having made it fast to the middle of a large lever A B (pl. 1 fig. 4) cause the extremities of this lever to rest on two shorter ones CD and E F, and place a man at each of the points C, D, E and F: it is evident that the weight will then be equally distributed among these four persons.

If eight men are required, pursue the same method with the levers CD and E F, as was employed in regard to the first; that is, let the extremities of CD be supported by the two shorter ones ab and cd; and those of E F by the levers ef and gh: if a man be then stationed at each of the points a, b, c, d, e, f, g, h, they will be all equally loaded.

The extremities of the levers or poles ab, cd, ef, and gh, might, in like manner, be made to rest on others placed at right angles to them: by means of this artifice the weight would be equally distributed among sixteen men. And so of any other number. We have heard that this artifice is employed at Constantinople, to raise and carry the heaviest burthens, such as cannons, mortars, enormous stones, &c. The velocity, it is added, with which burthens are transported from one place to another by this method, it is truly astonishing.

PROBLEM VII.

A rope AGB (pl. I fig. 5), of a determinate length, being made fast by both ends, but not stretched, to two points of unequal height, A and B; what pesition will be assumed by the weight P, suspended from a pulley, which rolls freely on that rope?

VOL. II.

FROM the points A and B, let fall the indefinite vertical lines AD and B G; then from the point A, with an opening of the compasses equal to the length of the rope, describe an arc of a circle, intersecting the vertical line B G, in E; and from the point B describe a similar arc of a circle, intersecting the vertical line A D in D: if the lines A E and BD be then drawn, the point C, where they cut each other, will give the position of the rope A CB, when the weight has assumed that position in which it must rest; and the point C will be that in which the pulley will settle. For it may be easily demonstrated, that in this situation the weight P will be in the lowest position possible, which is an invariable principle of the centre of gravity.

PROBLEM VIII.

To cause a pail full of water to be supported by a stick, one half of which only, or less, rests on the edge of a table.

To make the reader comprehend properly the method of performing this trick, in regard to equilibrium; which is but ill explained in the old books of Mathematical Recreations, both in the text and in the engraving; we have given, in the 6th figure of the 1st plate, a section of the table and the bucket.

In this figure, let A B be the top of the table, on which is placed the stick C D. Convey the handle of the bucket over this stick, in such a manner that it may rest on it in an inclined position; and let the middle of the bucket be within the edge of the table. That the whole apparatus may be fixed in

this situation, place another stick GFE, with one of its ends resting against the corner G of the bucket, while the middle part rests against the edge F, of the bucket, and its other extremity against the first stick CD, in E, where there ought to be a notch to retain it. By these means the bucket will remain fixed in that situation, without being able to incline to either side; and if not already full of water, it may be filled with safety; for its centre of gravity being in the vertical line passing through the point H, which itself meets with the table, it is evident that the case is the same as if the pail were suspended from the point of the table where it is met by that vertical. It is also evident that the. stick cannot slide along the table, nor move on its edge, without raising the centre of gravity of the bucket, and of the water it contains. The heavier therefore it is, the greater will be the stability.

REMARK.

According to this principle, various other tricks of the same kind, which are generally proposed in books on mechanics, may be perforined. For example, provide a bent hook DGF, as seen at the opposite end of the same figure, and insert the part, FD, in the pipe of a key at D, which must be placed on the edge of a table; from the lower part of the hook suspend a weight G, and dispose the whole in such a manner that the vertical line. G D may be a little within the edge of the table. When this arrangement has been made, the weight will not fall, and the case will be the same with the key, which had it been placed alone in that situation would perhaps have fallen; and this resplves

the following mechanical problem, proposed in the form of a paradox: A body having a tendency to fall by its own weight, how to prevent it from falling, by adding to it a weight on the same side on which it tends to fall.

The weight indeed appears to be added on that side, but in reality it is on the opposite side.

PROBLEM IX.

To hold a stick upright on the tip of the finger, without its being able to fall.

AFFIX two knives, or other bodies, to the extremity of the stick, in such a manner that one of them may incline to one side, and the second to the other, as seen in the figure (pl. 2 fig. 7): if this extremity be placed on the tip of the finger, the stick will keep itself upright, without falling; and if it be made to incline, it will raise itself again, and recover its former situation.

For this purpose, the centre of gravity of the two weights added, and of the stick, must be below the point of suspension, or the extremity of the stick, and not at the extremity, as asserted by Ozanam; for in that case there would be no stability..

It is the same principle that keeps in an upright: position those small figures furnished with two weights, to counterbalance them; and which are. made to turn and balance, while the point of the foot rests on a small ball, loosely placed on a sort of stand. Of this kind is the small figure. D (fig. & pl. 2), supported on the stand I, by a ball E

through which passes a bent wire, having affixed to its extremities two balls of lead C and F. The centre of gravity of the whole, which is at a con siderable distance below the point of support, maintains the figure upright, and makes it resume its perpendicular position, after it has been inclined to either side; for this centre tends to place itself as low as possible, which it cannot do without making the figure stand upright.

By the same mechanism, three knives may be disposed in such a manner as to turn on the point of a needle; for being disposed as seen in the figure (fig. 9 pl. 2) and placed in equilibrio on the point of a needle held in the hand, they cannot fall, because their common centre of gravity is far below the point of the needle, which is above the point of support.

PROBLEM X.

To construct a figure, which, without any counterpoise, shall always raise itself upright, and keep in that position, or regain it, however it may be disturbed.

MAKE a figure resembling a man of any substance exceedingly light, such as the pith of the elder tree, which is soft and can be easily cut into any form at pleasure. Then provide for it an hemispherical base of some very heavy substance, such as lead. The half of a leaden bullet, made very smooth on the convex part, will be proper for this purpose. If the figure be cemented to the plane part of this hemisphere; then, in whatever position it may be placed, as soon as it is left to itself, it will rise upright (fig. 10 pl. 2); because the centre of