while commodity now signifies a thing, and has a strictly commercial import. The steps by which the derivation took place may be supplied from our older writers. Commodity is found signify. ing advantage; and as proportion, or due observance of measure, time, or opportunity leads to convenience, so does a regard to convenience conduce to advantage; but advantage is only interest or profit, and profit is by commodities, the sources of gain. Commodity as convenience :

"Travellers turn out of the highway, drawn either by the commodity of a footpath, or the delicacy or the freshness of the fields."-B. Jonson. Commodity as advantage :—

"They know that howsoever men may seek their own commodity, yet if this were done with injury unto others, it was not to be suffered." -Hooker.

Commodity as wares :—

"Of money in the commerce of mankind the principal use is that of saving the commutation of more bulky commodities.”—Arbuthnot, " On Coins."

Ule, as in globule, from the Latin globulus, a small globe or ball. The termination ule (in Latin both ulus and ula) is found in particule (Latin particula) shortened into particle. Animalcule, a little animal, is formed by analogy rather than authority, inasmuch as the only connected diminutive in Latin is animula, from anima, there being no diminutive from animal.

Ure, from the Latin ura; as, tinctura (a colour), tincture. It is found also in verdure (Latin, viridis, green), immediately from the French; and in tenure, from the word tenura, belonging to feudal or mediæval Latin.

Ute, from the Latin participial ending utus, as acutus (Latin, acu, a needle), sharpened, acute.

Ward appears in the German warts, as in vorwärts, forwards; and the Latin versus, towards. It forms many compounds, traces of which are found in the Anglo-Saxon, as thider-weard, thitherward; ham-ward, homeward. In the use of toward, the to and the ward were sometimes separated by the interposition of the noun under regimen, as in 1 Thess. i. 8"Your faith to God-ward is spread abroad."

Wise, from the Anglo-Saxon wise, manner, is used in both Anglo-Saxon and English as a suffix; as, rightwis, righteous, formerly rightwise; unrightwis, unrighteous. Wise, denoting manner, is found in the Bible.

"Now the birth of Jesus Christ was on this wise." (Matt. i. 18.) "If thou afflict them in any wise." (Exod. xxii. 23.)

Webster, in his dictionary, under wise, states that wise is corrupted into ways, as in lengthways. This position may be questioned. Way, signifying manner, is good English. Why, then, may we not say lengthways? The s is merely a terminating consonant for the voice to rest on, as in always. Good writers use longways no less than longwise. Sideways is more common than sidewise. For always, algates; and for otherwise, othergates (which are the same as our always and otherways; gates being from the German gehen, to go; and gasse, a street or way), are not uncommon in the north of England.

Y, a Saxon termination, in adjectives representing ig, as myrig, merry; wässerig, watery; and in nouns representing for the Latin ia, as victoria, victory; for the Greek, also, ia, as geometria, geometry. See the terminations ance and ce. In such words as yclept, that is, called; yclad, that is, clothed; the y is a softened sound of the German ge, which is prefixed to the past participles, as geboren, born.

Meaning.

result being personality condition effect

government habit

quality

discredit

condition

...

14 kin 15 let 16 ling

17 ness 18 ock

possession quality female diminution result agent condition family being sonship action division adherence place female sonship diminution descent result effect quality diminution greatness

19 ric

...

agency

condition

authority

20 ship

condition

From the above table it appears that there are 82 English suffixes, of which 7 are of Greek origin; 28 Latin; 8 French, and 39 Saxen.

It is of little consequence in general whether the suffixes ascribed to the French be ascribed to it or to the Latin, whence they originally came. If the eight French suffixes are added to the twenty-eight Latin ones, then the Latin suffixes are nearly equal to those of Saxon origin. Adding all the foreign suffixes together, we find they amount to forty-three, and so outnumber our native or Saxon suffixes.

The metals of the alkalies (K, Na, etc.) and of the alkaline earths (Ca, Sr, and Ba) have the power of decomposing water at ordinary temperatures. If a piece of potassium be thrown on water, the potassium takes the oxygen, forming potash, and the chemical action is so vigorous, that sufficient heat is developed to set fire to the escaping hydrogen. Care must be taken not to hold the face too near when the flame has ceased; for there remains a globule of potash, which is in a melted state, and when it cools down to such a temperature as to permit the water to come in contact with it, steam is generated in a large quantity, and the melted potash blown out of the water.

