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PNEUMATICS.-V.

HEIGHT OF ATMOSPHERE-ELASTICITY OF AIR-BOYLE AND MARIOTTE'S LAW-MANOMETER-AIR-GUN-AIR-THERMO

METER-EXPANSION OF GASES BY HEAT-CO-EFFICIENT OF

EXPANSION.

We have now seen the most important effects of the weight and consequent pressure of the air, and also the means of measuring this pressure and its variations. The question, what is the true height of the atmosphere, is one which we cannot fully solve. Each succeeding layer of air which we meet in ascending is less dense than the one below it, and thus, theoretically, the limit to the height of the air is when the repulsive force exerted by its particles on each other is exactly balanced by the earth's attraction for those particles. We cannot calculate exactly at what height this would occur, but the question is of no great practical importance, and we may safely say that the limit of the atmosphere is about fifty miles above the surface of the earth. A few scientific men have, as a result of observations on the refractive power of the air as shown in its causing twilight, stated the limit to be much above this; but if any air does exist at a greater height, it is in a state of such rarity that it would scarcely be possible to prove its presence even by the most delicate tests.

We now pass on to notice the compressibility and elasticity of the air. As we saw in our first lesson, if any gas be confined in a vessel, it exerts a pressure against the sides altogether apart from its weight, and this pressure is exerted against the upper part of the vessel as well as upon the lower side. Now, this pressure arises from the elastic force of the gas, and depends alone upon its compression and temperature. If the volume occupied by it be in any way diminished, that is, if the same quantity of gas be made to occupy a smaller space, the pressure will be increased; or if the space occupied remain the same, and the temperature be raised, the pressure will also be increased.

Fig. 15.

We have, then, to investigate the proportion which this increase of pressure bears to the diminution of volume. That air is compressible to a very great extent, and that the pressure it exerts increases with the compression, is readily seen. Procure a stout glass or metal tube A, (Fig. 14), with a stopcock, B, let into it near the lower end, and a piston, c, fitting it air-tight. When the tap, B, is open, we can place the piston at any part of the tube, and the pressure on each side of it will be the same. If now we close the stopcock, the air within will be cut off from all communication with the external air, and therefore no pressure will be communicated to the under side of the piston from without; and yet it does not fall, though pressed upon by the air with a force of 15lbs. per square inch. The reason is that the elastic force of the confined air is sufficient to balance this pressure, and therefore the piston remains at rest. Were we to place the whole under the receiver of an air-pump, and thus diminish the internal pressure, we should find that the elastic force of the air within would overcome the diminished pressure, and cause the piston to rise. If now we increase the pressure, either by adding weights to the top of the piston or by pressing with the hand, we shall find an increasing resistance to our efforts. This arises from the increased tension of the air, and, if a weight has been placed on, we shall find that after sinking a little way the piston will come to rest, showing that the elastic force of the enclosed air is then equal to the pressure of 15lbs. per inch, and to the added weight in addition. Let another similar weight be now added to the piston, and it will sink still lower, though it will not move as much as it did before. In this way we shall find that by adding more weights we can compress the air to almost

VOL. IV.

any extent, the elastic force, however, increasing greatly. If we now remove the pressure the air will expand again, so as to fill exactly the same space as it did before, and the piston will stand just where it did at first.

A familiar example of this compressibility of the air is seen if we invert a tumbler over a piece of cork floating on the surface of water. The water will rise a little way inside the tumbler, just as it does in a diving-bell, unless a fresh supply of air is introduced from above by means of the force-pump.

Though the apparatus just described shows very clearly the fact of the compressibility of the air, and the consequent increase of its elastic pressure, yet it does not afford a very ready way of measuring exactly the alteration of volume, and a different plan has therefore been adopted by experimentalists on this point. The laws of this compression were studied at the same time in France by M. Mariotte, and in England by Mr. Boyle, and they both arrived at the same result, which is known as Boyle and Mariotte's law, and may be stated as follows:

Fig. 16.

A

The temperature remaining the same, the volume of a given quantity of gas varies inversely as the pressure which it bears.

