is obvious that the boy and the sledge move with equal velocity; there is, therefore, no mechanical advantage obtained by the pulleys. The weight that he can draw will be about half a hundred, if he weigh about nine stone; but the exact force with which the boy draws, is to be known by Experiment I.
The wheel and axle
This organ is usually called in mechanics, The axis in peritrochio. A hard name, which might well be spared, as the word windlass or capstan would convey a more distinct idea to our pupils.
EXPERIMENT VI
To the largest drum, Plate 2. Fig. 1. fasten a cord, and pass it through the pulley P downwards, and through the pulley P 4 to the sledge placed at the end of the wooden road, which is farthest from the machine. Let the boy, by a rope fastened to the extremity of one of the arms of the capstan, and passed over his shoulder, draw the capstan round; he will wind the rope round the drum, and draw the sledge upon its road. To make the sledge advance twenty-four feet upon its road, the boy must have walked circularly 144 feet, which is six times as far, and he will be able to draw about three hundred weight, which is six times as much as in the last experiment.
It may now be pointed out, that the difference of space, passed through by the power in this experiment, is exactly equal to the difference of weight, which the boy could draw without the capstan.
EXPERIMENT VII
Let the rope be now attached to the smaller drum; the boy will draw nearly twice as much weight upon the sledge as before, and will go through double the space.
EXPERIMENT VIII
Where there are a number of boys, let five or six of them, whose power of drawing (estimated as in Experiment I) amounts to six times as much as the force of the boy at the capstan, pull at the end of the rope which was fastened to the sledge; they will balance the force of the boy at the capstan: either they, or he, by a sudden pull, may advance, but if they pull fairly, there will be no advantage on either part. In this experiment, the rope should pass through the pulley P 3, and should be coiled round the larger drum. And it must be also observed, that in all experiments upon the motion of bodies, in which there is much friction, as where a sledge is employed, the results are never so uniform as in other circumstances.
The Pulley
Upon the pulley we shall say little, as it is in every body's hands, and experiments may be tried upon it without any particular apparatus. It should, however, be distinctly inculcated, that the power is not increased by a fixed pulley. For this purpose, a wheel without a rim, or, to speak with more propriety, a number of spokes fixed in a nave, should be employed. (Plate 2. Fig. 9.) Pieces like the heads of crutches should be fixed at the ends of these spokes, to receive a piece of girth-web, which is used instead of a cord, because a cord would be unsteady; and a strap of iron with a hook to it should play upon the centre, by which it may at times be suspended, and from which at other times a weight may be hung.
EXPERIMENT IX
Let the skeleton of a pulley be hung by the iron strap from the transom of the frame; fasten a piece of web to one of the radii, and another to the end of the opposite radius. If two boys of equal weight pull these pieces of girth-web, they will balance each other; or two equal weights hung to these webs, will be in equilibrio. If a piece of girth-web be put round the uppermost radius, two equal weights hung at the ends of it will remain immoveable; but if either of them be pulled, or if a small additional weight be added to either of them, it will descend, and the web will apply itself successively to the ascending radii, and will detach itself from those that are descending. If this movement be carefully considered, it will be perceived, that the web, in unfolding itself, acts in the same manner upon the radii as two ropes would if they were hung to the extremities of the opposite radii in succession. The two radii which are opposite, may be considered as a lever of the first sort, where the centre is in the middle of the lever; as each end moves through an equal space, there is no mechanical advantage. But if this skeleton-pulley be employed as a common block or tackle, its motions and properties will be entirely different.
EXPERIMENT X. PLATE 2. FIG. 9
Nail a piece of girth-web to a post, at the distance of three or four feet from the ground; fasten the other end of it to one of the radii. Fasten another piece of web to the opposite radius, and let a boy hold the skeleton-pulley suspended by the web; hook weights to the strap that hangs from the centre. The end of the radius to which the fixed girth-web is fastened, will remain immoveable; but, if the boy pulls the web which he holds in his hand upwards, he will be able to lift nearly double the weight, which he can raise from the ground by a simple rope, without the machine, and he will perceive that his hand moves through twice as great a space as the weight ascends: he has, therefore, the mechanical advantage which he would have by a lever of the second sort, as in Experiment iii. Let a piece of web be put round the under radii, let one end of it be nailed to the post, and the other be held by the boy, and it will represent the application of a rope to a moveable pulley; if its motion be carefully considered, it will appear that the radii, as they successively apply themselves to the web, represent a series of levers of the second kind. A pulley is nothing more than an infinite number of such levers; the cord at one end of the diameter serving as a fulcrum for the organ during its progress. If this skeleton-pulley be used horizontally, instead of perpendicularly, the circumstances which have been mentioned, will appear more obvious.
Upon the wooden road lay down a piece of girth-web; nail one end of it to the road; place the pulley upon the web at the other end of the board, and, bringing the web over the radii, let the boy, taking hold of it, draw the loaded sledge fastened to the hook at the centre of the pulley: he will draw nearly twice as much in this manner as he could without the pulley.24
Here the web lying on the road, shows more distinctly, that it is quiescent where the lowest radius touches it; and if the radii, as they tread upon it, are observed, their points will appear at rest, whilst the centre of the pulley will go as fast as the sledge, and the top of each radius successively (and the boy's hand which unfolds the web) will move twice as fast as the centre of the pulley and the sledge.
