THE MECHANICS' REGISTER, OR JOURNAL OF THE USEFUL ARTS, TRADES, MANUFACTURES, SCIENCE, &c. Vol. I. February 22, 183% MECHANICS ---No. 2. OF THE MECHANICAL POWERS. THE mechanical powers comprehend such simple machines as are useful in comparing the velocity of various bodies, and impressing on them at pleasure a greater or lesser degree of their power; such as making a great weight overcome a smaller one. By any of these powers, we may cause a weight of one pound, by moving through the space of ten feet, raise another of ten pounds through one foot, or vice versa. But none of the mechanical powers will be able to move a weight of ten pounds through eleven feet; nor by a single pound moving through a space of nine feet are we able to raise a weight of ten pounds through the space of one foot; so that the mechanical powers cannot make any absolute increase of the power applied; they can merely alter the velocity of that power, and thus transfer it either to a larger or smaller body at pleasure. The whole practical part of mechanics depends upon this principle. The mechanical powers are six in number -namely, the lever, the wheel and axle, the inclined plane, the wedge, the pulley, and the screw. OF THE LEVER. Fig. 4. No. 2. mechanical powers, and is generally only a straight bar of wood or iron, supported by a prop, as in the preceding figure: The weight to be raised is suspended at the short arm of the lever A; and exactly in the inverse proportion of the distance of the weight from the fulcrum, or prop C, is the quantity of weight, at B, necessary to keep it in equilibrio. Thus, if the weight at A be distant one foot, or one inch (for it signifies nothing which,) from the prop, it will require an equal weight placed at the same distance on the other side to balance it; that is, if the prop were placed equidistant between where it is at present and the end to which the two balls are suspended. But where it is now placed, it only requires half the quantity of weight to keep it in equilibrio; and if it were removed a tenth part nearer the centre, then only one-third will Fig. 5. be required to balance it. It must still be remembered, however, that, if the lever is put in motion, the small or single weight must move through a space ten times as great as that through which the large one passes; so that, in point of fact, there is not any acquisition of power by means of the lever, although it is one of the instruments most commonly used in mechanics, and extremely serviceable in loosening stones in quarries, or in raising great weights to a small dis The lever is the most simple of all the tance from the ground; after which, the No. 2-VOL. I. 18 Mechanics, No. 2-Of the Wheel and Axle. VOL. I. may be elevated to greater heights by ma- the point is to the centre of gravity of the chines. Figure 5, represents the most simple || height to be raised.* application of the lever. The weight to be raised is a log of wood; the lever or handspoke is in the hand of the man; a stone is laid on the ground to act as a prop or fulcrum; the log of wood is to be raised and suspended at the short arm of the lever, on that portion of it which extends beyond the stone. In making experiments with this sort of lever, it is necessary either to have the short arm greatly thicker than the long one, so that it may exactly balance the longer end, that portion of it which extends beyond the fulcrum, or a weight must be appended to it exactly sufficient to keep it in equilibrio, otherwise no accuracy can be expected in the experiments. The lever is the foundation of every kind of balance, whether the common kinds or those known by the name of steelyard, which latter is simply the lever represented in fig. 4. For if a scale is appended to the end A of the lever, and a weight, suppose of one pound, be used as a counterpoise to the body which is to be put into the scale, it will show exactly the weight of that body, by putting it at a proper distance from the fulcrum upon the long arm. Suppose the lever to be divided into twelve parts, and if the weight, when placed at the division five from the longer arm, counterpoises that placed in the scale, it shows the body weighs exactly five pounds: if it balance at the sixth division, then it proves that the body weighs six pounds. To this kind of lever may be reduced several useful instruments, such as scissors, snuffers, pin cers, &c. Levers are generally divided into three kinds, according to the respective dispositions of the fulcrum, the power, and the resistance; of these, two are very different in their action. One of these is where the forces act on contrary sides of the centre of motion or fulcrum, and another which acts on the same side. OF THE WHEEL AND AXLE. This power acts entirely on the same principle as the lever, and has in consequence been termed the perpetual lever. In the axle the power is applied to the circumference of a wheel by means of a rope or otherwise, the weights raised being fastened to a rope which winds round the axis, in order to overcome the resistance or elevate the weight. By means of this power, with a small force a great burden may be elevated by a rope which warps round a cylinder, by the aid of a handle, or by means of cogs or bars used as levers, acting on the circumference. Fig. 6. E Suppose that B C represents the radius of a cylinder, and that B A represents the arm of a lever, by which the power A acts; if the length of B A is to that of B C as three to one, a power of one hundred pounds at A acting in a perpendicular direction at A B will balance a weight E of one hundred pounds. Hence it follows, that to elevate a weight by means of this machine, it is required that the power A should be to the weight E as the radius of the cylinder B C The first kind are those where the fulcrum is to the lever BA; or, which amounts to is between the power and the resistance; as the same thing, as the radius of the cylinder the balance, snuffers, scissors, steelyards, &c. is to the radius of any wheel or handle by The second kind are those where the re- which it is turned. If in a state of equisistance is between the librium, the power is less than the