Part 7

_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 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 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 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 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 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.

_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.)

8. (Pg. 55) Why would they not balance with unequal weights?

9. (Pg. 55) Were the fulcrum removed from the middle of the beam what would result?

10. (Pg. 55) What do we mean by the arms of a lever?

11. (Pg. 56) How may a pair of scales be false, and yet appear to be true?

12. (Pg. 56) If the fulcrum be removed from the centre of gravity, how may the equilibrium be restored?

13. (Pg. 56) How is this exemplified by fig. 3. plate 4?

14. (Pg. 56) What proportion must the weights bear to the lengths of the arms?

15. (Pg. 57) On what principle do we weigh with a pair of steelyards, and what will be the difference in the motion of the extremities of such a lever?

16. (Pg. 58) How is this exemplified by fig. 4. plate 4?

17. (Pg. 58) What line is described by the ends of a lever? fig. 4. plate 4.

18. (Pg. 58) How many kinds are there; and in the first how is the fulcrum situated?

19. (Pg. 58) When may the fulcrum be so situated that this lever is not a mechanical power, and why?

20. (Pg. 59) What is represented by fig. 5. plate 4?

21. (Pg. 59) Give a familiar example of the use of a lever of the first kind.

22. (Pg. 59) In what instruments are two such levers combined?

23. (Pg. 59) How may two horses of unequal strength, be advantageously coupled in a carriage?

24. (Pg. 60) Describe a lever of the second kind. (Fig. 6. plate 4.)

25. (Pg. 60) What is represented in fig. 7. plate 4, and in what proportion does this lever gain power?

26. (Pg. 60) What is said respecting a door?

27. (Pg. 60) Describe a lever of the third kind.

28. (Pg. 60) In what instance do we use this?

29. (Pg. 61) What remarks are made on its employment in the limbs of animals?

30. (Pg. 61) What are the conditions of equilibrium in every lever?

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.

MRS. B.

The pulley is the second mechanical power we are to examine. You 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.

_Mrs. B._ The next figure represents a pulley which is not fixed; (fig. 2.) and thus situated, you will perceive that it affords us mechanical assistance.

A is a moveable pulley; that is, one which is attached to the weight to be raised, and which consequently moves up or down with it. There is also a fixed pulley D, which is only of use to change the direction of the power P. Now it is evident that the velocity of the power, will be double that of the weight W; for if the rope be pulled at P, until the pulley A ascends with the weight to the fixed pulley D, then both parts of the rope, C and B, must pass over the fixed pulley, and consequently the hand at P, will have descended through a space equal to those two parts; but the weight will have ascended only one half of that distance.

_Caroline._ That I understand: if P drew the string but one inch, the weight would be raised only half an inch, because it would shorten the strings B and C half an inch each, and consequently the pulley with the weight attached to it, can be raised only half an inch.

_Emily._ But I do not yet understand the advantage of moveable pulleys; they seem to me to increase rather than diminish the difficulty of raising weights, since you must draw the string double the length that you raise the weight; whilst with a single pulley, or without any pulley, the weight is raised as much as the string is shortened.

_Mrs. B._ The advantage of a moveable pulley consists in dividing the difficulty; we must, it is true, draw twice the length of the string, but then only half the strength is required that would be necessary to raise the weight without the assistance of a moveable pulley.

_Emily._ So that the difficulty is overcome in the same manner as it would be, by dividing the weight into two equal parts, and raising them successively.

_Mrs. B._ Exactly. You must observe, that with a moveable pulley the velocity of the power, is double that of the weight; since the power P (fig. 2.) moves two inches whilst the weight W moves one inch; therefore the power need not be more than half the weight, to make their momentums equal.

_Caroline._ Pulleys act then on the same principle as the lever; the deficiency of weight in the power, being compensated by its superior velocity, so as to make their momentums equal.

_Mrs. B._ You will find, that all gain of power in mechanics is founded on the same principle.

_Emily._ But may it not be objected to pulleys, that a longer time is required to raise a weight by their aid, than without it? for what you gain in power, you lose in time.

_Mrs. B._ That, my dear, is the fundamental law in mechanics: it is the case with the lever, as well as the pulley; and you will find it to be so with all the other mechanical powers.

