THE WEDGE.

THE fifth mechanical power is the wedge; one form of which is shown at fig. 21. It operates in a similar manner to the inclined plane; but instead of the resistance or force to be overcome being moved along its surface, the plane itself, which is now called the wedge, is forced beneath the object to be raised. Thus, if the wedge A B move upon a level plane to the position A 1, the weight D will be raised from its position to the height D1; and, consequently, will pass over the whole upper plane of the wedge A B, and ultimately attain the perpendicular height B C. If AB be divided by BC, the quotient, as in the inclined plane, will represent the power which the wedge is capable of exerting; or if AB is four times B C, the power forcing forward the wedge to Al is capable of raising the body D four times its own amount to the position D 1. The wedge represented in fig. 22, is most generally applied to the purpose of dividing wood, where the resisting force to be overcome acts on both sides of it. To estimate the amount of power gained by this form of the instrument, we must consider it as two inclined planes, ABC and CBD conjoined; and as the forces operating at E and F are equal, we shall have, as AC is to CB, so is the resistance F to the force necessary to overcome it; and as the force E and the other portion of the wedge are similarly opposed, the total AD is to CB, as the total resistance Fand E is to the power necessary to be exerted to counterbalance that resistance; or, as many times as A D will go into C B, so many times may the resistance contain the amount of the applied force.

THE SCREW.

THE Screw is the sixth and last of the mechanical powers. In the manner of its construction it is in general said to bear reference to an inclined plane wound about a cylinder; but as the power of the inclined plane corresponds with that of the wedge, and the mode of applying the facilities they possess, alone forms their difference, and as the screw is almost universally moved to effect the same purposes as the wedge, it would, with greater propriety, as regards its action, bear reference to that instrument.

Fig. 23 represents a cylinder EE, upon which we will suppose the wedge-shaped piece, ABC, is capable of being wound; when wrapped round such cylinder, it will, by its

upper edge BC, represent spiral lines, similar to BD and FG. Now, as the piece ABC is in the shape of a wedge or inclined plane, it should have its power estimated by the line A C compared to the height AB; and if the line BC, wound in its spiral direction, shall just circumscribe the cylinder, the point C will be found directly beneath B, and the distance between C and B, when thus lapped on the cylinder, will represent the line AB, on the perpendicular of the inclined plane or wedge; which, when compared with AC, now represented by the circumference of the cylinder, will give the same data from which the of the screw, so formed, should be calculated. power Consequently the comparison of the circumference of the screw, and the distance between one thread and another, measured on a line parallel to the axis of the screw, is that from which its power should be calculated, or as the distance between the two threads is to the circumference, so the power to be applied is to the resistance to be overcome; or if the circumference be three, and the power one, the force equal to one shall overcome a force equal to three.

Fig. 24 represents a screw of more perfect formation; but the general construction of the screw is so familiar to every one, that we conceive it to be almost needless to enter upon a more minute description. A B represents the acclivity of the plane from which such screw is formed, and the distance between B and C represents what should be compared to the circumference in order to discover the power it possesses.

The screw is applied to mechanical purposes chiefly to obtain great pressures in small distances; and upon examination it will be seen, that they afford a method of using a wedge of an extremely small inclination, and by consequence of great power. The screw is sometimes used for raising exceedingly heavy weights. The hollow screw, or the counterpart in which a screw operates, when in the form of a small movable piece, is called a nut, and the cavity is termed a female screw, the properties of which are, as respects power, exactly similar to the screw.

We have now duly considered the nature and properties of the mechanical powers when in a state of uncombined action; and shall, in the next place, previously to representing them in some of the simplest forms in which they are combined, examine into one more attribute of matter, resulting from gravity.

THE CENTRE OF GRAVITY.

THE force of gravitation, as we have already shown, acts upon matter in proportion to its quantity: thus, if a line be drawn through any body in such manner, that the quantity of matter multiplied into its distance from the line on one side shall equal the quantity of matter multiplied into its distance on the opposite side, and if another line be drawn passing through the body in another direction, dividing it in a similar manner, the point where those two lines meet, whether it be situated within or about the body, is the centre of gravity; and if that point or centre, supposing it within the body, be supported, the body will remain in a state of equilibrium. Suppose the body D, fig. 25, to be suspended by a line from C, then the point H, which is called the point of suspension, and at which the body is suspended in a state of rest, will be directly above the centre of gravity. For if the perpendicular line HI be drawn, and the quantity of matter multiplied into the distance on one side of the line be not equal to the quantity of matter multiplied into the distance on the other side, the body will not be at rest; but as the body is at rest, the quantity of matter multiplied into its distance on the one side, is exactly equal to the quantity of matter multiplied into its distance on the other. Again, suspend the body as at fig. 26, and let a perpendicular fall similarly from K, the point of suspension, to L, the body will be again divided in like manner, and the point E, where the perpendicular K L intercepts the line HI, will be the centre of gravity.

If any force acting in a direct line pass through the centre of gravity of a body, it will produce uniform motion in that body; but if the force so impressed do not pass through the centre of gravity, that motion will be unequally communicated. Thus, if at fig. 26, M I represent a force striking the irregularly shaped body D, in a line of direction passing through its centre of gravity E, the force so impressed on that body will cause it to proceed with a uniform velocity, as regards all its parts; but should the force M I be impressed at the point F, as M 1, the line of direction not being through the centre of gravity, an irregular motion will be communicated, and the body will acquire a revolving motion round its centre of gravity.

As the centre of gravity is the most advantageous point for

giving to a body uniform motion, so also it is the best to apply resistance to arrest the progress of that motion.

Most writers on Mechanics speak of the common centre of gravity as of more than one body, or as a system of bodies; but as they mean that those bodies should be conjoined, or their relative position maintained by some force, they may properly be considered as but one body, and the centre of gravity of the whole assemblage may be estimated in a similar manner to that of one. Thus, if the bodies A and B, fig. 27, be conjoined by a line, their common centre of gravity will be the point E; for if a line be drawn through that point in any direction, the masses of matter, multiplied into their respective distances on each side, will equal each other.

What has been said concerning the centre of gravity, is also applicable to practical points; as no body can be supported in a state of equilibrium, if the point of suspension be not exactly above or beneath its centre of gravity

SIMPLE COMBINATIONS OF THE MECHANICAL POWERS.

HAVING Considered the capacities of the mechanical powers, and the modes used for calculating their effects, we will now turn our attention to them in a state of combination and as all of these instruments are in themselves gainers of power, power must be considerably increased when they become adjuncts to each other. Thus, in fig. 28, we have a combination of three levers, each of them, by the disproportion of their arms, gainers of power as three to one; GGG being their several fulcrums, the weight H will operate with thrice its power at B, by means of the lever AB; the effect will be again trebled by CD; and that amount again trebled by the action of the lever EF. Consequently, if we call H one, by AB it will be raised to three, by CD to nine, and by EF to twenty-seven; so that a weight of one pound at A will support twenty-seven pounds at F.

The combination of the action of levers may thus be extended to the gain of almost any amount of power; and when bent levers are introduced, their powers, which in peculiar situations have been shown to be very great, may in like manner be multiplied.

The wheel and axle is an implement not frequently used in its simple state. In machinery, wheels are mostly turned by means of prominences upon their peripheres, called