The following equation expresses the action :-
H2O+2K = K,0 + 2H.

The potash (K,O) is dissolved in the water, which then possesses the "greasy" feel of an alkaline liquid. It will "blue" red litmus paper, and convert oil poured into it into soap.

Fig. 22.

If sodium be used instead of potassium, the metal will melt into a globule, and run about on the water, being pushed by the atoms of hydrogen escaping from its under-surface; but the action is not violent enough to set fire to the gas. If, however, the water be thickened with starch, so as to increase the vigour of the action, the hydrogen will be lit. In this case soda (Na,O) and hydrogen are the products of the reaction.

To collect the gas in these cases, fill a test-tube with water, place the thumb over its end, and then invert it in a bowl of water. Wrap a small piece of the metal in paper, and quickly pass it under the mouth of the test-tube, which is, of course, beneath the surface of the water. The gas thus collected will exhibit the properties of hydrogen. To prepare this gas in large quantities, some iron turnings are placed in a porcelain tube, a b (Fig. 22), which passes through a charcoal furnace. Steam is generated in the flask, B, and as it passes over the red-hot iron it is deprived of its oxygen, which forms with the iron the same compound as was produced when the iron was burnt in oxygen (Fe,O,, the magnetic oxide): thus the action will be

3Fe+ 4H,O=Fe,0, +8H.

Zinc, tin, and some other less important metals, also have this power of decomposing water at a high temperature.

But the property which these metals likewise possess of decomposing water in the presence of an acid is taken advantage of in the laboratory for obtaining the gas. A "Woulff's bottle" with two necks-as is shown in Fig. 23-is used, or a bottle with one wide neck, into which a cork is fitted, pierced with two holes. The long tube with a funnel is a "safety tube," by which the acid is added; the other tube is the "delivery tube," from which the gas is conducted into a receiver, as in the case of oxygen.

On account of the lightness of the gas, it is frequently collected

by "displacement," as in this diagram. The hydrogen rises to the top of the jar, and displaces the air.

To prepare the experiment, some granulated zinc-which is obtained by pouring melted zinc into cold water-is placed in the bottle. Water is added, and

then sulphuric acid (1 part of the acid to 8 of water) gradually. Bubbles of the gas rapidly rise. Iron may be used; but it generally contains carbon, and the gas comes off mixed with some compound of carbon and hydrogen, and is rendered explosive. The action is thus represented:

Thus zinc sulphate (white vitriol) is formed, which is dissolved in the water. If the water be evaporated slowly, this salt crystallises out in white needles.

The decomposition of the water will be explained to be due to the agency of electricity. Hydrogen may also be set free from hydrochloric acid (HCl) and zinc: thus

Zn + 2HCl = ZnCl, + 2H, Fig. 23. forming zinc chloride and hydrogen. When hydrogen burns, it of course forms with the oxygen water. If into a jar full of hydrogen a burning taper be introduced, it will be extinguished; but the gas will burn with a pale yellow flame at the place where it meets the oxygen of the air. During the experiment the jar must be held mouth downwards, and the disc of yellow flame gradually passes up it.

The gas may be lit as it escapes from the generating jar. For this purpose the delivery tube must be drawn to a point. If over this flame a dry jar be held, the water formed in the combustion will be deposited as dew on the sides of the jar.

A singular property of the hydrogen flame may be shown by allowing it to burn in a tube of glass or metal: a musical note is produced; the explanation being, that the flame of hydrogen is in reality a series of rapid explosions, which cause the air in the tube to vibrate, thus producing the note.

In lighting the gas, the greatest care must be taken to allow sufficient time for all the air to be expelled from the bottle. Should there be any oxygen in it, the mixture will explode with great violence; and in all cases it is a safe preservative to wrap a damp cloth round the bottle, which will prevent the glass from flying, should there be an accident. To show the lightness of the gas, a balloon of gold-beater's skin may be fastened to the delivery tube, which will rise when it becomes filled. If the india-rubber balloons be used, it will be necessary to pass the

CuO + H, H2O + Cu.

The same experiment may be performed with iron filings. Iron has such a strong affinity for oxygen that it is never obtained in a pure state, save by this means. The filings will assume the colour of pure iron-dark blue; and when scattered out of the tube into the air, so rapidly do they combine with the oxygen again, that they become red-hot.

