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MECHANICS.—XIX.

IMPACT-CENTRIFUGAL FORCE-THE PENDULUM-CENTRE OF OSCILLATION.

WHEN two bodies strike one another, they touch first in some one or more points, and the motion of these is usually commanicated to the whole body. Thus, when a carpenter strikes a nail with his hammer, it only touches part of the head, but the momentum acquired by this part is shared by the whole. If, however, the blow be not true, the head alone may receive the motion, and fly off by itself, leaving the rest unmoved. Sometimes, especially if the body struck be soft or brittle, and the velocity of the other be great, there is no time for the motion to be thus shared, and then the shape of the mass is altered, or the part struck flies off as a chip. A homely illus. tration of this is afforded by a simple experiment which all

may try.

Balance a small piece of card on one of the fingers of the left hand, and lay a shilling on the top of it. By a sudden blow with the finger and thumb of the other hand the card may be jerked away without moving the shilling. Care must, however, be taken to strike the card exactly in the direction of its surface, as if it be tilted up or down the shilling will, of course, be jerked off. After a few trials, however, you may be pretty certain of wuccess. The explanation is, that the motion of the card is so rapid that it has moved quite away before it has had time to communicate its motion to the shilling.

There are many other familiar examples of this, some of which verge on the marvellous.

If a bullet be fired at a door set half open, it will pass through the panel without shutting the door or moving it on its hinges. We may even go further, and, instead of a bullet, put a tallow candle into the gun and fire it at the door, it will be found to pass through instead of being smashed against it, as we should naturally expect. The velocity of the particles of tallow is so great that they have passed through the door before they have time to alter their relative position. So, if we fire a ball at a window, it will pass through the pane without cracking it, merely making a clean round hole. If, however, the bullet be nearly spent, or its velocity be not sufficiently great, the glass

will be shivered to pieces.

This, too, explains why a good skater will glide swiftly over ice far too thin to sustain his weight. His motion is so rapid, that before the ice has time to yield he has passed on to another portion of it. We see, then, that a certain amount of time is required for any motion to be imparted from one body to another.

CENTRIFUGAL FORCE.

If a lump of metal or other heavy substance be fastened to a piece of string, and then swung round and round, we shall find that the string is stretched with a strain which varies in proportion to the speed with which the body revolves. This strain is called centrifugal force, and is merely one of the results of the first law of motion.

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Fig. 104.

Let B (Fig. 104) represent a body revolving round a centre A, and confined by the string AB; its tendency at every instant is to continue in the same line in which it is travelling at that instant, that is, to fly off at a tangent, as along BC. We can easily prove that this is the case, for if, when whirling a sling, we suddenly cut the cord or leave the end free, the stone will fly off in a straight line. Suppose D to be the point which the stone has reached at the end of one second, then BD will represent the space passed over, and therefore the velocity of B. This we can resolve into two parts, BF acting along the tangent BC, and BG acting along the direction of the cord. The former represents the velocity the stone has acquired, the latter is the force exerted by the string to keep it moving in a circle; this, therefore, represents the centrifugal force. We can thus easily see that the greater the velocity with which в moves, the greater will the cord. If, for example, the velocity be so t at the end of one second B is at E instead

the cord will be represented by BH instead r, this tension always acts in a direction at

right angles to the motion of the body, no velocity is destroyed, the only alteration being in its direction.

We constantly meet with illustrations of the action of this force. A can filled with water may be swung round the head without a drop being spilt. When the can is at its highest point, and therefore mouth downwards, the water is attracted towards the earth; but this attraction is more than overcome by the centrifugal force, and hence it remains in the can as if it were a solid. So, too, when rapidly turning a corner or running round the inside of a ring, we lean inwards. The body has a tendency to move onwards in its previous direction, the feet are, however, compelled to move in another, and thus the head and body are thrown outward; to obviate this we lean in the contrary way. For the same reason, in a curve on a railway the inner rails are lower than the outer, so that the carriage inclines inwards, and thus removes the danger of its upsetting or tearing up the rails. A carriage is not unfrequently upset in this way while rapidly turning a corner.

