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POPULAR EDUCATOR.

LESSONS IN CHEMISTRY.—I.

INTRODUCTION-ATTRACTION OF GRAVITY-FORCE OF COHESION-FORCE OF AFFINITY.

THE object of Chemistry is to ascertain the nature and properties of the substances of which our world is composed. Of late years, the curiosity of the chemist has penetrated beyond the tangible, and by the aid of the "spectrum analysis," of which in due time we hope to treat, a new chapter has been added to the science on "Stellar Chemistry," which gives some insight into the composition of the great centre of our solar system, and even of the distant stars. In pursuing his investigations, the chemist submits the bodies under his consideration to experiment: he operates upon them with various forces-heat, electricity, etc.-brings them within the action of re-agents, watches their behaviour in all circumstances, and never predicts a result, but determines all by experiment; hence chemistry is purely an experimental science.

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Seeing that we have to do with bodies, let us in this lesson dwell upon the forces which act upon substance," and which oppose or assist the chemist in his research. What is body? "That which has weight" is, perhaps, the least objectionable definition. Gases, although they are so intangible, and unlike anything solid, are yet bodies; they have weight. The weight of air on every square inch is 14.67 lbs., and when set in motion it becomes wind, which sways the trees, carries before it clouds of dust, or in the hurricane devastates a country, which it could not do if the air were imponderable. There are, however, existences present in the world which have no weight. Caloric, which produces the phenomenon of heat; electricity; ether, whose waves cause the sensation of light, and the different forces of attraction-these, not being "bodies," do not strictly come within the range of Chemistry: they rather belong to the domain of the physicist; but it will be necessary to speak of them, seeing they take such a prominent part in the decomposition and combination of bodies.

The forces of attraction, by which the particles of bodies are bound together, are the attraction of gravity, the attraction of cohesion, the attraction of adhesion, and the force of affinity. The attraction of gravity is that mysterious power by which the Creator has linked to each other the suns and worlds which occupy space; for he has ordained that all matter should exert an attractive force on all bodies in its neighbourhood. This force varies with the mass of the bodies and their distances from each other.' If a stone be dropped over the edge of a perpendicular cliff into the sea beneath, it will strike the rock before it reaches the water, because the cliff attracts the stone and draws it towards it. If, however, the stone be carried away from the cliff, the attractive force decreases. The power which made the stone fall was 66 gravity," that is, the attraction which the earth has for the stone; the force of that attraction we call its "weight." That this force decreases with the distance the stone is taken above the earth, is proved by the fact that the stone would weigh less on the top of a high mountain than in the valley beneath. Of course, to test this fact a spring balance must be used.

The force of cohesion, which has more claim upon our attention, differs from "gravity" chiefly in this, that "gravity" acts upon bodies at a distance, whereas the force of cohesion only begins to operate when the particles of matter are brought into the closest contact.

It is due to this force that bodies possess solidity, and it would seem that in liquids "cohesion" was very weak, and had no existence at all in gases.

If I file a piece of iron, the teeth of the file separate small

VOL. II.

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The

pieces of the metal from the rest; that is, I have applied a force which has overcome the power of cohesion, and therefore certain particles have been wrenched from their neighbours. Now I may collect the "filings," and submit them to the greatest pressure I can exert, but I cannot bring them back into their solid state; no pressure which we at present possess seems to be capable of bringing the particles sufficiently near to each other to allow the force of cohesion to come into play. But although particles of bodies are bound thus closely together, yet in no body do they seem to be in actual contact, for all solids are porous. Two hundred years ago this was proved in the case of gold by the "Florentine Experiment;" and if gold, which is almost the densest of metals, can be shown to be porous, we may well believe it of the rest. The "Florentine Experiment" is so celebrated that it demands recital. question was raised concerning the compressibility of water, and it was determined to try the experiment in the following manner :-A hollow sphere of gold was filled with that liquid; and seeing that a sphere is that solid which possesses the maximum capacity, any alteration in its shape would therefore lessen the quantity of water it could contain. The gold globe was accordingly slightly flattened, and the water oozed through the gold, appearing as dew on the outside. The Florentines, therefore, declared that water was not compressible-a conclusion they had no right to draw unless they could have collected the dew, and found that it exactly filled the space by which the pressure had diminished the capacity of the hollow sphere. Water has been proved to be slightly compressible, and the only use of the Florentine Experiment is to assert that gold is porous.