THE DIFFUSION OF GASES.

If oil and water and mercury be shaken in a bottle for any length of time, the moment the motion ceases the mercury will sink to the bottom and the oil rise to the top, but this is not the case with gases; if it were, our world would not be habitable. Take two flasks, and connect them by a small tube passing through the cork of each. Place them as in Fig. 25; fill the top one with hydrogen, and the other with carbonic acid-a very heavy gas-and it will be found that the gases mix, the carbonic acid rising, and the hydrogen falling.

Fig. 25.

H

This fact may be strikingly shown by plugging up the end of a long tube with a little plaster of Paris. Moisten the powder into a clay, and then place some in the end of the tube quickly, for it soon "sets." Now fill the tube with hydrogen, and stand it in a glass containing some coloured water, and the water will be found to rise in the tube, for the hydrogen passes out through the plug with greater rapidity than the air passes in; hence the water rises.

It has been discovered that the rate of diffusion of different gases is inversely proportional to the square root of their densities. Thus oxygen is 16 times heavier than hydrogen; the square root of 16 is 4, and that of 1 is 1: therefore hydrogen passes through the diaphragm 4 times faster than

oxygen.

As hydrogen is the lightest of all bodies, it is taken as the standard of the atomic weight, and if we know its weight we can always find that of any other gas; for the densities of all these elements, which can be got in the gaseous state, are identical with their atomic weights. There are, however, two notable exceptions to this law, phosphorus and arsenic, whose vapours have densities just twice their atomic weights. In the case of almost all compound gases, the density is half the combining weight.

The weight of a litre of hydrogen at 0° Cent. and 760 mm. [millimètres] pressure (the standard temperature and pressure) is 0-08936 grammes. Therefore at the same temperature and

pressure

273 volumes of gas at 0° Cent.

become 274 275

1o

"

20

"

"

If, therefore, we require to know what volume 500 litres of hydrogen at 50° would become at 120°, we ask what 273 litres do under the same circumstances. 273 would become 323 at 50°, and 493 at 120°: hence this proportion will give us the required volume :-As 323: 493: 500: the new volume; or

according to the formula: V1=V V (1

+

273++),

in which V

and V are the new and old volumes, t is the temperature of V, and n the number of degrees the temperature is altered. For Fahrenheit degrees the expansion will be of the volume at 32° for each degree. It is right to observe that this law is not absolutely accurate; yet it is sufficiently so for all practical purposes. The reader will note that the increment is a fraction of the volume at zero, and therefore an absolute quantity; if it were a fraction of the volume at any temperaIt will be evident from ture, the increment would be variable. the above that it is necessary to have a standard temperature, to which to reduce all gases, in order that they may be com pared under the same circumstances. The temperature of melting ice, or 0o Centigrade, has been fixed upon.

EFFECT OF PRESSURE ON THE VOLUME OF GASES.

Boyle, an English, and Mariotte, a French philosopher, discovered independently of each other the law which bears their name-Boyle and Mariotte's law-"The volume of a gas is inversely proportional to the pressure to which it is subjected."

If, for instance, a litre of gas supports a pressure of 1 kilogramme, and the pressure be increased to 2 kilogrammes, the volume will soon become a litre. The pressure generally exerted on gases is the weight of the atmosphere, which is measured by the barometer. If a glass tube, A B (Fig. 26), sealed at one end, and about one yard long, be filled with mercury, and then inverted into a vessel also containing that metal, the mercury in the tube will be found to fall, leaving a space, AC, of about six inches empty; this is called "Torricelli's vacuum." That is, the column of mercury in the tube is exactly the weight of a column of air its own size, to the top of the atmosphere. If from any cause the weight of the air alter, the mercury will rise or fall accordingly. The standard pressure of the atmosphere is in English 30 inches, in French 760 millimètres. If the tube were a square inch in surface, then 30 inches of mercury would weigh 14.67 lbs., or the pressure of the atmosphere on pressures are used, they are measured by every square inch is 14.67 lbs. When great atmospheres." For instance, we say a gas liquefies with a pressure of 35 atmospheres, which will equal 35 x 14.67= 513-45 lbs. on every square inch.