If a glass of water be placed on a small whirling table so that it can be rapidly turned, the water will leave the centre and rise towards the edges; it may even be scattered over the sides if the rotation be rapid enough. The same effect if we rapidly stir a cup of tea, the level at the sides being above that at the centre.

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A practical application of these principles is seen in the centrifugal drying machine. This consists of a large hollow cylinder, the bottom of which is perforated by a number of holes. The linen is put into this, and it is then made to rotate rapidly. In this way it is closely pressed against the sides, and the water is given off and runs away through the holes in the cylinder. Linen can thus be rendered almost dry in a very short space of time. Another useful application of this force is seen in the "governors" of a steam-engine. These consist of two heavy balls suspended by rods, and when the speed of the engine is increased beyond the proper degree they fly apart, and in collar below them, and so doing raise a loose by a series of levers partly close the throttle valve, and thus diminish the supply of a

steam.

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Fig. 105.

In Fig. 105 a, a represent the balls suspended by rods, which are hinged at b to the vertical shaft g. Motion is imparted to this by means of a strap, which passes round the shaft of the fly-wheel, or some other convenient part of the engine, and then round the driving-pulley, d. When the engine is moving too rapidly the balls fly further apart, and by so doing raise the runner, e. This, by means of the bent lever, k, works the rods, f, and thus partly closes the valve.

Were it not for some such arrangement as this, there would be great danger of the engine at times moving so rapidly, that the fly-wheel would from the momentum of its particles be shivered to pieces. These balls keep the speed nearly uni form; for if it diminishes much they fall, and thus open the throttle-valve to a greater extent and allow more steam to pass.

The laws of centrifugal force are important, because they help to explain the motions of the heavenly bodies. The planets, when first made, were started from the hand of their Creator with a certain velocity. This produces a constant tendency to fly off at a tangent from their orbits. They are, however, restrained by another force, and that is the universal attraction of all bodies for each other. Gravity is but one manifestation of this: the earth draws the small bodies to it merely on account of its superior weight, and for the same reason the sun attracts all the planets; or, to speak more accurately, all are attracted to the common centre of gravity of our own solar system, which is situated very near to the sun.

This attraction, then, constantly deflects the planets from the line in which they would otherwise move, and as a result of these two forces they describe ellipses, in one focus of which

the sun is situated. As this motion is through space, and not through a resisting medium like the air, the retarding forces which diminish the motion of bodies near the earth do not affect them, and hence they move with undiminished speed. This speed, however, varies with their distance from the sun, and the following rule, discovered by Kepler, shows the relation that exists between the speed and the distance:-The straight line drawn from the planet to the sun always describes equal areas in equal times. This law partly depends on another, which teaches us that the attraction of any body for another diminishes with the square of the distance. If, for instance, we remove a body to double the distance, the attraction is, if to three times the distance, it is only, and so on. This is an experimental law, though by analogy with light we can easily see why it should be so. If we take a piece of board, and having cut out of it a piece a foot square, hold the board at any distance from a bright light, and place a screen behind it at twice the distance from the light, the illuminated space on the screen will measure 2 feet each way, or 4 feet in all. The light is thus spread over four times the area, and therefore the illumination at any point is only one-fourth as great.

Similarly, if the distance of the screen from the light be three times as great as that of the board, a space of 9 square feet will be illuminated, and each part will have one-ninth of the brilliancy.

From this we see that when a planet is in the part of its orbit most remote from the sun, it is attracted less powerfully, and therefore its velocity must be less than when nearer the sun, or else it would fly out of its path.

THE PENDULUM.

We must now notice this very important instrument, so valuable to us, not only as a regulating power for clocks, but also for calculating the force of gravity and its variations in different places.