This truth, that the particles of bodies, in spite of the great force of cohesion, are not in actual contact, may be inferred from the fact, that all bodies contract when cooled, which they could not do if their particles were already in contact. Thus it would appear that the particles or molecules of bodies are under two forces-one attracting, the other repelling them; and that the state of the substance, whether it be solid, liquid, or gaseous, will depend upon the ratio which these two forces bear to each other. In the solid state the molecular attraction, or cohesion, is by far the stronger. In the liquid condition the repelling power almost balances the attractive; in a gas it entirely supersedes it, and the atoms are solely under the influence of "molecular repulsion." When the temperature of a body is raised, this molecular repulsion is always increased, each atom being repelled from its neighbour. The body expands, and at last the cohesion is so nearly overcome that the solid becomes a liquid. If the temperature still increase, the atoms are still further repelled, until they cease to have any attraction for each other, and the body becomes a gas. The molecular repulsion is so closely allied to caloric, the one is so intimately dependent upon the other, that they have been thought to be the same thing.

That the physical condition of a body entirely depends upon heat may be shown in almost all bodies. Ice becomes, when heated, water-then steam. Put a small piece of zinc in the flame of a blow-pipe: it first becomes red-hot, then melts, and finally goes away in vapour, which burns with a bright white flame, into the oxide of zinc. There is the strongest evidence that all bodies are capable of assuming these three states. Solids may be gases under certain circumstances; and gases, by sufficiently reducing their temperatures, may become, first liquids, then solids. In future lessons we shall find many examples of this interesting fact.

Adhesion is a force which binds two bodies together by means of some adhesive substance, such as gum, glue, etc.

The force of affinity. This is eminently a chemical force.

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But before it can be understood, we must explain what is met by an atɔin. Suppose we had the power of dividing a grain of iron an unlimited number of times, it is believed that at last a particle would be reached, which would defy all power ether to divide it, or change it in any way. This would be an com (unable to be divided). These ultimate and unchange-, able particles were formed at the creation, and they will exist unaltered until the Creator wills otherwise. We have no power to change or destroy them.

The most minute particle, which even the microscope can only just discern, may contain millions of these atoms, so that they are far beyond the reach of the recognition of our senses.

A molecule (a little mass) will bear a definite meaning in these pages-namely, the least particle which is capable of existing by itscif. In fact, it is the ultimate particle of a compound body. Thus, we shall find that water is composed of two atoms of! hydrogen and one atom of oxygen; hence the molecule of water would be a group of these three atoms.

Of the extreme minuteness of these atoms we may gain some idea, by the extent to which we can subdivide matter by mechanical means. If a bar of silver be gilded and then drawn out into a wire, the thread may be so fine that the gold covering one foot weighs less than of a grain; an inch of this wire will contain of a grain; this may be divided into 100 parts, each visible to the eye, and each being covered by rob of a grain of gold. Under a microscope magnifying 500 times, each of these pieces may be subdivided by the eye into 500 parts, the gold retaining its original appearance, and showing no signs of dividing into its separate atoms; and yet the particle visible to the eye, that which covers the upper part of the wire, is 2000 of a grain.

One hundred cubic inches of a solution of common salt will be rendered milky by adding to it a cube of silver, each side of which measures of an inch, dissolved in nitric acid. The atoms of silver have found their way into every particle of water, and there with the salt formed the white chloride of silver, which rendered the solution milky; that is, the small cube of metal has divided itself into at least 100 billion parts, a number which the seconds' pendulum of a clock would beat in 31,688 years! and even yet we are not sure that we have approached the measure of an atom of silver-we have only reached the limit of our own powers of subdivision.

Affinity is that force, in virtue of which two or more of these atoms combine to form a molecule of a compound body. This body exhibits properties very different from those possessed by the combining atoms, and is said to be a chemical compound, We say, then, that chemical composition takes place when two or more bodies so unite as to form a compound body, which differs in its properties from its components. For example, if we take a piece of chalk and put it in a glass of water, in due time it will become softened, and if we stir the water the chalk will render it milky, but no change has taken place, for if we let it stand the chalk will sink to the bottom, or if we evaporate the water we shall rover the chalk unaltered. But had we added a little nitric acid to the water, bubbles of gas would have ren to the surface, and the water would have become clear. Here a ch Las taken place. The chalk was compost of t and a gas called carbonic acid, held together by Pafcity;" but the nithe avid had a stronger affinity for the live then für sarbonio a id possessed, therefore it displaced the ma which came away in Mes, and with the lime formed the • Litrate of me,' which is soluble in water, hence the water became clear; and if we now evaporate, we shall find no longer chalk, but a transparent crystallised substance—the "nitrat of lime"-very different from either the lime or the nitric acid, of which it is composed. Here, then, chemical combination has taken place.

