applied at A, act in the direction A D. The force A D being resolved into A B and B D, A B will represent the force acting in the line of the lever C A, and bearing on the fulcrum C: and B D will represent the force that causes the point A to revolve on the fulcrum C, and which consequently does not bear on the fulcrum. Now in the triangle D B A, the line B A is inversely as the angle B A D, that is, the greater the angle the less the line, and the line B D is directly as the angle B A D; that is, the greater the angle the greater the line: whence it follows, that as the angle at which the force is exerted increases, the pressure on the fulcrum diminishes, and the power of moving the lever increases till the angle B A D becomes a right angle when the sine B D, or power moving the lever, having arrived at its greatest extent, or being equal to radius, the co-sine B D, or power of pressure on the fulcrum has become nothing.

Corollary first.-The same is true if the line of direction be. beyond the arm of the lever, as at A E, only in this case the resistance is borne by the opposite point of the fulcrum.

Corollary second.-As the force is greatest at the right angle, so it is least when in a right line with the lever; for in this ease, the sine B D, or line representing the moving force, is nothing.

Proposition second.-The application of a force to the extremity of any lever, causes the point from which that force is made, the extremity of that lever and the fulcrum to form themselves into a right line, or what is the same, the line of direction will coincide with the plane of the lever. Let A C, be the Clever, and let a force at B draw

A

D

B

in the direction A B. Then since C is the centre of motion, the point A, in approaching the point B must move in the curve A D, but when the lever has arrived at C D, the force exerted from the point B is in a right

line with the lever, and its power of moving the lever, by the last corollary is nothing, therefore the lever must remain in the position C D, that is, in a right line with the point B.

Let us now consider the parts of this machine, to determine, if from their construction there can result a motion that will be

perpetual.

First, There is a frame which contains the machine. If we suppose the motion to originate in it, it must be by its gravity, or by the elasticity of its parts, brought into action by its construction. But the machine is connected with the frame only by gudgeons, and in no case can the pressure on an axle, cause that axle to revolve; we know too that the action of a spring, and in deed of any force implies its motion, but in this frame we see no motion; or if it be though a space undistinguishable by the eye, we know that there is no connexion of wheels for increasing the velocity to the degree that takes place in the large horizontal wheel.

Secondly. There are two vertical and two horizontal wheels, that play into each other. Now, a wheel has in itself no source of motion, since its centre of motion is also its centre of gravity. If the centre of motion be not the centre of gravity, then indeed it may move from a given position, but it will only be till that centre of gravity has made its nearest approach to the earth. But there is no wheel of this character in the machine. Now, what is true of one wheel, is true of any number of wheels, an infinity of them could not alter the qualities of each.

Thirdly. There are shafts serving as axles to the wheels, and there are gudgeons to these shafts. But shafts are only smaller wheels, and have their properties; and gudgeons are only a still greater diminution; now the properties of wheels are not altered by their diameters.

Fourthly. There are four chains that connect the large horizontal wheel to the small horizontal wheel, at the summit of the upright shaft. These chains are drawn somewhat out of the perpendicular line between the two wheels. Now it is to this part of the structure, that the inventor of the machine attributes a portion of its motion; and the motion is said to be generated and continued in this manner. Each of the chains represents the rod of a pendulum, and the wheel is the weight at the end of that rod. We know that every pendulum, left to itself, will come to the perpendicular: these chains, then, being out of the perpendicular, if not obstructed, would fall into it; but they

cannot fall to the perpendicular without causing the wheel to revolve on its centre of motion, and this wheel cannot move without, at the same time, causing a system of wheels to revolve with which it is connected, but the last of this system of wheels moves the upright shaft, and consequently, the small horizontal wheel, to which the upper end of the chains is attached, therefore, this upper end is always kept at the same distance before the lower end; now it has been said before, that when the upper end is before the lower end, or in other words, when the chains are not perpendicular, the lower end must move on to that perpendicular, that is, the lower wheel must revolve. But the upper end, by the construction, is always before the lower end; therefore, the wheel must always move.