According to Boyle and Mariotte's law, whenever we want to find the alteration the volume of a gas undergoes by a change of pressure, we form with the new pressure and the standard pressure, 760 mm., a frac

tion. If the pressure be increased 760 must

B

Fig. 26.

be the numerator, if diminished the denominator, and by this fraction we multiply the original volume of the gas. For example: 500 litres of air are now under the pressure of 712 mm.; what would be their volume at the standard pressure? Here the pressure will be increased, hence the volume diminished; the fraction must therefore be less than unity.

In the following example the volume of a gas will be "corrected" for temperature and pressure:-

What weight of potassium chlorate will be required to fill a gas bag of a capacity of 20 litres, the temperature of the room being 15° Cent., and the pressure of the air at the same time 750 mm. ?

KCIO KCl + 0,

39'1+355 + 48 39°1 +355 +48;

or 122.6 parts by weight of KCIO, give off 48 of O, or 100 parts of the salt yield 39-2 of the gas. We know that the weight of a litre of oxygen at the standard temperature and pressure will be 16 x 0.08936 grammes=1.4298 grammes; therefore 20 litres will weigh 1-4298 x 20: 28.596 grammes. We must know first what volume 20 litres would occupy at the given temperature and pressure.

-

273 + 15

To correct for temperature we must multiply 20 by 273

273 x 750

760 and for pressure by ; or at one operation, 750 21.38 litres at 15° Cent. and 750 mm. The weight of the gas has not been altered, and therefore this 21.38 litres at 15° Cent. and 750 mm. weighs what it did when it was 20 litres at 0° and 760 mm., that is, 28-596 grammes. What, then, will 20 litres of this more rarefied gas weigh? This proportion will give the answer—

= 26.7 grains.

In some modes of applying force nearly all the muscles of the body are set to work, and the strain is distributed, while in

PRIME MOVERS-ANIMAL FORCE, WATER, WIND, STEAM. HAVING in our last lesson seen a few of the principal ways of transmitting and modifying motion, we will now notice the most important of the prime movers or causes of motion, and then pass on to Dynamics.

As already stated, no machine can create force, there must be some original source whence it proceeds; and on examination we shall find that nearly all sources of power may be divided into these four classes: muscular action, whether of men or animals; the force of water; the power of the wind; and the expansive power of gases or vapours. There are a few other prime movers, as electricity, heat, and chemical action; these, however, are not used at all in practice, but merely for the sake of experiment, their cost being at present too great to allow of their employment.

Muscular action, the first of our four kinds, is the one earliest employed and most frequently used, when no very great exertion is required. The reason of this is, that it can always be employed without previous arrangement, and can readily be applied in almost any way that may be needed; it is, however, one of the most uncertain of the prime movers, as it is both limited in its power and irregular in its action. The two divisions of it are, the force of men and that of animals. But before noticing these we must decide what unit of work we are to adopt. In our second lesson we saw that the unit of force is that which is required to cause a round ball, equal in weight to a cubic inch of water, to move through one foot in one second, and that this unit is equal to 7.85 grains. This is, however, far too small for practical purposes, and the unit of work which has been fixed on and universally adopted in this country in calculations like those we are about to make, is the force required to raise a weight of 1 pound through a space of 1 foot. We call this the unit of work, and not of force, as time is not taken into account. The same amount of work is done in raising 100 pounds to a height of 50 feet, whether a minute or an hour be occupied; the force required would, however, be much greater in the former than in the latter case. This unit of work is called a foot-pound. In the example just taken, 50 x 100, that is, 5,000 units or foot-pounds, are required to raise the weight. The same force would also raise 5,000 pounds 1 foot, or 5 pounds

boat is propelled by oars, the force exerted is applied very advantageously; nearly all the body helps, and the strain is in the most favourable direction. When the foot is firmly planted against the foot-board, the strong muscles of the back and thighs exert their force; the hands, too, pull in a direction nearly at right angles with the oars. Hence we find that the amount of work a man can accomplish this way is half as great again as he can by turning a winch.