A simple pendulum is one all the weight of which is collected at a single point. Such a one can, of course, only exist theoretically; but we may obtain a near approach to it by suspending a small ball of some heavy substance, as lead or platinum, by a very fine string.

A common pendulum is called compound, for the weight is divided throughout it, and it may therefore be considered as a number of simple pendulums connected together, so that all swing at the same rate. All are familiar with its action, but many do not know why it is used as a regulator.

When a pendulum hangs freely, all its oscillations, if not of wide extent, occupy exactly the same time. If the pendulum be made to swing in a cycloidal curve, instead of an arc of a circle, then from whatever part of the arc it falls it always takes exactly the same time. This remarkable property is called the isochronism of the pendulum, this term being derived from two Greek words, meaning "equal" and "time." Galileo was the first to discover this law, and it is said his attention was called to it by observing a chandelier in a cathedral. By some cause it had been set swinging, and he noticed that however long the arc, it appeared to swing in exactly the same time. He accordingly tried some experiments on his return home, and found that such was the case.

sent the portion of gravity which produces motion in the pendulum, and A Y that which produces tension in the cord; and it is clear that the smaller the arc A C, the less will y X be, and therefore the less the velocity of the pendulum. This velocity is found to decrease in the same proportion of the length of the arc, and this accounts for the vibrations occupying equal times.

Now as the force which moves the pendulum is the resolved part of gravity, it clearly increases or decreases with that force, and thus the vibrations afford us a means of measuring the force of gravity and comparing its power at different parts of the earth. At the equator it is least, the diameter there being greatest, and a part of the force, which is reckoned at, being overcome by the centrifugal force produced by the earth's rotation. A pendulum will, therefore, make fewer vibrations there than it will as we move towards the poles. The times of oscillation vary, then, at different parts of the earth's surface. We find, too, that the time of oscillation depends upon the length of the pendulum, a longer pendulum making less vibrations in any given time than a short one. The rule about this is as follows:

The time of oscillation increases in the same ratio as the square root of the length of the pendulum.

If we take three pendulums whose lengths are in the proportion of 1, 4, and 9-say, for example, 6 inches, 2 feet, and 4 feet 6 inches, respectively-we shall find that while the long one makes one vibration, that two feet long will make two, and the shortest, three. In the latitude of London, a pendulum to beat seconds must have a length of 39.13 inches; at the equator, the length must only be 39.01 inches.

In the compound pendulum all parts must swing at exactly the same rate; but by what we have seen, those nearer the point of suspension have a tendency to swing more rapidly, and thus to accelerate the motion of those below, while those at the extreme end exert just the contrary influence. Now there is evidently some point where the particles are as much retarded by those below as accelerated by those above, and this point must move at the same rate as if it were free. We might, in fact, have all the weight collected at this spot without altering in any degree the rate of oscillation.

This point is called the "centre of oscillation," and when we speak of a pendulum of any length-as e.g., 39.13 incheswe measure from this point to that of suspension. This centre of oscillation is always below the centre of gravity. However much we alter the weight of the pendulum, provided we make no difference in the position of this point, the time of oscillation remains exactly the same. The rate of vibration, then, is not at all affected by the nature or weight of the pendulum, but depends alone upon its length. We see, thus, the way in which we can regulate the speed; we can either raise the bob by means of a small nut, as is usually done, or we can have a smaller weight sliding on the rod, and raise or lower this. In either case, the effect produced is the same-the position of the centre of oscillation is moved, and thus the length altered. When the pendulum rod is made of metal, as it usually is, it varies in length with the alterations of temperature, being lengthened by heat and contracted by cold, and thus a source of irregularity is introduced which would be very objectionable. This dif ficulty is met by what is called the compensation pendulum. In one form of this the bob consists of a cup of mercury. When the rod lengthens by the heat and lowers the centre of oscillation, the mercury expands and rises, and its bulk is so arranged that this expansion raises the centre in exactly the same degree as the expansion of the rod depresses it. In large church clocks the pendulum rod is frequently made of wood, and thus this difficulty is avoided.