weight, and the prop power; as oars, rudders of boats, and cutting-knives and that in the proportion of the radius of which are fixed at one end, and doors whose the cylinder to that of the handle which hinges serve as a fulcrum. Those of the turns it; so in a state of motion the power third kind are where the power acts between has more velocity than the weight, and that the prop and the resistance; as in sheep-in proportion as the radius of the handle or shears, tongs, &c. To this last kind of lever belongs animal action; as the bones which *See some instructive discussions on this are turned upon their joints have muscles interesting topic in Paley's Natural Thefor the means of doing so, whose insertions ology, chapters 7 and 8; also, Animal Memuch nearer to the centre of motion thanchanics-Library of Useful Knowledge. No. 2. Mechanics, No. 2-Of the Wheel and Axle. wheel that turns it is to that of the cylinder. This rule supposes that the power is always perpendicular to the radius by which it acts; for the direction of the weight is always perpendicular to the radius of the cylinder, since the cord that sustains it is always a tangent to its circumference. This machine is often constructed with a cylinder, at the ends of which are placed pivots or axles, turning on solid pieces of timber; and the weight intended to be raised is fixed to the end of a rope, which is coiled round the cylinder; the power being applied either by a cord or by means of a handle. Sometimes instead of the wheel we find this machine made up of levers fixed into the cylinder, as spokes into the nave of a wheel; at others a simple handle serves for the application of the power, as under : 19 The effect is still the same, only that the rotation is less uniform. In some cases the cylinder is horizontal, as in the above figure, and in some kinds of these machines called cranes; in others it is vertical, as in the capstan, &c. But whether the cylinder be horizontal or vertical, this machine has a manifest advantage over the simple lever in point of convenience; for by the continual rotation of the wheel, the weight may be raised to any height, or from any depth; while by means of a lever it can only be elevated a little way higher than where it rests. Where A B is the wheel (as represented by fig. 8,) and EDF its axis, P the moving power, and W the weight to be raised by means of the rope K coiling itself about the axis, it must be evident that when the large wheel has made one revolution, the weight P will have descended through a space equal to the circumference, and as much of the cord I by which it is suspended will be wound off. On the other hand, the weight W will have ascended only through a space equal to the circumference of the axle; and hence just as much of the rope K will be wound upon it. As the circumference of the wheel, therefore, is to that of the axis, so will the velocity of the moving power be to that of the weight to be raised, and of consequence such will be the force of the machine. Thus, if the circumference of the In great efforts, as it is necessary that the arms of the lever of power should be very long, when, therefore, it is extremely inconvenient to make them so, and when to mul tiply the number of them would weaken the head of the cylinder too much, it has been the practice to unite the extremities of the radii, or cogs, by a circumference, and form a kind of wheel to which other cogs are adapted, by which it is turned by men; as may be seen in the wheels used in quarries, and for cranes, as represented below. Sometimes cranes are moved by handles, SS, &c. (fig. 8,) placed in the circumference of the wheel, which is turned by men's Fig. 9. K hands. Sometimes the wheel is hollow, and 20 Mechanics, No. 2-Of the Wheel and Axle. 1 Fig. 10. VOL. I. which raises the weight above its axis. ||with such irresistible force, that it would When the crane is to be turned by means inevitably kill the man working it. For of men's hands, it may advantageously have want of this precaution, also, terrible accicogs all round the circumference, in which dents have happened to people inclosed in á small treddle may be made to work, and cranes, by their inadvertently missing a step. be turned by a winch, as represented in fig. The capstan is a real windlass, and differs 9. Thus, the power of the man who works only in the position of the cylinder being it will be greatly increased; for his strength vertical in place of horizontal, as in the will be augmented as many times as the windlass or crane. The manner of power number of revolutions of the winch exceeds acting upon a resistance or burden, by means that af the axle D, fig. 8, when multiplied of a wheel and axle or windlass, is entirely by the excess of the winch above the length applicable to the capstan, but the latter is of the semi-diameter, of the axle, added to more advantageous. Capstans are often the semi-diameter or half the thickness of the fixed in ships, to raise anchors or other burrope K, by which the weight is drawn up. dens, to which cables are fastened, which Thus, supposing the weight of the diameter are rolled or coiled upon the cylinder, as of the rope and axle taken together to be represented below:twelve inches, and, consequently, half their diameter to be six inches, so that the weight W will hang at six inches perpendicular distance from under the centre of the axle ; let us imagine the wheel A B, which is fixed on the axle, to have eighty cogs, and to be turned by means of a winch, six inches long, fixed on the axis of a handle of cight| staves or rounds, working in the cogs of the wheel. Hence it is evident that the winch and handle would make ten revolutions for one of the wheel A B, and its axis D, on which the rope K winds in raising the weight W; and the winch being no longer than the sum of the semi-diameters of the great axle and rope, the handle could have no more power on the wheel than a man could have by pulling it round by the edge, because the winch would then have no greater velocity than the edge of the wheel has, which is supposed to be ten times the velocity of the raising weight; so that, in this case, the