The observing read r will have gathered from this experiment that bodies differ in their affinities; some have strong inclination to combine with each other, while others exhibit little or no desire to do so. It is this fact which enables us to carry on chemical investigations. The difference between a mechanical mixture and a chemical combination is so important, that we select another illustration.

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we can easily separate them again by throwing the powder into water; the heavier, copper, will sink to the bottom first. But if we apply heat the whole will begin to glow, and a black substance will be the result, in which the microscope is unable to discern any copper, for another substance has been formed-the sulphide of copper-which is as different in its properties from sulphur and copper as they are from sand. The glow which passed over the mixture when heat was applied, is an example of a universal law-namely, that whenever chemical combination takes place heat is always developed.

In summing up this chapter, it appears that the three forces, gravity, cohesion, and affinity, act thus :

Gravity attracts masses of matter at any distance. Cohesion attracts particles generally of the same kind, and comes into play only at very limited distances.

Affinity attracts atoms of different substances, producing new bodies, and its action is infinitely more close and intimate than either of the two other forces.

LESSONS IN GREEK.-I.

INTRODUCTION.

THE Greek Language is the language of the Hellenes, or ancient Greeks. The ancient Greeks were early divided into three great races, each of which originally used a different dialect both in poetry and in prose. The Ionic dialect was spoken by the Ionic race in Asia Minor and in Attica, and latterly passed into the Attic dialect. The Eolic dialect was spoken by the Eolians in parts of Asia Minor, Boeotia, and Thessaly. The Doric dialect was spoken by the Dorians, chiefly in Northern Greece, in the Peloponnesus, as well as in Crete, Sicily, and Magna Græcia by the Dorian colonists. The Greek language and the Latin language form what are termed the classical languages. By the term classical languages we designate those languages in which are written the works which, in modern times, learned men have agreed to regard as classical; that is, works that stand in the first or highest class of the productions of the human mind. The Greek language is a branch of the great family of languages which, under the name of Indo-Germanic, is now known to have extended from Scandinavia to the Indus, embracing, as its two principal components, the Sanscrit, or ancient language of the Brahmins, on the East; and on the West, the Teutonic, including the German, the Dutch, and the English. It is thus seen that the Greek is allied to our own tongue. It is allied to the English in regard to structure. What is more obvious to the beginner is, that the Greek is allied to the English in words: thus, for example, our word one is the Greek év (hen); two is the Greek dvo (du-o); three is the Greek Tpes (trice). The English pronoun I is only an abbreviated form of the Greek eyw (5-0), which signifies I. Our verb know is the Greek ye (20) in the verb yiyvwokw, to know; the sound being identical, and the variation existing only in the letters. Many instances of identity between words in English and Greek will appear in the course of these instructions. At present, it is sufficient to state the general fact.

With the Latin the Greek is connected more intimately than with the English. So much in common have the two, both in words and in the inflection of words, that a knowledge of the one affords great assistance in the study of the other. In general, indeed, a thorough acquaintance with any one language condues s to the attainment of others. But here the relationship is so close that the aid is special. That aid may extend its operation to the whole class of languages known as the Indo-Germanic; so that those who become familiar with Greek thereby acquire facilities for studying not only Latin, but also Sanscrit, German, and English.

The Greek is a very old language. Homer's works go baca to nearly a thousand years before the birth of Christ, and at the time when they were produced the Greek language was already a settled tongue; and it must have existed and have been spoken by persons of no small culture for centuries. Under the name of the Romoic, the Greek language--a good deal modified-is still spoken and written, being the vernacular or native tongue of the modern Greeks, who are the descendants of the ancient Greeks, and dwell on the same soil.