Another compensating pendulum is composed of parallel bars of brass and zinc, so arranged that by their joint alterations in length the position of the bob remains unaltered.

In Fig. 106 let o represent the point of suspension. When oc is vertical the force of gravity is exactly overcome by the tension of the cord, and thus the pendulum serves as a plumb-line, for if c be raised above the lowest point it will swing backwards and forwards till it settles at that point. Now raise c to A. The same two forces act upon it, namely, tension along A O and the force of gravity acting vertically downwards along A X. Produce o A to Y, and draw A z a tangent to the arc. We can now resolve the force of gravity into two, acting along A Y and A Z. The former of these will be overcome by the tension of the string, the other part acting along A z will cause When a pendulum is made to swing by itself it soon comes to c the pendulum to move towards c. On arriving rest; and even if every care be taken to remove the air and rethere it will have acquired a velocity which duce the friction, it will not continue in motion more than about Fig. 106. will carry it on over an arc nearly equal to CA, twenty-four hours. A maintaining force is therefore needed, and thus it will continue to oscillate till its when it is employed as a measurer of time. This is supplied by motion is stopped by the resistance it meets with. If we the spring or weight of the clock. The pendulum rod works in now draw a line through Y parallel to A z, Y x will repre- a fork which is attached to the anchor and pallets. These

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The balance wheel of a watch acts on the same principle as the pendulum, its vibrations being isochronous.

catch in the teeth of the escapement wheel, and allow it at each oscillation to move forward half a tooth, and then again stop it. The motion of the escapement wheel is thus at each stoppage transferred to the pendulum, and keeps it in vibration. A train of wheels connects this escapement with the hands.

We have thus acquired a general acquaintance with the more important facts of Mechanics. The subject is far from exhausted, but we must leave you to follow it up in works specially devoted to it. Our attention will now be turned to the other branches of Natural Philosophy, all of which are of great interest and importance. The next branch we shall take up is Hydrostatics, a science which has been claimed as a branch of mechanics, but is more accurately considered as a separate science.

LESSONS IN ENGLISH.-XXIV. CONVERSATIONS ON ENGLISH GRAMMAR. - III. William. The substance of our two conversations are pretty clear to me now.

Thomas. I am glad you have carefully studied them, but you have just committed a grammatical error. William. You do not say so? right.

Thomas. No, it would be wrong; "the fleet has sailed" is correct English. The true rule in this matter is this: Nouns of multitude require their verb to be in the plural when the mind dwells on the individual objects which they comprise; but when those objects are presented or contemplated as a whole, then the verb must be in the singular. In the phrase "the majority of us," the idea of plurality is made prominent, you of necessity think of several persons, therefore your verb must be in the plural; but in the phrase "the fleet has sailed," you conceive of the component parts as forming a whole, several elements coalesce into one, unity is the predominant feeling, and consequently you must employ a singular verb. I give you another instance: "The imprisonment of us is wrong." What say you to that ?

William. It is correct.

Thomas. Yes, it is correct. Now do you not see the words "of us" hold in this sentence precisely the same relation or position that is held in the first sentence by the words "of our conversation?" Look at this arrangement

COMPOUND SUBJECT.

The imprisonment of us

PREDICATE.

Verb. is

Attribute. wrong.

I fear I shall never get Us, you see, is not the nominative case (or, as I prefer putting it, is not the subject), for we, you know, is the nominaYou would not say tive, and us is in the objective case.

Thomas. Yes, you will get right by perseverance. The error into which you have fallen is a very common one; I have heard it even from the lips of persons who do not think themselves ignorant of grammar.

William. Wherein does it lie?

us are.

William. Oh, no, that would be ridiculous.
Thomas. And yet I heard a man, the other day, say we is;

Thomas. You have used a plural verb where you should have nay, I am not sure that you yourself-speaking, for example, of used a singular one.