Fig. 15 represents the apparatus which is usually employed in the proof of this, and which is known as Mariotte's tube. A long glass tube is sealed at one end, and bent round not far from this end, as shown in the figure. It is then fixed to a board, and a scale divided into inches and decimals of an inch is placed against each limb. Both these scales commence at exactly the same level, and a little mercury is first poured into the tube, so as to fill the bend and stand in each tube even with the lower end of the scale. This may with a little practice be easily accomplished. The air in the shorter leg is now exposed to the pressure of the atmosphere, which, for simplicity, we will suppose to be just equal to that of a column of mercury 30 inches high. Now pour mercury into the longer limb till it stands 30 inches higher than in the other limb; the air in this will then be compressed with double the force that it was before, and, by noticing the height on the scale, we shall find that it now occupies 10 divisions instead of 20-that is, under double the pressure it occupies half the space. Let a further quantity of mercury be now poured into the tube, till it stands in the long limb 60 inches above the height in the other, and again notice the space occupied by the confined air; we shall now find it to be 6 divisions, showing that with three times the pressure it occupies only one-third the space. Experiments have been carried on in this way till a pressure of nearly 30 atmospheres has been obtained, and this law is found to hold true with most gases. With some, however-as, for instance, carbonic acid-it is found that when very high pressures are attained they suffer rather more diminution in volume than this law points out, but the cause of this is believed to be that they are then approaching the degree of condensation at which they assume the liquid state. In fact, carbonic acid has been liquefied at a pressure of about 50 atmospheres. In conducting these experiments, allowance must be made for the increase of temperature in the gas caused by the condensation. It should, therefore, be allowed to cool to its original temperature before the measurement is taken. We may state, then, generally that the volume of a gas varies inversely as the pressure. The importance of knowing this is great, for, as the pressure of the air is continually changing, a given weight of any gas will occupy more space at one time than at another. Hence, in all experiments with gases, the pressure as shown by a barometer has to be noted. As we have already stated, 30 inches is taken as the standard height; if, then, we have an amount of any gas which occupies, say, 230 cubic inches when

Fig. 14.

81

the barometer stands at 28'90, we must find how much space it would occupy when the pressure is increased to 30 inches, and this we can easily do by the following equation:

As 30 28.90 :: 230: 221-56 cubic inches.

This, then, is the space which the gas would occupy when the barometer stands at 30.

=

When we speak of a pressure of so many atmospheres, it must be remembered that by an atmosphere is meant a pressure of 30 inches of mercury; and as a cubic inch of mercury weighs 0-491lb., the pressure on a square inch is 30 x 0.491lb. 14.73lbs. We can thus easily solve questions like the following:What is the pressure on a portion of the surface of a boiler measuring 3 inches each way, when the steam has a tension of 4 atmospheres ?

The pressure on each square inch is equal to the weight of 4 X 30, or 135 inches of mercury, and the surface has an area of 9 square inches; the total pressure, therefore, amounts to 135 x 9 x 0.491lb. 596-565lbs.

In many operations it is important to have some means of measuring the pressure exerted by a gas or vapour, and the instruments employed for this end are called manometers. In nearly all of these the pressure of the atmosphere is taken as the unit. The pressure-gauge of a steam-engine is merely one form of this instrument.

The most common manometer is that which acts by means of compressed air. It consists of a small vessel of mercury with a tube closed at the upper end dipping down into it. This vessel is so placed that the surface of the mercury is exposed to the pressure which we want to measure, and as this increases the mercury is forced up into the tube, compressing the air above it, and indicating the pressure by a scale marked at the side of the tube. The graduations on the scale are not equidistant, that marked 2 being at the middle, that marked 3 one-third of the height from the top, and so on. Sometimes, instead of a vessel of mercury there is merely a U shaped tube, with the bend filled with mercury and the open end connected with the boiler. It acts, however, in the same way.

If, instead of the pressure on any gas being greater than that of the air, it is less, the gas still expands in the same proportion. Thus, if one-half the pressure be removed it will fill twice the space. To prove this, a graduated tube is nearly filled with mercury, and inverted into a tubular vessel filled with the same liquid. It is first sunk so deep that the level of the mercury is the same inside as outside, and the volume of the contained air is carefully noted. The tube is now raised till the air has expanded to exactly double this volume, and the mercury in the tube will then be found to stand at just half the height of the barometer above that outside.