The falacy of this reasoning lies in this, that the upper horizontal wheel cannot move, and, consequently, the system of wheels behind this must remain at rest. The upper wheel cannot move for this reason: the chain and lower wheel being a pendulum, its gravitating to the perpendicular, and of consequence its motion is effected by the force of its weight only, and the resistance the upper small horizontal wheel has to overcome, in order to move on, is to draw after it this lower wheel or weight: since these two wheels are by the tense chain, drawn with equal force in opposite directions. But by the construction of this machine, it is the gravitation of this lower wheel that propels the upper; if, therefore, the upper wheel move, it must be from one force overcoming a force equal to itself; or, as there is in this case, the resistance of medium, and the waste of friction, a less force must overcome a greater, which is absurd. It may be said in objection to this, that a less force may overcome a greater, by the lesser force acting on a longer lever, and this principal is said,

Fifthly, by the believers in the machine, to be the cause of its motion. Let C B and C A be a long and shorter le

D

E

B

ver, representing the large and small wheel, and moving on the same centre C, and let A B be a force as a tense chain, drawing these points with a power of ten pounds: now, if the force at

the point B, causing that point to describe the arc B E be greater than the force at A, causing the point A to describe the arc AD, then would the point B move on in the arc D E: but there is a force of ten pounds at each of those two points, and as the lever C B is twice the length of C A, ten pounds at A may be counterbalanced by five pounds at B, now there is ten pounds at B, therefore, the force with which B moves in the arc B E, is five pounds above that which draws the point A in the arc A D, that is the point B must go on, and the two levers must revolve on the centre C. Now the falsehood of this is demonstrable. It has been proved in prop. 1, that the greatest force is exerted at right angles to a lever, and we know that in any triangle, as C A B (fig. 3.) the greatest angle is opposite the greatest side, and by proportionals, the line C B is to CA as the angle C A B is to the angle C B A, that is as much as the line or lever C B exceeds the line or lever C A, so much does the angle at A, or the force applied at that point, exceed the angle at B, or the force exerted at that point; but the line C B is double the line C A, therefore, the angle A, is double the angle B; hence, whatever advantage B gains by the length of the lever, A gains by the direction of the force.

Sixthly. The inclined planes on the horizontal wheel, are said by the inventor, and the advocates of the machine, to be the cause of the movement. It is effected they say thus: these planes being at an angle of forty-five degrees, the whole weight is divided between the pressure on the plane, and the motion down it. If the whole weight be ten pounds, then five presses on the plane, and five runs down. Now the five on the plane pushes on that plane, and the lever attached to it, in one direction, and the five that runs down the plane is upheld by an opposite lever, that is thereby drawn in a contrary direction. But these two forces of five are exerted on different levers; therefore, the longest will move forward. Now the fallacy of this may be seen by referring to the last head; for it was there shown that the advantage of the length of a lever was counterbalanced by the direction of the force, being nearer to a right angle on the end of the smaller lever. Therefore, in this case the powers of action and re-action are equal, and the planes cannot move.

Seventhly. The weight on the inclined planes is supposed to act also by the mode in which it is connected to the opposite

lever by the crooked iron. Under the last head, we have seen that the action in one direction is opposed by the reaction in an opposite direction. In objecting to the agency of the weight on the planes, much has been said about the impossibility of the weight operating without descending or moving; and the impossibility of gravity moving any body but in a perpendicular to the earth. Now, it seems to me, that this alone is no objection to the construction of a perpetual movement, since I can state a case in which, though these difficulties should exist, yet a motion would result. Let G C H be a plane inclined at an

ang le of 45 degrees,and moving on wheels; let

W be a

weight of 40 pounds, susE pended on

that plane from the

point A, of

G

a rod H A,

which is attached to the plane. Now, of the forty pounds, twenty will be held by the point A, and twenty will press on the plane; the pressure on the plane being in the direction W C, W C may be resolved into W D and D C, each of which will be ten pounds, that is, ten pounds will press the plane perpendicularly in the direction D C, and ten pounds will drive the plane horizontally in the direction W D. In the same way, the force of the descent W A, being resolved into A B and B W, each of these will be ten pounds; one pulling back the plane in the direction A B, and the other pressing the plane perpendicularly in the direction B W. The whole amount of force on the plane then, will stand thus: twenty pounds perpendicular pressure by the lines D C and B W, and ten pounds pressing onward in the direction W. D, and ten pounds drawing backward in the direction A B, but these two powers being op