If a person, holding a stick in his hand, observes the relative motions of the top, and the middle, and the bottom of the stick, whilst he inclines it, he will see that the bottom of the stick has no motion on the ground, and that the middle has only half the motion of the top. This property of the pulley has been dwelt upon, because it elucidates the motion of a wheel rolling upon the ground; and it explains a common paradox, which appears at first inexplicable. "The bottom of a rolling wheel never moves upon the road." This is asserted only of a wheel moving over hard ground, which, in fact, may be considered rather as laying down its circumference upon the road, than as moving upon it.
The inclined Plane and the Wedge
The inclined plane is to be next considered. When a heavy body is to be raised, it is often convenient to lay a sloping artificial road of planks, up which it may be pushed or drawn. This mechanical power, however, is but of little service without the assistance of wheels or rollers; we shall, therefore, speak of it as it is applied in another manner, under the name of the wedge, which is, in fact, a moving inclined plane; but if it is required to explain the properties of the inclined plane by the panorganon, the wooden road may be raised and set to any inclination that is required, and the sledge may be drawn upon it as in the former experiments.
Let one end of a lever, N. Plate 2. Fig. 7. with a wheel at one end of it, be hinged to the post of the frame, by means of a gudgeon driven or screwed into the post. To prevent this lever from deviating sideways, let a slip of wood be connected with it by a nail, which shall be fast in the lever, but which moves freely in a hole in the rail. The other end of this slip must be fastened to a stake driven into the ground at three or four feet from the lever, at one side of it, and towards the end in which the wheel is fixed (Plate 2. Fig 10. which is a vue d'oiseau) in the same manner as the treadle of a common lathe is managed, and as the treadle of a loom is sometimes guided.25
EXPERIMENT XI
Under the wheel of this lever place an inclined plane or half-wedge (Plate 2. Fig. 7.) on the wooden road, with rollers under it, to prevent friction;26 fasten a rope to the foremost end of the wedge, and pass it through the pulleys (P 4. and P 3.) as in the fifth experiment. Let a boy draw the sledge by this rope over his shoulder, and he will find, that as it advances it will raise the weight upwards; the wedge is five feet long, and elevated one foot. Now, if the perpendicular ascent of the weight, and the space through which he advances, be compared, he will find, that the space through which he has passed will be five times as great as that through which the weight has ascended; and that this wedge has enabled him to raise five times as much as he could raise without it, if his strength were applied, as in Experiment i, without any mechanical advantage. By making this wedge in two parts hinged together, with a graduated piece to keep them asunder, the wedge may be adjusted to any given obliquity; and it will be always found, that the mechanical advantage of the wedge may be ascertained by comparing its perpendicular elevation with its base. If the base of the wedge is 2, 3, 4, 5, or any other number of times greater than its height, it will enable the boy to raise respectively 2, 3, 4, or 5 times more weight than he could do in Experiment i, by which his power is estimated.
The Screw
The screw is an inclined plane wound round a cylinder; the height of all its revolutions round the cylinder taken together, compared with the space through which the power that turns it passes, is the measure of its mechanical advantage.27 Let the lever, used in the last experiment, be turned in such a manner as to reach from its gudgeon to the shaft of the Panorganon, guided by an attendant lever as before. (Plate 2. Fig. 8.) Let the wheel rest upon the lowest helix or thread of the screw: as the arms of the shaft are turned round, the wheel will ascend, and carry up the weight which is fastened to the lever.28 As the situation of the screw prevents the weight from being suspended exactly from the centre of the screw, proper allowance must be made for this in estimating the force of the screw, or determining the mechanical advantage gained by the lever: this can be done by measuring the perpendicular ascent of the weight, which in all cases is better, and more expeditious, than measuring the parts of a machine, and estimating its force by calculation; because the different diameters of ropes, and other small circumstances, are frequently mistaken in estimates.
The space passed through by the moving power, and by that which it moves, are infallible data for estimating the powers of engines. Two material subjects of experiments, yet remain for the Panorganon; friction, and wheels of carriages: but we have already extended this article far beyond its just proportion to similar chapters in this work. We repeat, that it is not intended in this, or in any other part of our design, to write treatises upon science; but merely to point out methods for initiating young people in the rudiments of knowledge, and of giving them a clear and distinct view of those principles upon which they are founded. No preceptor, who has had experience, will cavil at the superficial knowledge of a boy of twelve or thirteen upon these subjects; he will perceive, that the general view, which we wish to give our pupils of the useful arts and sciences, must certainly tend to form a taste for literature and investigation. The sciolist has learned only to talk– we wish to teach our pupils to think, upon the various objects of human speculation.
The Panorganon may be employed in trying the resistance of air and water; the force of different muscles; and in a great variety of amusing and useful experiments. In academies, and private families, it may be erected in the place allotted for amusement, where it will furnish entertainment for many a vacant hour. When it has lost its novelty, the shaft may from time to time be taken down, and a swing may be suspended in its place. It may be constructed at the expense of five or six pounds: that which stands before our window, was made for less than three guineas, as we had many of the materials beside us for other purposes.