A simple experiment shows that if external pressure be removed air will expand forcibly. Procure a very shrivelled apple, and having placed it under the receiver of the pump, remove the air. The apple will expand, and look quite plump and fresh. If, however, you admit the air in order to remove and enjoy the apple, the pressure at once shrivels it up as before. In the same way, if one of the thin india-rubber balls frequently sold in the streets be nearly emptied of air and tied at the mouth, the little air left in will, when it is placed under the receiver, expand with sufficient force to distend the ball. So, too, if a hole be pricked in the large end of an egg, the bubble of air at the other end will expand sufficiently to drive out all the contents.

Several experiments may also be easily performed showing the large amount of elastic force which may be stored up in compressed air. The air-gun is, perhaps, the simplest illustration of this. In it the elastic force of the air takes the place of gunpowder, and propels the bullet with great velocity. A strong copper ball is made to screw on just below the lock of the gun. By means of a condensing syringe, air is powerfully compressed into this, and when the trigger falls it presses a pin, and thus opens a valve in the ball and allows a portion of the air to escape. This strikes the bullet, and imparts such velocity to it as to make it a very deadly missile. If the ball be well charged, the gun may be discharged from twelve to twenty times successively without condensing the air in it afresh; the power, however, diminishes slightly each time that it is fired, as the air becomes less dense.

This expansive force of compressed air is sometimes employed

in the construction of a fountain. A strong metal vessel is constructed, and a tube, dipping nearly to the bottom, is fitted tightly to its mouth. A stopcock is inserted in this tube, and a screw is also cut in the upper end of it. The vessel is then filled to about three-fourths of its height with water, and, by means of a condensing syringe screwed on to the pipe, the air within is powerfully compressed, the fresh air bubbling up through the water. The tap is then closed and the syringe removed, and when it is desired to start the fountain we have only to screw a jet on the tube, and on turning the tap the tension of the air will be such as to force the water through the jet with sufficient velocity to raise it to a considerable height.

The air, it must be remembered, does not create any force; it merely stores up the force exerted by the hand in working the syringe. It is, in fact, a reservoir of power, and in many instances it becomes of great service by its action in this way. In this case the air was condensed, and its elastic force thereby greatly increased; at ordinary pressures, however, it has quite enough elastic force to act in the same way if we allow the jet to play into a vacuum. There are two modes of showing this experiment.

If a small vessel, similar to that described above, be placed under a tall receiver, and the air rapidly removed, the effect will be seen. The simplest plan of making the vessel is to take a small flask with a tightly-fitting cork, through which is passed a glass tube, drawn to a jet at the upper end, and reaching nearly to the bottom of the flask. To show the experiment well, the receiver must be very rapidly exhausted, otherwise the air slowly expands, and merely causes the water to run slowly out of the jet. The plan usually adopted is to exhaust a second large receiver on another pump-plate, and so arrange the two that a connection may be made between them by opening a tap. The air is thus almost instantaneously rarefied to a considerable extent, and the experiment answers. The second plate in this description of pump is known as the transfer-plate, and is frequently found very convenient.

The other mode of exhibiting the experiment is rather simpler. A jet is screwed into the aperture of the pump-plate, and the pump is so constructed that the plate, together with a portion of the exhaust-pipe closed by a stopcock, may be removed without the admission of any air. The end of this tube is then plunged beneath the surface of water, and on opening the tap, the water will be forced up through the jet by the pressure of the air, and thus produce a very pretty fountain in vacuo.

Having seen the mode of ascertaining the alteration which is caused in the volume of any quantity of a gas by variation in the pressure, we have now to examine the effects produced by variations in the temperature. These variations are considerable; it is therefore necessary, in order to measure the exact quantity of a gas, to bring it to a standard temperature, and, as already stated, 60° has been fixed on as the most convenient. There is. however, often difficulty and loss of time in bringing a gas exactly to any temperature; we want, therefore, when we know the volume at any other temperature, to be able to calculate what it would be at 60°.