William. But "conversations" is in the plural.

Thomas. It is. That word, however, is not the subject to the verb of the sentence; it comes immediately before the verb, and so has led you to put the verb into the plural, by a kind of latent attraction, against the influence of which I must put you on your guard.

William. What, then, is the subject?

Thomas. "Substance" is the subject, or what in common grammars is called the nominative case, and the sentence should have stood thus: "The substance of our two conversa

the potatoes you might have had to-day for dinner-did not say, "they is good." What think you?

William. It is not impossible; these things are very perplexing.

Thomas. Yes, at first they are troublesome; but study and practice will remove all difficulties. They have done so in my case, why not in yours?

William. Well, I am not going to yield.

Thomas. Certainly not. Bonaparte is reported to have said that the French had not such a word as "impossible" in their language. However this may be, you, as an Englishman, will

tions is pretty clear to me now." "Substance," I repeat, is not, I am sure, easily admit the idea into your mind, or the the subject. What is clear? You do not mean that the "conversations" are clear?

William. No; for there are some things in them that I do not quite comprehend; but they are clear on the whole.

Thomas. Yes, your language expressed your meaning correctly, although your grammar is at fault. This I have often observed in persons of defective education. Right in their logic, and having a good command of words, they are unable to put them together correctly, and so lose a large part of the advantage they ought to derive from their efforts at self-culture. Observe, now, "conversations is dependent on the preposition "of." In the ordinary phraseology, it is governed by that preposition; and being governed by it, is in what is called the objective case-it cannot be the nominative, or the subject to the ensuing verb. In fact, the word "conversations" is a part of the compound subject of the sentence, as you may see exhibited thus:

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Thomas. I beg your pardon, it is quite correct.
William. How so?

Thomas. Because the word "majority" is what is called a noun of multitude-a noun, that is, which being singular in form, is plural in signification. In a majority, you know, there must be more than one. Now nouns of this kind, as they imply more than one, are constructed according to their sense, and not according to their form. Consequently, "majority" requires its verb to be in the plural.

im. Then it would be right to say, "The fleet have for a fleet consists of many ships.

thing itself into your conduct. "Impossible?" No, nothing that is good and honest is impossible. What man has done, man may do. Now I must put you to rights in regard to this verb is and are; it is a word against which many, very many, persons sin grievously. Study this form :

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This surely is not very complicated, yet it contains all you need know in order to speak and write correctly, so far as this point is concerned. Take care, then, not to separate the pronouns from the proper forms of the verb. Take care not to mix together verbs and pronouns that should be kept apart. Do not take the first person I, and put it before the third person is. In other terms, 1 and i. must go together; 1 and iii. must not be combined. You must say we were (1 and i.), and not they was (iii. and 1). Before I conclude, let me impress it on your mind that you will never speak grammatically, or, at any rate, never be sure that you speak grammatically, unless you take the trouble to make yourself familiar with the terms and the laws of grammar. Many, finding the study somewhat difficult, after a little while give it up in a sort of confident spirit, thinking such drudgery beneath them, and fancying they can do all that is necessary by a sort of nondescript grammatical feeling. This is silly. Accurate knowledge is not obtained by genius, or inspiration, or any other fancied short cut to science. If you would know, you must condescend to learn, and all true learning demands, as it well rewards, diligent and constant labour.

William. Well, I do not know that I am in that danger; I never thought myself a "genius," and as for "inspiration," that belongs to a subject too sacred for me to venture on-a subject on which I had rather worship than speculate, much less be over-confident.

Thomas. Those are wise words; the man who is without reverence will be a small man to the end of his days.

LESSONS IN CHEMISTRY.-XI.

CARBON AND ITS OXIDES.

CARBON. SYMBOL, C; ATOMIC WEIGHT, 12.

No solid plays a more prominent part in the economy of nature than carbon, as it forms the wood of vegetation. It is a very remarkable substance, for it appears in three perfectly distinct states-the diamond, graphite, and charcoal.

