Emily. No; it appears to me to rise and descend perpendi cularly; at least I always thought so.

Mrs. B. I believe I must make a sketch of you and your brother riding on a plank, in order to convince you of your error. (fig. 4. plate 4.) You may now observe that a lever can move only round the fulcrum, since that is the centre of motion; it would be impossible for you to rise perpendicularly, to the point A; or for your brother to descend in a straight line, to the point B; you must in rising, and he in descending, describe arcs of your respective circles. This drawing shows you also how much superior his velocity must be to yours; for if you could swing quite round, you would each complete your respective circles, in the

same time.

Caroline. My brother's circle being much the largest, he must undoubtedly move the quickest.

Mrs. B. Now tell me, do you think that your brother could raise you as easily without the aid of a lever?

Caroline. Oh no, he could not lift me off the ground.

Mrs. B. Then I think you require no further proof of the power of a lever, since you see what it enables your brother to perform.

Caroline. I now understand what you meant by saying, that in mechanics, velocity is opposed to weight, for it is my brother's velocity which overcomes my weight.

Mrs. B. You may easily imagine, what enormous weights may be raised by levers of this description, for the longer, when compared with the other, that arm is to which the power is applied, the greater will be the effect produced by it; because the greater is the velocity of the power compared to that of the weight. Levers are of three kinds; in the first the fulcrum is between power and the weight.

the

Caroline. This kind then comprehends the several levers you

have described.

Mrs. B. Yes, when in levers of the first kind, the fulcrum is equally distant from the power and the weight, as in the balance, there will be an equilibrium, when the power and the weight are equal to each other; it is not then a mechanical power, for nothing can in this case be gained by velocity; the two arms of the lever being equal, the velocity of their extremities must be so likewise. The balance is therefore of no assistance as a mechanical power, although it is extremely useful in estimating the respective weights of bodies.

But when (fig. 5.) the fulcrum F of a lever is not equally dis

17. What line is descri

16. How is this exemplified by fig. 4. plate 4? bed by the ends of a lever? fig. 4. plate 4. 18. How many kinds are there; and in the first how is the fulcrum situated? 19. When may the fulcrum be so situated that this lever is not a mechanical power, and why?

tant from the power and the weight, and the power Pacts at the extremity of the longest arm, it may be less than the weight W; its deficiency being compensated by its superior velocity, as we observed in the see-saw.

Emily. Then when we want to lift a great weight, we must fasten it to the shortest arm of a lever, and apply our strength to the longest arm?

Mrs. B. If the case will admit of your putting the end of the lever under the resisting body, no fastening will be required; as you will perceive, when a nail is drawn by means of a hammer, which, though bent, is a lever of the first kind; the handle being the longest arm, the point on which it rests, the fulcrum, and the distance from that to the part which holds the nail, the short arm. But let me hear, Caroline, whether you can explain the action of this instrument, which is composed of two levers united in one common fulcrum.

Caroline. A pair of scissors!

Mrs. B. You are surprised; but if you examine their construction, you will discover that it is the power of the lever, that assists us in cutting with scissors.

Caroline. Yes; I now perceive that the point at which the two levers are screwed together, is the fulcrum; the power of the fingers is applied to the handles, and the article to be cut, is the resistance; therefore, the longer the handles, and the shorter the points of the scissors, the more easily you cut with them.

Emily. That I have often observed, for when I cut pasteboard or any hard substance, I always make use of that part of the scissors nearest the screw or rivet, and I now understand why it increases the power of cutting; but I confess that I never should have discovered scissors to have been double levers; and pray are not snuffers levers of a similar description?

Mrs. B. Yes, and most kinds of pincers; the great power of which consists in the great relative length of the handles.

Did you ever notice the swingle-tree of a carriage to which the horses are attached when drawing?

Emily. O yes; this is a lever of the first kind, but the fulcrum being in the middle, the horses should draw with equal power, whatever may be their strength.

Mrs. B. That is generally the case, but it is evident that by making one arm longer than the other, it might be adapted to horses of unequal strength.

Caroline. And of what nature are the other two kinds of levers?

20. What is represented by fig. 5. plate 4? 21. Give a familiar example of the use of a lever of the first kind. 22. in what instruments are two such levers combined? 23. How may two horses of unequal strength, be advantageously coupled in a carriage?

Mrs. B. In levers of the second kind, the weight, instead of being at one end, is situated between the power and the fulcrum, (fig. 6.)

Caroline. The weight and the fulcrum have here changed places; and what advantage is gained by this kind of lever?

Mrs. B. In moving it, the velocity of the power must necessarily be greater than that of the weight, as it is more distant from the centre of the motion. Have you ever seen your brother move a snow-ball by means of a strong stick, when it became too heavy for him to move without assistance?