The Greek language, as developed and perfected in its Attic form, is the richest and most perfect and philosophical language

in the world. No modern tongue, except the German, can endure a comparison with the Greek. The Greek language owes its superiority to the richness of its vocabulary, the variety of its inflections, its power of forming compounds, its expressiveness, its adaptability, and its harmony. It was said of old that if the gods were to descend to earth, they would speak the language of Plato, the famous Greek philosopher. The spirit of the saying is borne out by fact. The Greek is a wonderful and beautiful instrument of human thought.

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example, the word bronchitis. Now I have never studied medicine, yet, from my knowledge of Greek, I know that bronchitis is a disease whose seat is in the Spoyxia, (bron'-ki-a), that is, the extremity of the wind-pipe.

In proceeding to the study of Greek, you are stopped at the very threshold, for the characters of the letters are not the same as those of your native tongue. The diversity, however, is in appearance more than in reality. In fact, the English alphabet was derived from the Latin, and the Latin alphabet was derived from the Greek. It may be added, that the Greek letters can be traced back to the Phoenician. Thus we

But the study of Greek is worthy of attention, if only as a means of self-discipline. Self-discipline is the true end of education. Nothing better can be given to any mortal than a well-learn from this statement that the English and the Phoenician cultivated mind. The man whose faculties are in their highest state of development, and their greatest degree of activity and productiveness, stands at the summit of humanity, and now enjoys what he has reached, namely, the perfection of his earthly being. Pre-eminently fitted is the study of the Greek to educate our mental powers. All linguistical studies are useful for that purpose. Looking at their effects in their several bearings, I am free to declare that the study of languages is of all studies the most useful. But the Greek has the special recommendation of being more subject to rule than other languages. The Greek, too, deals with wider reaches of intellect and subtler distinctions of thought than most other tongues can comprise or define. But there is a recommendation of the study of Greek which throws all others into the shade, for in Greek are the Scriptures of the New Testament written. Strange is it that, in a Christian country, the records of salvation should be so little read in their originals. What a privilege is the power to do so! How much better are the teachings of the Apostle to the Gentiles understood, when the student applies his mind to the very words which fell from his lips or flowed from his pen! How much more easily, and how much more thoroughly, do we enter into the spirit, and feel at once the beauty and the power of the lessons of the Divine Master, when we have thrown aside the veil of a translation, and reverently with our own eyes look upon his sacred presence!

alphabets are related to each other. In the descent of the letters, however, from age to age, and in their passage from one people to another, they underwent considerable changes; so that, at least in some instances, it is only a practical eye that, by supplying the intermediate forms, can discover the identity. Yet scarcely is the difference in any case much greater than exists between what we call Old English or Black Letter, and the letters now employed in ordinary printing; or those you see when you compare a written with a printed composition. I have made these remarks in order not only to state an important fact, but to induce you to compare the forms of the Greek letters with the corresponding English forms. By so doing you will be much aided in becoming familiar with the Greek letters.

In connection with the study of theology, we may observe that the word "theology," and almost all our ecclesiastical and theological terms, are derived from the Greek. The English words bishop, baptism, atheist, liturgy, diocese, cathedral, with a host of others, are all drawn from the Greek.

While, however, the Greek language commends itself very specially to the attention of all who seek an acquaintance with Divine truth, and offers its aid for the general culture and improvement of human intelligence, it is not without a claim which, though more humble, may with some persons be more valid. That claim it lays before all who study or propose to study the sciences. Though some of the sciences existed not, even in rudiments, during the classical days of Aristotle, and though other sciences have been carried far beyond the boundaries where they were left by Euclid and by Galen, yet in general the language of science is Greek; for such is the readiness with which the Greek lends itself to combination, that the moment a new science is elaborated-nay, the moment a new fact is ascertained, or a new elementary substance is discovered -that moment some form or forms of words are produced from Greek elements, which exactly set forth the novelty. Hence these scientific names are so many definitions, and being definitions they describe the objects which they are used to designate; they, I say, describe those objects to such students as are familiar with Greek. Take photography as an instance. This word is made up of two Greek words, pws (phose), light, and ypapn (graph'-phoe), a painting, and so means light-painting; that is, a painting made by the solar rays. If the student will take the trouble of turning to the Greek stems as set forth in the lessons on the English language published in the POPULAR EDUCATOR, be will find many illustrations of the fact that, in English, Greek is the language of science.

medical men.