_Caroline._ I do not see any advantage in the mechanical powers then, if what we gain by them in one way, is lost in another.

_Mrs. B._ Since we are not able to increase our natural strength is not any instrument of obvious utility, by means of which we may reduce the resistance or weight of any body, to the level of that strength? This the mechanical powers enable us to accomplish. It is true, as you observe, that it requires a sacrifice of time to attain this end, but you must be sensible how very advantageously it is exchanged for power. If one man by his natural strength could raise one hundred pounds only, it would require five such men to raise five hundred pounds; and if one man performs this by the help of a suitable engine, there is then no actual loss of time; as he does the work of five men, although he is five times as long in its accomplishment.

You can now understand, that the greater the number of moveable pulleys connected by a string, the more easily the weight is raised; as the difficulty is divided amongst the number of strings, or rather of parts into which the string is divided, by the pulleys. Two, or more pulleys thus connected, form what is called a tackle, or system of pulleys. (fig. 3.) You may have seen them suspended from cranes to raise goods into warehouses.

_Emily._ When there are two moveable pulleys, as in the figure you have shown to us, (fig. 3.) there must also be two fixed pulleys, for the purpose of changing the direction of the string, and then the weight is supported by four strings, and of course, each must bear only one fourth part of the weight.

_Mrs. B._ You are perfectly correct, and the rule for estimating the power gained by a system of pulleys, is to count the number of strings by which the weight is supported; or, which amounts to the same thing, to multiply the number of moveable pulleys by two.

In shipping, the advantages of both an increase of power, and a change of direction, by means of pulleys, are of essential importance: for the sails are raised up the masts by the sailors on deck, from the change of direction which the pulley effects, and the labour is facilitated by the mechanical power of a combination of pulleys.

_Emily._ But the pulleys on ship-board do not appear to me to be united in the manner you have shown us.

_Mrs. B._ They are, I believe, generally connected as described in figure 4, both for nautical, and a variety of other purposes; but in whatever manner pulleys are connected by a single string, the mechanical power is the same.

The third mechanical power, is the wheel and axle. Let us suppose (plate 6. fig. 5) the weight W, to be a bucket of water in a well, which we raise by winding round the axle the rope, to which it is attached; if this be done without a wheel to turn the axle, no mechanical assistance is received. The axle without a wheel is as impotent as a single fixed pulley, or a lever, whose fulcrum is in the centre: but add the wheel to the axle, and you will immediately find the bucket is raised with much less difficulty. The velocity of the circumference of the wheel is as much greater than that of the axle, as it is further from the centre of motion; for the wheel describes a great circle in the same space of time that the axle describes a small one, therefore the power is increased in the same proportion as the circumference of the wheel is greater than that of the axle. If the velocity of the wheel is twelve times greater than that of the axle, a power twelve times less than the weight of the bucket, would balance it; and a small increase would raise it.

_Emily._ The axle acts the part of the shorter arm of the lever, the wheel that of the longer arm.

_Caroline._ In raising water, there is commonly, I believe, instead of a wheel attached to the axle, only a crooked handle, which answers the purpose of winding the rope round the axle, and thus raising the bucket.

_Mrs. B._ In this manner (fig. 6;) now if you observe the dotted circle which the handle describes in winding up the rope, you will perceive that the branch of the handle A, which is united to the axle, represents the spoke of a wheel, and answers the purpose of an entire wheel; the other branch B affords no mechanical aid, merely serving as a handle to turn the wheel.

Wheels are a very essential part of most machines; they are employed in various ways; but, when fixed to the axle, their mechanical power is always the same: that is, as the circumference of the wheel exceeds that of the axle, so much will the energy of the power be increased.

_Caroline._ Then the larger the wheel, in proportion to the axle, the greater must be its effect?

_Mrs. B._ Certainly. If you have ever seen any considerable mills or manufactures, you must have admired the immense wheel, the revolution of which puts the whole of the machinery into motion; and though so great an effect is produced by it, a horse or two has sufficient power to turn it; sometimes a stream of water is used for that purpose, but of late years, a steam-engine has been found both the most powerful and the most convenient mode of turning the wheel.

