to the depth where the water or the ore is to be drawn up, and to affix the buckets to two points of the rope in such a manner that when one of them is at the highest part, the other shall be at the lowest. For it is evident that, as equal parts of the chain ascend and descend, these parts will counterbalance each other; and the weight to be raised, were the pit several thousand feet in depth, will be that only of the ore or other substances drawn up.

The case would evidently be the same if there were only one bucket: in every position, the only weight to be raised would be that of the bucket, and the matter it contained; but the machine would be attended with only one half of its advantage; for, by having no more than one bucket, the time which the bucket when emptied would employ in descending would be lost.

4

REMARK.

In the Memoirs of the Academy of Sciences for 1731, M. Camus gave another method of remedying the above inconvenience. It consists, when there is only one bucket, in employing an axis nearly in the form of a truncated cone; so that when the bucket is at the lowest depth, the rope is rolled round the part which has the least diameter; and when the bucket is at the top, it is rolled round that which has the greatest. By these means, the same force is always required. But it is evident that, in every case, more must be applied than is

necessary.

When there are two buckets, M. Camus proposes that one half of the rope should be rolled round

one half of the axis, which he divides into two equal parts; so that one half is covered by the rope belonging to the bucket raised up, while the other is uncovered, the bucket which corresponds to it being at the bottom. By these means the two efforts are combined in such a manner, that nearly the same force is always required to overcome them. But these inventions, though ingenious, are inferior to that of M. Loriot.

PROBLEM XXXI.

Method of constructing a jack which moves by means of the smoke of the chimney. (Fig. 30 pl. 6.)

THE Construction of this kind of jack, which is very ingenious, is as follows. An iron bar fixed in the back of the chimney, and projecting from it about a foot, serves to support a perpendicular spindle, the extremity of which turns in a cavity formed in the bar; while the other extremity is fitted into a collar in another bar, placed at some distance above the former. This spindle is surrounded with a helix of tin plate, which makes a couple of revolutions, or turns round the spindle, and which is about a foot in breadth. But instead of this helix, it will be sufficient to cut several pieces of tin plate, or sheet iron, and to fix them to the spindle in such a manner that their planes shall form with it an angle of about 60 degrees; they must be disposed in several stories, above each other; so that the upper ones may stand over the vacuity left by the lower ones. The spindle, towards its summit, bears a horizontal wheel, the teeth of which turn a pinion having a horizontal axis, and the latter, at

its extremity, is furnished with a pulley, around which is rolled the endless chain that turns the spit. Such is the construction of this machine, the action of which may be explained in the following manner. When a fire is kindled in the chimney, the air which by its rarefaction immediately tends to ascend, meeting with the helicoid surface, or kind of inclined vanes, causes the spindle, to which they are affixed, to turn round, and consequently communicates the same motion to the spit. The brisker the fire becomes, the quicker the machine moves, because the air ascends with greater rapidity.

When the machine is not used, it may be taken down, by raising the vertical spindle a little, and removing the point from its cavity; which will allow the summit to be disengaged from the collar in, which it is made to turn. When wanted for use, it may be put up with the same ease.

REMARKS.

1st. The following mechanical amusement is founded on the same principle. Cut out from a card as large a circle as possible; then cut in this circle a spiral, making three or four revolutions, and ending at a small circle, reserved around the centre, and of about a line or two in diameter; extend this spiral by raising the centre above the first revolution, as if it were cut into a conical surface or parabolid; then provide a small spit made of iron, terminating in a point, and resting on a supporter. Apply the centre or summit of the helix to this point; and if the whole be placed on the top of a warm stove, the machine will soon

put itself in motion, and turn without the assistance of any apparent agent. The agent however in this case is the air, which is rarefied by the contact of a warm body, and which ascending forms a cur

rent.

2d. There is no doubt that a similar invention might be applied to works of great utility: it might be employed, for example, in the construction of wheels to be always immersed in water, their axis being placed parallel to the current: to give the water more activity this helicoid wheel might be inclosed in a hollow cylinder, where the water, when it had once entered, being impelled by the current above it, would in our opinion act with a great force.

If the cylinder were placed in an erect position, so as to receive a fall of water through the aperture at the top, the water would turn the wheel and its axis, and might thus drive the wheel of a mill, or of any other machine. Such is the principle of motion employed in the wheels of Basacle, a famous mill at Toulouse.

3. The smoke jacks here in England are made somewhat different from that above described; being mostly after the manner of that exhibited in fig. 55 plate 13: where A B is a circle containing the smoke vanes, of thin sheet iron, all fixed in the centre, but set obliquely at a proper angle of inclination. The other end of the spindle has a pinion C, which turns the toothed wheel D, on the spindle of which is fixed the vertical wheel E, over which passes the chain EF which turns the spit below. There are other forms of this useful machine also made; but all or most of them having

the same kind of vanes in the circle A B, instead of the spiral form in the original.

PROBLEM XXXII.

What is it that supports in an upright position, a top or tetotum, while it is revolving?

It is the centrifugal force of the parts of the top of tetotum, put in motion. For a body cannot move circularly without making an effort to fly off from the centre; so that if it be affixed to a string, made fast to that centre, it will stretch it, and in a greater degree according as the circular motion is more rapid.

The top then being in motion, all its parts tend to recede from the axis, and with greater force the more rapidly it revolves; hence it follows that these parts are like so many powers acting in a direction perpendicular to the axis. But as they are all equal, and as they pass all round with rapidity by the rotation, the result must be that the top is in equilibrio on its point of support, or the extremity of the axis on which it turns.

PROBLEM XXXIII.

How comes it that a stick, loaded with a weight at the upper extremity, can be kept in equilibrio, on the point of the finger, much easier than when the weight is near the lower extremity; or that a sword, for example, can be balanced on the finger much better, when the hilt is uppermost?

THE reason of this phenomenon, so well known to