advantage is gained is by ascending a ladder, and then allowing The mode of employing human power by which the greatest the weight of the body to act, and, by descending, raise a weight nearly equal to itself. An interval of rest is gained in this way while descending, and experience shows that more work can be accomplished if frequent short intervals of rest are thus taken between short periods of work. The body being specially framed for walking, nearly all the force expended is effective. When a large amount of heavy matter, such as building material, or earth for an embankment, has to be raised to a height, human power is sometimes thus applied:-A bucket in which a man can sit, or the material to be raised can be placed, is fixed at each end of a rope, which passes over a pulley fixed a little above the level to which the material has to be raised. The length of the rope is so adjusted, that when one bucket is on the ground, the other shall be at the required height. The lower bucket is then loaded, and one or more men ascend a ladder or incline and enter the upper one; their weight causes it to descend, and thus the material is raised. Nearly all the labour is thus expended in raising themselves to the top of the ladder, and while they are descending, and the material is being removed from the upper bucket, they have an interval of rest. In the treadmill the power is applied in a very similar way. consists essentially of a large and very broad wheel, with steps fixed all round it; the men hold on to a fixed bar, and attempt to ascend the steps. The wheel, however, turns with their weight as fast as they ascend, and thus they do not raise themselves at all; but still the principle is the same, and nearly as much effect is gained from the power in this way as in the former, the slight difference arising mainly from the fact that the intervals of rest are less frequent.

This

In some quarries the mineral is raised in a similar way, by men climbing on cross-pieces fixed through the rim of a very large wheel, round the axle of which the rope winds. This is an example of the employment of the wheel and axle; the power, however, does not act at the circumference of the large wheel, for the men are not on a level with the axle, but at a radius which varies with the weight to be raised.

To calculate the gain, we must imagine a vertical line to pass through the centre of gravity of the men; this line will meet the spoke which is horizontal in some point, and the distance of this

point from the centre is the radius at which the power really acts. Hence, when the weight to be raised is greater, the men are higher up on the wheel, and thus their weight acts at a greater leverage. Animal power is sometimes applied in a similar way, the animal being made to walk round the inside of a large cylinder, and thus to turn it.

The following table, which is the result of many experiments and calculations by different scientific men, shows approximately the effect produced by human power when employed in different ways, and gives us a good idea of their comparative efficacy. The average duration of the labour may be reckoned at eight hours per day.

UNITS OF WORK DONE BY A MAN IN A DAY.
Raising his own body

2,000,000 1,900,000 1,870,000

1,500,000

1,250,000

1,000,000 500,000

We now pass to the power of animals, which is much more frequently applied than that of man-it being found better to employ man where skill and thought, and not mere mechanical labour, are required; hence skilled labour is always more highly paid than unskilled. The animal most commonly employed in this country is the horse, and Watt estimated the amount of work it was capable of performing at 33,000 foot-pounds per minute. This amount was accordingly adopted as a unit of measurement, and is called a horse-power. Thus, when we speak of a steam-engine of 12 horse-power, we mean one capable of raising 12 times 33,000, which is 396,000 pounds, 1 foot high in 1 minute, or 1,000 pounds 396 feet, for each requires the same amount of power. Though this unit of measurement is still retained, it is more than a horse can accomplish continuously, and in practice its power is not found to be more than 22,000 units, or of the nominal amount. The power of a mule is about that of a horse, while that of an ass is only .

The most common way of employing animal power is in drawing or carrying a load, and it is clear that if this load be increased, the speed with which it is carried must be diminished. Hence it is an important question to decide at what rate of motion the greatest effect can be obtained, and the best way of determining this is by experiment. There are two extreme cases: the animal may sustain so heavy a load that it can scarcely move; or, on the other hand, it may travel very rapidly, but without being able to carry any load at all. The greatest effect is at some intermediate speed, and the weight that can be carried varies inversely as the speed. The useful effect is the product of the numbers which represent the speed and the load. Thus, if a horse can carry 12 hundred-weight 6 miles an hour, or 15 hundred-weight 5 miles an hour, it is most advantageous to let him take the heavier load, the useful effect then being 15 x 5, or 75, while in the other case it is 12×6, or 72 only. Now, it is found that the largest amount of work is done by giving such a load that the animal can travel about three miles an hour; if the speed be increased much beyond this, the weight must be diminished in a more than equal proportion.