1. The diamond is found in alluvial débris-that is, in water-worn deposits of gravel. It is presumed that the gem was formed by crystallisation when the rock was in a fluid state, and when in after ages it became broken in pieces by the action of water and other geological forces, the hard diamond was delivered from its matrix, and mixed with the débris. The chief diamond mines are those of Golconda and Bundelcund, in India, Borneo, and Brazil.

When found, the stone has the appearance of a piece of white glass; occasionally there is an approach to the crystal form of the octahedron.

It is the hardest of all known bodies, and is capable of dispersing light-that is, of breaking up white light into its coloured component rays-in a greater degree than any other body except chromate of lead. To exhibit this property to its full advantage, the gem must be cut. This was once an operation of the greatest difficulty, and could only be executed by the Dutch diamond-cutters, who fastened two stones in cement, and then rubbed them against each other until a facet was produced. Now, diamond-cutting is much less laborious. The stone is fixed, as before, in a metallic cement, and pressed upon a disc of steel about eight inches in diameter, which revolves horizontally with a great velocity. As with all crystals, there are certain directions in which the diamond is more readily cut. It is the skill of the cutter to place the stone upon the disc in the right position. The steel, were this not done, would itself be cut, instead of making any impression on the diamond. The secret of the disc being enabled to wear down the hard mineral is, that the minute interstices of the metal become filled with dust from the diamond. This is in many instances applied to the plate mixed with olive oil; but when a disc has been some time in work, it is sufficiently impregnated with the dust not to need this addition.

In the Brazil mines is found a dark brown carbonaceous matter, in small pieces, which is as hard, if not harder, than the diamond itself; and it commands as high a price on account of its use in forwarding the cutting of the stones.

The most important use of the diamond is the cutting of glass. This is effected by a natural face of the crystal. If the edge be formed by the intersection of two artificial faces, the cut produced on the glass is not a true cut, but only a scratch with rugged edges. The natural faces of the diamond are frequently curved. The diamond may be heated intensely in an atmosphere of any gas except oxygen, but if it be suspended in a cage of platinum wire, and heated to a bright redness, and then plunged in a jar of that gas, it burns with a steady red light, producing carbonic acid gas (CO2).

It was reserved for Sir H. Davy to show that this gas was the sole product of the combustion of the diamond, though the fact that it was combustible was known in 1694 to the philosophers at Florence. The combustion, however, is not complete, as there always remains an ash, which is generally in the form of 2 cellular network-the skeleton, as it were, of the gem, and which consists of silica and the oxide of iron. With this excep tion the diamond is pure carbon. When submitted to the most intense of heats, that of the voltaic arch, the diamond loses its transparency, begins to swell, and is converted into a black mass resembling coke, the amorphous form of carbon. In this state it is a good conductor of electricity, a property it does not possess in its transparent condition.

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2. Graphite or Plumbago, erroneously called blacklead, is all but pure carbon, slight traces of iron generally being present. It is a crystallised body, belonging to the third or Rhombohedral system. The distinction between this and the first or regular system, in which the diamond crystallises, will be explained in a future chapter on crystallisation. It occurs in veins, always in rocks of the earliest formations. The most celebrated mine is that of Borrowdale, in Cumberland. Here it is found in "nests" in trap traversing clay slates. It is a good conductor of electricity, and is as difficult to burn as the diamond. It is chiefly used for manufacturing lead pencils. Being very friable, it leaves its particles on paper when passed across it. The particles themselves, however, are extremely hard, and soon wear out the saws with which the graphite is cut.

Formerly good pencils could only be made from lumps sufficiently large to permit of long pieces being cut. The small masses and dust were cemented together with sulphur, but by this the "marking" quality of the graphite was so injured that only the coarsest pencils could be made of it. But it has been discovered that by submitting this dust to enormous pressure it will cohere, forming plates fit for the manufacture of the best pencils.

