CONVERSATION XV.

Of the Lever.

Father. We will now consider the Lever, which is generally called the first mechanical power.

The Lever is any inflexible bar of wood, iron, &c. which serves to raise weights, while it is supported at a point by a prop or fulcrum, on which, as the centre of motion, all the other parts turn. A B (Plate III. Fig. 17.) will represent a lever, and the point c the fulcrum or centre of motion, Now, it is evident, if the lever turn on its centre of motion c, so that A comes into the position a; B at the same time must come into the position b. If both the arms of the lever be equal, that is, if A c is equal to в c, there is no advantage gained by it, for they pass over equal spaces in the same time; and according to the fundamental principle already laid down (p. 76) " as advantage or power is gained, time must be lost :" therefore, no time being lost by a lever of this kind, there can be no power gained.

Charles. Why then is it called a mechanical power?

Father. Strictly speaking perhaps it ought not to be numbered as one. But it is usually reckoned

among them, having the fulcrum between the weight and the power, which is the distinguishing property of levers of the first kind. And when the fulcrum is exactly the middle point between the weight and power, it is the common balance: to which, if scales be suspended at A B, it is fitted for weighing all sorts of commodities.

Emma. You say it is a lever of the first kind; are there several sorts of levers?

Father. There are three sorts; some persons reckon four, the fourth however, is, but a bended one of the first kind. A lever of the first kind (Plate III. Fig. 18, 19.) has the fulcrum between the weight and power.

The second kind of lever (Plate 11. Fig. 20.) has the fulcrum at one end, the power at the other, and the weight between them.

In the third kind (Plate III. Fig. 21.) the power is between the fulcrum and the weight.

Of Lever's powers the different sorts are three,
The first in steel-yards and in scales you see;
The best and second is the miller's lift,

Where power and fulcrum to each end you shift;
And in the third, the worst of all, my friend,
You find the weight and fulcrum at each end,

Let us take the lever of the first kind, (Fig. 18.) which if it be moved into the position a b, by turning on its fulcrum c, it is evident that while 4 has travelled over the short space a α, B has travelled over the greater space в b, which

spaces are to one another, exactly in proportion to the length of the arms A c and в C. If now you apply your hand first to the point A, and afterwards to B, in order to move the lever into the position a b, using the same velocity in both cases, you will find that the time spent in moving the lever when the hand is at B, will be as much greater, as that spent when the hand is at A, as the arm B C is longer than the arm a c, but then the exertion required will, in the same proportion, be less at в than at A.

Charles, The arm B C appears to be four times the length of 4 c.

Father. Then it is a lever which gains power in the proportion of four to one. That is, a single pound weight applied to the end of the arm B C, as at P, will balance four pounds suspended at A, as w.

Charles. I have seen workmen move large pieces of timber to very small distances, by means of a long bar of wood or iron; is that a lever?

Father. It is; they force one end of the bar under the timber, and then place a block of wood, stone, &c. beneath, and as near the same end of the lever as possible, for a fulcrum, applying their own strength to the other: and power is gained in proportion as the distance from the fulcrum to the part where the men apply their strength, is greater than the distance from the fulcrum to that end under the timber.

Charles. It must be very considerable, for I have seen two or three men move a tree, in this way, of several tons weight I should think.

Father. That is not difficult; for supposing a lever to gain the advantage of twenty to one, and a man by his natural strength is able to move but a hundred weight, he will find that by a lever of this sort, he can move twenty hundred weight or a ton; but for single exertions, a strong man ean put forth a much greater power, than that which is sufficient to remove a hundred weight; and levers are also frequently used, the advantage gained by which is still more considerable than twenty to one.

Charles. I think you said, the other day, that the common steel-yard made use of by the butcher, is a lever.

Father. I did; the short arm a c (Plate III. Fig. 19.) is, by an increase in size, made to balance the longer one в C, and from c, the centre of motion, the divisions must commence. Now if B c be divided into as many parts as it will contain, each equal to a c; a single weight, as a pound P, will serve for weighing any thing as heavy as itself, or as many times heavier as there are divisions in the arm c. If the weight P be placed at the division 1, in the arm B c, it will balance one pound in the scale at A: if it be removed to 3, 5, or 7, it will balance 3, 5, or 7 pounds in the scale; for these divisions being respectively 3, 5, or 7 times the distance from the

centre of motion c, that a is, it becomes a lever, which gains advantage at those points, in the proportion of 3, 5, and 7. If now the intervals between the divisions on the longer arm be subdivided into halves, quarters, &c. any weight may be accurately ascertained to halves, quarters of pounds, &c.

CONVERSATION XVI.

Of the Lever.

Emma. What advantage has the steel-yard, which you described in our last conversation, over a pair of scales?

Father. It may be much more readily removed from place to place; it requires no apparatus, and only a single weight for all the purposes to which it can be applied. Sometimes the arms are not of equal weight. In that case the weight P must be moved along the arm в c, till it exactly balance the other arm without a weight, and in that point a notch must be made, marking over it a cipher 0, from whence the divisions must commence.