If we dip the neck of a retort beneath the surface of water. and apply heat to the bulb, we shall find a number of bubbles of air passing off through the water; and when the source of heat is removed and the air cools again, the water will rise in the neck of the retort to take the place of the displaced air. So, likewise, if we nearly fill a bladder with air, and, having tied the neck tightly, place it before the fire, the air in it will expand so as completely to distend, and perhaps burst the bladder. We see, then, that the air alters in its volume by a change of temperature.

This property of air is sometimes employed in the construction of a thermometer. Two forms of air-thermometer are represented in Fig. 16. In one, a straight glass tube, B, with a bulb blown at one end, is placed with its open end downwards in a vessel of coloured water, A. Heat is first applied to the bulb, c, greater than that which it is required to indicate; a portion of the air is thus driven out of the tube, B, and the water rises to replace it. The height at which this water stands depends upon the pressure of the air in the bulb, c, and as this varies with the temperature, the column serves as a thermometer. In the other form represented, the tube is turned up so that a small quantity of air may be included in the bulb, c, above the water, and this, as it expands or contracts by the heat, causes the water to

rise or fall in the limb, A B. Both are graduated by comparison | with a standard thermometer. These instruments are highly sensitive to slight changes of temperature; they are, however, affected by the height of the barometric column, and therefore a certain amount of uncertainty is introduced into their indications.

The law showing the relation between the temperature and the volume of any gas was discovered by Dalton, and has been checked by many philosophers since that date. It may be stated as follows:

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canis

auris finis hostis

oculus

ager, agri
grex, gregis
tutela

manus

merces

insula

culina

lax, lucis
pulmo

ocular

Saxon Nouns.

cow.
discase.
dog.

car.

end.

enemy.
eye.

held.
flock.

agrarian

gregarious

tutelary

guardianship.

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equus, or eques
domus

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vulgus
annulus (annus)
emulus

vulgar

annular

emulous

radical
regular

mens, mentis
pecunia

If any gas be allowed to expand freely under a constant pressure, its increase of volume when raised from 32° to 212° will caput, capitis be equal to 0-366 of its original volume, and this law of increase holds true in the same proportion for intermediate temperatures. Now, there are 180° between these two temperatures; the expansion for each degree is, therefore, of 0-366, or about 3 and this fraction is called the co-efficient of expansion. A gas, then, expands of its volume at 32° for each degree that it is raised above that point. This rule enables us to make the calculations we required, for 492 cubic inches at 32° will occupy 493 at 33°, 510 at 50°, 520 at 60°, and so on. Suppose, then, we have the following question:-A quantity of gas is measured at a temperature of 76°, and is found to occupy 427 cubic inches; what is its volume at 60°? We first find the proportion between the space a gas occupies at 60° and at 76°, and, as we have seen, 492 cubic inches at 32° will occupy 520 at 60°, and 536 at 76°. The volumes are therefore in the proportion | radix, radicis of 520 to 536, and the following rule of three sum will therefere give us the required volume :

As 536 520 427: 414.

luna
os (oris)

nasus

locus

visus

maritime

moon.
mouth.

nose.

place.
rabble.

a ring.

a rival. root. rule.

sea.

shepherd.
shoulder.

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pastoral

humeral

lateral

miles, militis

visual
military

sido.
sight.
soldier.

spring.

sun.

theft.

thigh.

tooth.

treaty.

Very often in chemical experiments corrections have to be latus, lateris made for pressure as well as for temperature. The process is, however, the same, and each correction may be made separately. The following examples will give the student good practice in the application of these rules:

EXAMPLES.

1. If the barometer stands at 29-04, what is the pressure of the air on a surface measuring 5in. x 6in.?

2. In Fig 15, if the length of the graduated portion of the shorter limb be 10 inches, and the mercury rise in it to a height of 5 inches, at what height does the mercury stand in the other limb, the barometer being at 29in. ?

3. A volume of gas measures 249 cubic inches when the barometer stands at 28-7. How much will it measure at the standard pressure? 4. Some gas at a temperature of 155° measures 1 cubic foot; how much space will it occupy when cooled to 609 ?

5. 140 cubic inches of air at 60° is heated till it occupies 215 cubic inches; what temperature has it attained?