Caroline. Oh yes; and this was a lever of the second kind, (fig. 7.) the end of the stick, which he thrusts under the ball, and which rests on the ground, becomes the fulcrum; the ball is the weight to be moved, and the power his hands, applied to the other end of the lever. In this instance there is a great difference in the length of the arms of the lever; for the weight is almost close to the fulcrum.

Mrs. B. And the advantage gained is proportional to this difference. The most common example that we have of levers of the second kind, is in the doors of our apartments.

Emily. The hinges represent the fulcrum, our hands the power applied to the other end of the lever; but where is the weight to be moved?

Mrs. B. The door is the weight, which in this example occupies the whole of the space between the power and the fulcrum. Nut crackers are double levers of this kind: the hinge is the fulcrum, the nut the resistance, and the hands the power.

In levers of the third kind (fig. 8.) the fulcrum is again at one extremity, the weight or resistance at the other, and the power is applied between the fulcrum and the resistance.

Emily. The fulcrum, the weight, or the power, then, each in its turn, occupies some part of the lever between its extremities. But in this third kind of lever, the weight being farther than the power from the centre of motion, the difficulty of raising it seems increased rather than diminished.

Mrs. B. That is very true; a lever of this kind is therefore never used, unless absolutely necessary, as is the case in raising a ladder in order to place it against a wall; the man who raises it cannot place his hands on the upper part of the ladder, the power, therefore, is necessarily placed much nearer to the fulcrum than to the weight.

Caroline. Yes, the hands are the power, the ground the fulcrum, and the upper part of the ladder the weight.

24. Describe a lever of the second kind. (Fig. 6. plate 4.) 25. What is represented in fig. 7. plate 4, and in what proportion does this lever gain power? 26. What is said respecting a door? 27. Describe a lever of the third kind. 28. In what instance do we use this?

Mrs. B. Nature employs this kind of lever in the structure of the human frame. In lifting a weight with the hand, the lower part of the arm becomes a lever of the third kind the elbow is the fulcrum, the muscles of the fleshy part of the arm, the power; and as these are nearer to the elbow than to the hand, it is necessary that their power should exceed the weight to be raised. Emily. Is it not surprising that nature should have furnished us with such disadvantageous levers?

Mrs. B. The disadvantage, in respect to power, is more than counterbalanced by the convenience resulting from this structure of the arm; and it is that no doubt which is best adapted to enable it to perform its various functions.

There is one rule which applies to every lever, which is this: In order to produce an equilibrium, the power must bear the same proportion to the weight, as the length of the shorter arm does to that of the longer; as was shown by Emily with the weights of 1lb. and of 3lb. Fig. 3. plate 4.

We have dwelt so long on the lever, that we must reserve the examination of the other mechanical powers, to our next interview.

29. What remarks are made on its employment in the limbs of animals? 30. What are the conditions of equilibrium in every lever?

F

CONVERSATION V.

CONTINUED.

ON THE MECHANICAL POWERS.

OF THE PULLEY.-OF THE WHEEL AND AXLE. OF THE INCLINED PLANE. -OF THE WEDGE.-OF THE SCREW.

ine.

MRS. B.

THE pulley is the second mechanical power we are to examYou both, I suppose, have seen a pulley?

Caroline. Yes, frequently: it is a circular, and flat piece of wood or metal, with a string which runs in a groove round it: by means of which, a weight may be pulled up; thus pulleys are used for drawing up curtains.

Mrs. B. Yes; but in that instance the pulleys are fixed; that is, they retain their places, and merely turn round on their axis; these do not increase the power to raise the weights, as you will perceive by this figure. (plate 5. fig. 1.) Observe that the fixed pulley is on the same principle as the lever of a pair of scales, in which the fulcrum F being in the centre of gravity, the power P and the weight W, are equally distant from it, and no advantage is gained.

Emily. Certainly; if P represents the power employed to raise the weight W, the power must be greater than the weight in order to move it. But of what use then is a fixed pulley in

mechanics?

Mrs. B. Although it does not increase the power, it is frequently useful for altering its direction. A single fixed pulley enables us to draw a curtain up, by pulling the string connected with it downwards; and we should be at a loss to accomplish this simple operation without its assistance.

Caroline. There would certainly be some difficulty in ascending to the head of the curtain, in order to draw it up. Indeed I now recollect having seen workmen raise weights to a considerable height by means of a fixed pulley, which saved them the trouble of going up themselves.

31. Describe a pulley, and its use. 32. What is meant by a fixed pulley and why is not power gained by its employment? (fig. 1. plate 5.) 33. Of what use is the fixed pulley?