Graphite is used for lubricating machinery, and also for making crucibles. For this purpose it is mixed with fire-clay. These crucibles are not so liable to crack as those made of clay only.

3. The third form of carbon has no appearance of crystallisation. It is therefore said to be "amorphous," or without form. This state is shown in coal, charcoal, soot, etc. Of the composition of coal we shall treat in the next chapter. Charcoal is got from the "destructive distillation" of wood-that is, the wood is heated in vessels of iron, closed so that no air can cause the carbon in the wood to burn. Of course there is a pipe to carry off the gases liberated by the heat. If blood or bones be submitted to this process, the result is animal charcoal.

Wood charcoal is also made by cutting the wood into logs, and arranging them on end, then covering the whole with sods, and setting fire to the heap at some central point. A portion of the wood is consumed, but the heat thus produced converts the remainder into charcoal. Charcoal is a bad conductor of heat and electricity. It is very porous, in virtue of which, like spongy platinum, it absorbs gases, the quantity varying with the nature of the gas. Thus, boxwood charcoal absorbs of

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This power is also shown in what are termed the antiseptic properties of charcoal-that is, the power it has of removing offensive smells. If putrefying meat or fish be packed in charcoal, all smell is removed; for the gases which cause the unpleasant effluvia are absorbed by the charcoal; and while in this state the oxygen, previously in its pores, attacks and changes the various gases, or oxidises the volatile organic matter. The process of putrefaction, however, is not arrested, but rather increased. This is often resorted to by unprincipled butchers and fishmongers who present tainted meat or fish for sale, which escapes detection for the moment by its inodorousness. Yet it possesses all the deleterious properties of unwholesome food. Charcoal, especially animal charcoal, clears coloured liquids which are passed through it. This may be well illustrated by shaking a little of it with a few ounces of port wine in a bottle, and then filtering the mixture; the liquid which passes the filter will be colourless.

Sugar is clarified by means of charred bullock's blood. After being in use for some time the charcoal is found to lose it

catch in the teeth of the escapement wheel, and allow it at each oscillation to move forward half a tooth, and then again stop it. The motion of the escapement wheel is thus at each stoppage transferred to the pendulum, and keeps it in vibration. A train of wheels connects this escapement with the hands.

We have thus acquired a general acquaintance with the more important facts of Mechanics. The subject is far from exhausted, but we must leave you to follow it up in works specially devoted to it. Our attention will now be turned to the other branches of Natural Philosophy, all of which are of great interest and importance. The next branch we shall take up is Hydrostatics, a science which has been claimed as a branch of mechanics, but is more accurately considered as a separate science.

LESSONS IN ENGLISH.-XXIV. CONVERSATIONS ON ENGLISH GRAMMAR.— III. William. The substance of our two conversations are pretty clear to me now.

Thomas. I am glad you have carefully studied them, but you have just committed a grammatical error. William. You do not say so? right.

Thomas. No, it would be wrong; "the fleet has sailed" is correct English. The true rule in this matter is this: Nouns of multitude require their verb to be in the plural when the mind dwells on the individual objects which they comprise; but when those objects are presented or contemplated as a whole, then the verb must be in the singular. In the phrase "the majority of us," the idea of plurality is made prominent, you of necessity think of several persons, therefore your verb must be in the plural; but in the phrase "the fleet has sailed," you conceive of the component parts as forming a whole, several elements coalesce into one, unity is the predominant feeling, and consequently you must employ a singular verb. I give you another instance: "The imprisonment of us is wrong." What say you to that?

William. It is correct.

Thomas. Yes, it is correct. Now do you not see the words "of us" hold in this sentence precisely the same relation or position that is held in the first sentence by the words "of our conversation?" Look at this arrangement

COMPOUND SUBJECT.

The imprisonment of us

PREDICATE.

Verb.
is

Attribute. wrong.