6. When the barometer was standing at 28 78, and the thermometer at 71°, a quantity of gas was found to measure 158 cubic inches. How much would it occupy at the standard pressure and temperature?

LESSONS IN ENGLISH.-XXXVI.
LATIN STEMS (concluded).

SOME Latin stems supply us only in part with derivatives, giving,
for instance, the noun, and leaving the Saxon to furnish the
adjective; or giving the adjective, and leaving the Saxon to
furnish the noun.
Such a fact illustrates the composite cha-
racter of our present English tongue. If it be a token of perfec-
tion in a language that it is produced and evolved out of its own
elements like a tree, with its stem, branches, and leaves, the
English has little claim to perfection. But a perfection of this
kind is only theoretical. That is the best language which most
effectually answers the purpose of speech. Thus viewed, the
English possesses very high qualities. In virtue of the facts
just mentioned, examples of which I am about to append, the
English possesses a most desirable variety, which adds not only
to the colouring and polish of our style, but also to its capability

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ver

sol
furtum
femur, femoris
dens, dentis
fœdus, fœderis

vernal solar furtive femoral dental federal

The similarity which exists between the Latin and the corresponding English affords the student aid either to learn the words which are of Latin extraction found in English, or to become acquainted with the Latin vocabulary itself. Suppose, for instance, that you meet with the word lateral, and know, or, not knowing, ascertain, that it is a word of Latin origin which signifies that which pertains to the side. Having this information, you are enabled to remember that latus, the noun whence lateral comes, denotes the side. Or if you know that latus means the side, then you readily infer that lateral means that which pertains to the side. In this way, you may make the Latin roots with which you have become acquainted teach you the import of scores, nay, hundreds, of derivatives.

And observe, too, the specific service which the Latin element renders. We have the noun side, but we have no corresponding Saxon adjective. The want is supplied by the Latin.

In meaning, these nouns and adjectives do not always strictly correspond. Thus ager, field, and agrarian do not strictly correspond; I mean, you cannot infer the exact meaning of agrarian, for instance, from the meaning of ager. You are thus taught that it is an intelligent, not a slavish, study in which you are engaged. Rules are not chains, but guiding-posts.

Rule

Some of the words in the last lists, and in previous lists, which appear as Latin or Saxon, are not exclusively of Latin or Saxon origin. To wade, given as a derivative of vado, is a Saxon root, being common to both the Latin (Celtic) and the Saxon tongues., Waddle, a diminutive of wade, is also Saxon. and regula may be considered as the same werd in different forms; also oculus and eye; so insula and island; leo and lion; mens and mind. Similar facts abound in our language, and show that in order to know one language well you must study several, and that the proper way to study languages is to study them in their mother tongues-in the primitive groups or classes where they are found, and whence they shoot and branch.

I subjoin a list in which the richness of our language is still more exemplified :

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The diverse meanings of capillary and hairy suffice to prevent you from thinking that these pairs of adjectives-one from the Latin, one from the Saxon-are in each case identical in meaning. Frequently, however, that which is indicated by the one is that which the other signifies. When the two are of the same import, the one may be used for the other. To which of the two you should give the preference depends on circumstances. If you are addressing the people, you will do well to employ words of Saxon origin. Nor fancy that by so doing you lower your style. Simplicity in diction, like simplicity in dress, betokens real respectability. Write, because you have something to say; and if you have nothing to say, do not write; and if you write, write so as to be understood by those for whom you write; the best style is that which is most readily understood.

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THE LOVE OF KNOWLEDGE.