_Caroline._ Do not the vanes of a windmill represent a wheel, Mrs. B.?

_Mrs. B._ Yes; and in this instance we have the advantage of a gratuitous force, the wind, to turn the wheel. One of the great benefits resulting from the use of machinery is, that it gives us a sort of empire over the powers of nature, and enables us to make them perform the labour which would otherwise fall to the lot of man. When a current of wind, a stream of water, or the expansive force of steam, performs our task, we have only to superintend and regulate their operations.

The fourth mechanical power is the inclined plane; this is generally nothing more than a plank placed in a sloping direction, which is frequently used to facilitate the raising of weights, to a small height, such as the rolling of hogsheads or barrels into a warehouse. It is not difficult to understand, that a weight may much more easily be rolled up a slope than it can be raised the same height perpendicularly. But in this, as well as the other mechanical powers, the facility is purchased by a loss of time (fig. 7;) for the weight, instead of moving directly from A to C, must move from B to C, and as the length of the plane is to its height, so much is the resistance of the weight diminished.

_Emily._ Yes; for the resistance, instead of being confined to the short line A C, is spread over the long line B C.

_Mrs. B._ The wedge, which is the next mechanical power, is usually viewed as composed of two inclined planes (fig. 8:) you may have seen wood-cutters use it to cleave wood. The resistance consists in the cohesive attraction of the wood, or any other body which the wedge is employed to separate; the advantage gained by this power is differently estimated by philosophers; but one thing is certain, its power is increased, in proportion to the decrease of its thickness, compared with its length. The wedge is a very powerful instrument, but it is always driven forward by blows from a hammer, or some other body having considerable momentum.

_Emily._ The wedge, then, is rather a compound than a distinct mechanical power, since it is not propelled by simple pressure, or weight, like the other powers.

_Mrs. B._ It is so. All cutting instruments are constructed upon the principle of the inclined plane, or the wedge: those that have but one edge sloped, like the chisel, may be referred to the inclined plane; whilst the axe, the hatchet, and the knife, (when used to split asunder) are used as wedges.

_Caroline._ But a knife cuts best when it is drawn across the substance it is to divide. We use it thus in cutting meat, we do not chop it to pieces.

_Mrs. B._ The reason of this is, that the edge of a knife is really a very fine saw, and therefore acts best when used like that instrument.

The screw, which is the last mechanical power, is more complicated than the others. You will see by this figure, (fig. 9.) that it is composed of two parts, the screw and the nut. The screw S is a cylinder, with a spiral protuberance coiled round it, called the thread; the nut N is perforated to receive the screw, and the inside of the nut has a spiral groove, made to fit the spiral thread of the screw.

_Caroline._ It is just like this little box, the lid of which screws on the box as you have described; but what is this handle L which projects from the nut?

_Mrs. B._ It is a lever, which is attached to the nut, without which the screw is never used as a mechanical power. The power of the screw, complicated as it appears, is referable to one of the most simple of the mechanical powers; which of them do you think it is?

_Caroline._ In appearance, it most resembles the wheel and axle.

_Mrs. B._ The lever, it is true, has the effect of a wheel, as it is the means by which you turn the nut, or sometimes the screw, round; but the lever is not considered as composing a part of the screw, though it is true, that it is necessarily attached to it.

_Emily._ The spiral thread of the screw resembles, I think, an inclined plane: it is a sort of slope, by means of which the nut ascends more easily than it would do if raised perpendicularly; and it serves to support it when at rest.

_Mrs. B._ Very well: if you cut a slip of paper in the form of an inclined plane, and wind it round your pencil, which will represent the cylinder, you will find that it makes a spiral line, corresponding to the spiral protuberance of the screw. (Fig. 10.)

_Emily._ Very true; the nut then ascends an inclined plane, but ascends it in a spiral, instead of a straight line: the closer the threads of the screw, the more easy the ascent: it is like having shallow, instead of steep steps to ascend.

_Mrs. B._ Yes; excepting that the nut takes no steps, as it gradually winds up or down; then observe, that the closer the threads of the screw, the less is its ascent in turning round, and the greater is its power; so that we return to the old principle,--what is saved in power is lost in time.