The second prime mover is the force of water. Of this, how. ever, we shall treat more fully when we pass on to Hydrostatics, and need, therefore, say little now. We may have the force of a running stream, or that of the ebb and flow of the tide. The latter of these is a source of power very little used, but which might often be well employed. Water has always a tendency to obey the law of gravity and sink to the lowest point; in doing this it presses against or moves any obstacle that opposes its motion, and this pressure may in many different ways be employed to drive machinery. The simplest mode of applying it is seen in the common water-mill, where the stream presses against the floats of the wheel, and thus turns it.

We can calculate the force of a stream or waterfall by measuring the distance through which the water falls, and multiplying the weight of the water by this, we thus obtain the number of units of work it is capable of effecting. If, for instance, 1,000 gallons of water pass every minute, and the fall is 6 feet, then, since a gallon of water weighs 10 pounds, we have a moving force of 1,000 x 10 x 6, which is 60,000 footpounds. But even in the best modes of employing this, there is a very great loss.

The next of the prime movers is the force of the wind. Heat expands all substances; hence, when any place is greatly heated by the sun's rays, the air over it expands and rises, and cold air from around rushes in to fill its place. This air in motion is called wind, and produces the effects with which all are familiar. It acquires momentum as it travels, and when any object obstructs it, presses against the obstacle with a force proportional to its speed. This pressure produces the greatest effect when it acts in the direction in which motion is required, as, for instance, when a ship is propelled by a stern wind. The sails are spread as nearly as possible across the ship, and the full force of the wind drives it onward.

If the vanes of a windmill are arranged like the float of a paddle-wheel, so that the wind acts sideways on the wheel, no effect will be produced unless one-half of it is protected from the wind; for its action on those floats which are uppermost tends to turn the wheel one way with exactly the same force that its action on the lower ones does the other way. Even if the lower half be thus shielded the wind acts on those at the side very obliquely, and these keep it off from the vertical ones. Hence little effect can be gained in this way, and the vanes are always arranged so as to make a small angle with the plane in which they revolve, and it is found that most effect is produced when different parts of the vane have a different inclination, those nearest the centre being inclined at a greater angle than those more remote. Wo saw in our last lesson how in all such cases to ascertain what portion of the force of the wind is thus rendered effective.

The fourth, and in some respects the most important of the prime movers, is the expansive force of gases and vapours. The great advantage of this class is, that an almost unlimited amount of power may always be obtained, and that the cost is much less. Wind and water power often fail, but a steamengine, which is the most common example of this class of prime movers, can work as well at one time as another.

We cannot stop now to explain the details of the construction of an engine, but the principle on which it acts is simply this :— When water is heated to 212°, a portion of it is converted into an invisible vapour called steam; this occupies a space nearly 1,800 times as large as the water, and we have thus an expansive force which is utilised and converted into any kind of motion we may require. The usual plan of employing it is to procure a large cylinder, with a piston capable of moving up and down in it; the pressure of the steam is first caused to act below this piston, which it drives to the top of the cylinder; by an arrangement of the valves the steam is then caused to act above instead of below, and thus an alternating motion is produced from the pressure, and this is, by means of a crank, changed into one of rotation. If we have a piston with a surface of one square inch, the evaporation of a cubic inch of water will raise it 1,800 inches, or 150 feet. Now the pressure of the air on the piston is 15 pounds, and as this is overcome, the work done is 15 pounds raised 150 feet. This is 2,250 foot-pounds; or, to put it in a way more easy to remember, the evaporation of a cubic inch of water will produce force enough to raise a ton to a height of 1 foot.

Now this force is not created; something must be consumed in order to produce it, and this something is the fuel employed. A very important question, therefore, is to ascertain how much work ought to be accomplished by a given quantity of fuel. Of course this varies much with the construction of the furnace and boiler, but it is reckoned that a pound of good coal will, when employed in the best way, evaporate about 240 cubic inches of water, and therefore produce a force of about 540,000 foot-pounds.

The explosive force of gunpowder and similar explosive compounds come under this class of prime movers, though they are sometimes set down to chemical agency.

When they are ignited they set free a large amount of different gases, which occupy a space many hundred times greater than that of the substances themselves, and this sudden liberation gives rise to the violent effects we are accustomed to see produced by their employment.

We have thus seen what are the main moving forces, and are now prepared to enter fully on the study of Dynamics.

EXAMPLES.

1. How many units of work are required to raise 60 gallons of water to a height of 70 feet?

2. What power must an engine have to raise 20 tons of coal per hour from a mine 400 feet deep?