acquisition of power would be ten to one; but if the length of the winch be twelve inches, the power gained will be as twenty to one; and if eighteen inches, which is sufficient length for any man to work with, then the acquisition of power will be as thirty to one; because the velocity of the handle would be thirty times as great as that of the raising weight. And the absolute force of any machine is exactly in proportion to the velocity of the weight raised by it; for none of the mechaninal powers are capable of gaining both power and velocity at the same time. In every kind of crane, it is necessary to have a racked-wheel, as represented at G, on one end of the axle, with a catch H to fall into its teeth, which will at any time support the weight, and keep it from descending if the workman should happen to slip his hold; for in such a case, if there were not a racked or safety-wheel, dreadful accidents would occur in case of suddenly letting go the winch, which would run backwards The vertical position of the cylinder in the capstan is obviously advantageous, as it permits a number of men to be employed at one time, by inserting levers in holes made to receive them; these men walk round with the cylinder, and move it upon its axle, by pushing the levers before them; and with this additional advantage, that there is no intermission of the power employed. One of the most useful machines by which a great resistance or weight may be overcome by a small force, is the creek or jack. It consists of a perpendicular iron bar, as at AB in the following cut: Fig. 11. This bar is provided with teeth on one No. 2. Elements of Mechanics-Of Matter and its qualities. of its sides, and works in a moveable case CD; the teeth of the bar fit into those of the nut D D, which turns upon an axis by the means of its handle GN. The action of the nut protrudes the bar, and the weight is raised in consequence, and placed at its head A. When the exertion that each tooth of the nut makes in D to raise the bar, is considered as a weight applied to a lever, it is evident that the power applied to the handle is to that weight as the radius of the nut is to the arm of the handle G N: from which it may be observed, that, by making the radius of the nut very small in proportion to that of the handle, a very considerable weight may be raised by a moderate force. Elements of Mechanics. Of Matter and its Qualities. I. MATTER is the general name of every thing of substance, that has length, breadth, and thickness. Obs. Philosophers have in all ages discussed the general nature of matter, but without arriving at any satisfactory results. This is certain, that all we know of matter is merely relative to our own powers and senses; and those relative properties, being all we can know, are the proper objects of philosophical enquiry. 21 by which its parts may be divided and separated from each other. Of this division there can be no end. Illus. 1. Since matter can never be anni hilated by division, so we can never imagine it to be cut into such small particles, that any one of them shall not have an upper and under surface, which may be separated, if we have instruments fine enough for the purpose. 2. It would also be absurd to say, that the greatest mass has more halves, quarters, or thousandth parts, than the smallest particle of matter. Exp. 1. If a grain of gold be melted with a pound or 57 60 grains of silver, and a single grain of the mass be dissolved into diluted nitric acid, the gold, which is only the 57 61st part of a grain, will fall to the bottom and be visible; but the silver will be dissolved in the acid. the gold beaters to such a degree of fineness, 2. A grain of gold may be hammered by that the two millionth part of the grain may be seen by the naked eye. 3. In addition to these experiments we may observe, that there are animalcule so small, that many thousands of them taken together are smaller than the point of a needle. Mr. Leewenhoeck informs us, that there are more animals in the milt of a cod-fish, than there are men on the whole earth, and a single grain of sand is larger than four mil II. The Properties of all matter, or sub-lions of these animals. Moreover, a particle stance, are, SOLIDITY, DIVISIBILITY, MOBILITY, and INERTNESS. III. Solidity is that property which every substance possesses of not permitting any other substance to occupy the same place at the same time. of the blood of one of these animalcule has been found, by calculation, to be as much smaller than a globe of the 1 10th of an inch in diameter, as that globe is smaller than the whole earth. 4. The natural divisions of matter are still more wonderful. In odoriferous bodies a surprising subtility of parts is perceived: several bodies scarcely lose any sensible part of their weight in a great length of time, and yet continually fill a very large space with odoriferous particles. Dr. Keill has computed the magnitude of a particle of 2. Water, and even air, have this pro-assafoetida to be only 38 trillionths of a cubic perty. Illustration 1. If a piece of wood or metal occupy a certain space, before any thing else can take possession of that space, the wood or metal must be removed. Experiment 1. If some water be put into a tube closed at one end, and a piece of wood be inserted that fits the inside of the tube very accurately, it will be impossible by any force to get the wooden piston to the bottom of the tube, unless the water is first taken away. 2. The experiment may also be made with air instead of water. Corollary. Therefore, water, air, and all other fluids, are, with reference to space, equally solid with the hardest bodies. V. Divisibility is that property of matter inch. Coral. From all which it is evident, that matter is actually divisible to a degree much greater than we can imagine: and to which divisibility we can set no limits. V. Mobility is that property of matter by which it is capable of being moved from one part of space to another. Illus. It is found, from experiment and observation, that all matter is capable of being moved if a sufficient force can be applied for this purpose. VI. Inertness, or inactivity, is that pro |