But while I am descanting so minutely upon the conduct of the understanding, and the best modes of acquiring knowledge, some men may be disposed to ask, "Why conduct my understanding with such endless care?-and what is the use of so much knowledge?" What is the use of so much knowledge ?-what is the use of so much life?-what are we to do with the seventy years of existence allotted to us?-and how are we to live them out to the last? I solemnly declare that, but for the love of knowledge, I should consider the life of the meanest hedger and ditcher as preferable to that of the greatest and richest man here present. For the fire of our minds is like the fire which the Persians burn in the mountains-it flames night and day, and is immortal and not to be quenched! Upon something it must act and feed-upon the pure spirit of knowledge, or upon the foul dregs of polluting passions. Therefore, when I say, in conducting your understanding, Love knowledge with a great love, with a vehement love, with a love coeval with life, what do I say but love innocence-love virtue-love purity of conduct-love that which, if you are rich and great, will sanctify the blind fortune which has made you so, and make men call it justice; love that which, if you are poor, will render your poverty respectable, and make the proudest feel it unjust to laugh at the meanness of your fortunes; love that which will comfort you, adorn you, and never quit you-which will open to you the kingdom of thought, and all the boundless regions of conception, as an asylum against the cruelty, the injustice, and the pain that may be your lot in the outer world; that which will make your motives habitually great and honourable, and light up in an instant a thousand noble disdains at the very thought of meanness and fraud! Therefore, if any young man here have embarked his life in the pursuit of knowledge, let him go on without doubting or fearing the event; let him not be intimidated by the cheerless beginnings of knowledge, by the darkness from which she springs, by the difficulties which hover around her, by the wretched habitations in which she dwells, by the want and sorrow which sometimes journey in her train; but let him ever follow her as the angel that guards him, and as the genius of his life. She will bring him out at last into the light of day, and exhibit him to the world comprehensive in acquirements, fertile in resources, rich in imagination, strong in reasoning, prudent and powerful above his fellows, in all the relations and in all the offices of life.-Sydney Smith.

LESSONS IN GEOGRAPHY.-XXXV.

CONSTRUCTION OF MAP OF AFRICA, ETC. THE projection for a map of Africa is constructed on a principle entirely different to that of the conical form of projec tion used for Europe and Asia. It will be seen, on reference to our map of the continent of Africa (Vol. III., p. 357), that this division of the world is pretty nearly bisected, as far as length is concerned, by the equator, the most northern point of the mainland being rather more than 37° north of the equator, while its most southern point is nearly 35° to the south of that line. Considering the equator, then, as the centre parallel of the parallels of latitude that traverse Africa, it is plain that a straight line supposed to pierce the sphere at 20° or 25° north and south of the equator, would be parallel to the axis of the sphere, and not inclined to

it, as in the case of straight lines piercing the sphere in two points, both of which are on the same side of the equator; and it is equally clear that a line entering the sphere and coming out of it again in such a manner as to be parallel to the axis of the sphere, would lie in the surface of a cylinder as in the annexed figure, and not in a cone. It is true that the projection of a map of Africa might be developed on the surface of a cylinder supposed to circum

scribe the sphere after the manner of the kind of projection called "Mercator's Projection," in which all the meridians and parallels are represented by straight lines at right angles to each other, and which peculiar mode of con struction will be explained in a future lesson. This style of projection, however, which is used in charts and nautical maps, is not so well suited for representations of very large areas of land, as the parts at the top and bottom-or, in other words, north and south of the map-are distorted, and larger in proportion than the central parts; and the mode of projection most generally adopted for a map of Africa is, in consequence, that which we are now going to describe.

The main features of this projection consist in tracing the | To do this, a diagonal scale must be constructed (as in the case of parallels in parallel straight lines, instead of representing projections for the maps of Europe and Asia) on the line assumed them by arcs of concentric circles as in the conical projec- at first as being equal to a space of five degrees of latitude. The tion, and by using curved lines for the meridians, instead of method of constructing this diagonal scale has been explained straight lines converging to a certain fixed point, as in the in Vol. II., page 356. We must now turn to the table of geoprojections for maps of Europe and Asia. graphical miles in a degree of longitude under each parallel of latitude (Vol. II., page 357), and from this we find that the length of a degree of longitude on the fifth parallel north or south of the equator is 59.77 geographical miles. Opening the compasses to this extent, as represented on our diagonal scale, set off distances along the fifth parallel of latitude north and south of the equator, on either side of the central meridian, as far as the border-line of the map will permit, and proceed in the same manner along each pair of parallels of latitude north and south of the equator, ascertaining the distance equivalent to five degrees of longitude under each parallel in question from the table already mentioned, and opening the compasses to the proper extent in each case by aid of the diagonal scale. The points thus found on each parallel will be those through which the meridians must be traced. This may be effected by drawing short straight lines from point to point in each successive parallel to the north and south, or by means of a thin band of steel, so bent that its edge may pass through every point marked for the passage of each meridian across the parallels. The border must now be completed, the degrees numbered, and the title of the map and scales of geographical and English miles inserted, after which the outline and different places may be fixed in position as before.