I fear I shall never get Us, you see, is not the nominative case (or, as I prefer putting it, is not the subject), for we, you know, is the nominaYou would not say tive, and us is in the objective case.

Thomas. Yes, you will get right by perseverance. The error into which you have fallen is a very common one; I have heard it even from the lips of persons who do not think themselves ignorant of grammar.

William. Wherein does it lie?

us are.

William. Oh, no, that would be ridiculous.
Thomas. And yet I heard a man, the other day, say we is;

Thomas. You have used a plural verb where you should have nay, I am not sure that you yourself-speaking, for example, of used a singular one.

William. But "conversations" is in the plural. Thomas. It is. That word, however, is not the subject to the verb of the sentence; it comes immediately before the verb,

and so has led you to put the verb into the plural, by a kind of latent attraction, against the influence of which I must put you on your guard.

William. What, then, is the subject?

Thomas. "Substance" is the subject, or what in common grammars is called the nominative case, and the sentence: should have stood thus: "The substance of our two conversations is pretty clear to me now." 'Substance," I repeat, is

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the subject. What is clear? You do not mean that the versations" are clear?

con

William. No; for there are some things in them that I do not quite comprehend; but they are clear on the whole.

Thomas. Yes, your language expressed your meaning correctly, although your grammar is at fault. This I have often observed in persons of defective education. Right in their logic, and having a good command of words, they are unable to put them together correctly, and so lose a large part of the advantage they ought to derive from their efforts at self-culture. Observe, now, "conversations" is dependent on the preposition "of." In the ordinary phraseology, it is governed by that preposition; and being governed by it, is in what is called the objective case-it cannot be the nominative, or the subject to the ensuing verb. In fact, the word "conversations" is a part of the compound subject of the sentence, as you may see exhi

bited thus:

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Thomas. I beg your pardon, it is quite correct.
William. How so?

Thomas. Because the word "majority" is what is called a noun of multitude-a noun, that is, which being singular in form, is plural in signification. In a majority, you know, there must be more than one. Now nouns of this kind, as they imply more than one, are constructed according to their sense, and not according to their form. Consequently, "majority" requires its verb to be in the plural.

Wild Then it would be right to say, "The fleet have cet consists of many ships.

the potatoes you might have had to-day for dinner-did not say, "they is good." What think you?

William. It is not impossible; these things are very perplexing.

practice will remove all difficulties. They have done so in my Thomas. Yes, at first they are troublesome; but study and

case, why not in yours?

William. Well, I am not going to yield.

Thomas. Certainly not. Bonaparte is reported to have said that the French had not such a word as "impossible" in their language. However this may be, you, as an Englishman, will not, I am sure, easily admit the idea into your mind, or the thing itself into your conduct. "Impossible?" No, nothing that is good and honest is impossible. What man has done, man may do. Now I must put you to rights in regard to this verb is and are; it is a word against which many, very many, persons sin grievously. Study this form :

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PAST TENSE.

I was.
Thou wast.
He was.

We were.

You were.
They were.

This surely is not very complicated, yet it contains all you need know in order to speak and write correctly, so far as this point is concerned. Take care, then, not to separate the pronouns from the proper forms of the verb. Take care not to mix together verbs and pronouns that should be kept apart. Do not take the first person I, and put it before the third person is. In other terms, 1 and i. must go together; 1 and iii. must not be combined. You must say we were (1 and i.), and not they was (iii. and 1). Before I conclude, let me impress it on your mind that you will never speak grammatically, or, at any rate, never be sure that you speak grammatically, unless you take the trouble to make yourself familiar with the terms and the laws of grammar. Many, finding the study somewhat difficult, after a little while give it up in a sort of confident spirit, thinking such drudgery beneath them, and fancying they can do all that is necessary by a sort of nondescript grammatical feeling. This is silly. Accurate knowledge is not obtained by genius, or inspiration, or any other fancied short cut to science. If you would know, you must condescend to learn, and all true learning demands, as it well rewards, diligent and constant

labour.

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