_Caroline._ Yes; I have the most weight, he the greatest velocity; so that upon the whole our momentums are equal. But you said, Mrs. B., that the power should be greater than the resistance, to put the machine in motion; how then can the plank move if the momentums of the persons who ride are equal?

_Mrs. B._ Because each person at his descent touches and pushes against the ground with his feet; the reaction of which gives him an impulse which produces the motion; this spring is requisite to destroy the equilibrium of the power and the resistance, otherwise the plank would not move. Did you ever observe that a lever describes the arc of a circle in its motion?

_Emily._ No; it appears to me to rise and descend perpendicularly; 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 the power and the weight.

_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 a.s.sistance 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 distant from the power and the weight, and the power P acts 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 a.s.sists 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 paste-board 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?

_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 a.s.sistance?

_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 s.p.a.ce 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.

_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 1 _lb._ and of 3 _lb._ 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.

Questions

1. (Pg. 54) How many mechanical powers are there, and what are they named?

2. (Pg. 54) What is a mechanical power defined to be?

3. (Pg. 54) What four particulars must be observed?

4. (Pg. 54) Upon what will the velocities depend?

5. (Pg. 55) What is a lever?

6. (Pg. 55) Give a familiar example.

7. (Pg. 55) When and why do the scales balance each other, and where is their centre of gravity? (fig. 1. plate 4.)