On examination of our map of Africa, to which reference has been made above, it will be seen that the meridian of 15° E. has been selected as the central meridian of the map, which crosses the equator at right angles, but which does not appear in the map itself. For this central meridian line our readers may select the meridian of 15° or 20°, as may appear most desirable. We shall, however, in the following description, take the meridian of 15° as the central meridian in our map, and supposing that the majority of our students who are following these lessons in Geography, and constructing maps from our instructions, are working on a large instead of a small scale-imagine meridians and parallels to be drawn intermediate to those which appear in our map, so that these lines would be but five degrees apart in our learner's projections, instead of ten degrees as in the map; that is to say, a parallel would be drawn at every fifth degree north and south of the equator, instead of every tenth degree, as in the map, and a meridian at every fifth degree east and west from the meridian of 15° east from Greenwich, which we have assumed as the meridian in our projection that crosses the equator at right angles, instead of marking in a meridian five degrees east and west of this central meridian, as in our map, and then drawing meridians ten degrees apart east and west, proceeding in each direction from the meridians that have been traced five degrees each way from the central meridian.

Having drawn two straight lines at right angles to each other, one to represent the equator and the other the meridian of 15° east from Greenwich, we must, in order to draw the parallels, first assume a space equal to five degrees of latitude, and set off eight of these spaces north and south of the equator along the central meridian. Through the points thus marked draw straight lines parallel to the equator on either side of it. Those on the north of it will represent the parallels of 5°, 10°, 15°, 20°, 25°, 30°, 35°, 40° north latitude; while those on the south of it will represent the parallels of 5°, 10°, 15°, 20°, 25°, 30°, 35°, 40° south latitude. If the learner wish to do so, he may delineate more of the southern part of Europe, as in our map, and more of the ocean to the south of Cape Colony, by setting off more spaces to the north and south of the equator; there is, however, no necessity for doing this, as it has been done in our map merely for the sake of filling up a given space, namely, that of a page of the POPULAR EDUCATOR. The parallels of 40° north and south will serve very well as the inner line of the border of the map at top and bottom, and define the limits of the map to the north and south. It will now be necessary to insert the dotted lines representing the Tropic of Cancer and the Tropic of Capricorn, which must be drawn parallel to the equator through points at the distance of 23° 30′ from it on either side of it, north and south.

In order to draw the meridians, because at the equator the degrees of longitude are equal in length to those of latitude, we must again open our compasses to the extent of the line assumed as equal to a space of five degrees of latitude, and set off eight of these spaces east and west, or right and left, of the central perpendicular line which represents the meridian of 15° E. from Greenwich. The points thus obtained will be those through which the meridians must pass at the equator; those on the right of the central meridian being points through which the meridians of 20°, 25°, 30°, 35°, 40°, 45°, 50°, 55° east from Greenwich will pass; while those to the left hand are those through which the meridians of 10°, 5° east from Greenwich, 0°, or the meridian of Greenwich itself, and 5°, 10°, 15°, 20°, 25° west from Greenwich will pass. The points through which the meridians of 55° east from Greenwich and 25° west from Greenwich pass may be taken as points through which to draw straight lines parallel to the central meridian, to form the limits of the

map to the east and west and the inner line of the border of the map on either side.

As the distance between each meridian decreases gradually from the equator to the poles, means must now be taken to determine the relative distance of every fifth meridian from the central meridian along each parallel drawn in our projection.

The following table will afford sufficient names for the construction of a map of Africa on a small scale. If a large scale be adopted, as we have advised, the latitudes and longitudes may be obtained from the index of places appended to any ordinary atlas. Our readers will often find that the latitude and longitude of a place according to one index will differ from the latitude and longitude assigned to the same place in another index. This arises in most cases from a difference in the results obtained at different times by independent observers, or some different point being selected by each for making the observation.

TABLE OF LATITUDES AND LONGITUDES OF PLACES IN
AFRICA.

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