As the language of science, Greek is of special service to all men of science; in particular is it of great service to A vast number of the words with which they have to do in their studies are of Greek origin. Those words, to persons ignorant of the Greek tongue, are so many unknown terms, the meaning of which has to be learnt as a mere matter of routine; but to the proficient in Greek they define themselves, and so describe the objects which they represent. Take, as an

Characters.

Capitals.

Γ

Δ

THE GREEK ALPHABET.

English
Equivalents

Ιωτα.
Καππα.

Small
Letters.

in Sound.

Name in
English.

Name in

Greek.

a

a

Alpha

Αλφα.

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Λαμβδα.

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Tav.

Of these five columns the first gives the Greek letters in capitals; the second gives the same letters in small forms; the third gives the corresponding English letters, that is, the forms in English which have sounds similar to the several Greek letters; the fourth gives the Greek name of the letters; and the fifth gives the same name in Greek characters. The names, as they appear in the last column, are the designations which you are to assign to the Greek letters; that is, you are to call a not a, but alpha; B not b, but beta, and so on.

Before you can advance another step, you must make yourself thoroughly familiar with these characters-with their names and their values or sounds. In general, you may follow your ordinary English methods of pronunciation; one or two exceptions will be pointed out immediately. Your present business is to acquire a facility of transferring the Greek characters into corresponding English characters, and to read the former in the sounds of the latter. In the requisite application I advise you to employ a slate and pencil. Write the alphabet several times merely in Greek. Then compare together such Greek characters as resemble each other, and carefully mark wherein they differ. Having become familiar with the mere forms, associate with each its own name. Then study the sounds, that is, pronounce each Greek letter in the corresponding English sound. These

THROWERKER FOR HOst go over again and again, until you are perdemy master of the whole, and can from memory write down the plater, with all its forms and parts, as here given. I Lora Jos to take great pains in this matter, and not to pass en may have thoroughly accomplished this task. Your BIDATUMOR 10 Vola recommendation will save you a world of trouble. In the commencement, you will do well to confine yourself to the mulce character; having acquired them, you will readily make pref familiar with the capitals.

In the ental. characters, you will at once discover similarities terveen the Greek and the English forms. The Greek a and the Eagleh a are obviously the same. The English e and the koors e in ureek are very nearly alike. The two b's differ little. The two va are identical; so are the two o's (o short); and the meng's is nothing but two short o's (oo) put together. For ... notice, in the Greek, two forms of the small letter s. These two forma are o and 1. Of these, the first occurs at the regsung and in the body of a word; the second stands at the end of a word. This form of the sigma, namely, s, may also he seed in the middle of compound words, when the first of the world which the compound is formed ends in s: for example :Sigma at the end. Grants Myma, Sigma in Compounds. δρασμος δυσγενης

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Gamma, y, has the sound of n before y, K, X, ; thus, turns is pronounced gan'-ghees; σvукown is pronounced sunekut. Keyxpios, ken'-kri-os; and Aapuy, lar-unx.

Chi, x, ham a guttural sound, and so differs from kapра, к. The letter is never pronounced like our ch in church, but always In a way resembling our k in kite, kitchen, kick.

Over vowels, e in beta, i in epsilon, etc., this mark will be It is used to denote a long vowel. The force of it you may give by throwing the stress of the voice on the vowel Of syllable over which it is placed. Thus omicron is to be prowounded a mi krom. The opposite of is", as in omega; the mark denotona short syllable; accordingly, omega is pronounced Blum, o' meg at, with the stress on the o A vowel of doubtful length is marked thun *, as ď. When two vowels come together, the former is generally short, as IXtor, -lison. Diphthongs, howave, me long; that is, on them you must throw the stress, as autoru, dic's a no. Syllables are short or long, as they contain a short or long vowel. Syllables containing a diphthong are long. You may ascertain whether you have mastered the letters, by practising yourself in the following

EXERCISE FOR PRONUNCIATION.

NB. Every vowel in Greek, whether at the end of a word or not, is pronounced as a separate sylable.

Κα, κα, κη, κι, κο, κυ, κω. Γε, το, γη, γω, γα, για Xn, xa. Ta, TE, TO. Aε, on. Θη, θι, θεα, θητα. Πι, πω, πας. Baw κι, φέρω. Σα, σον, σιγη. φυγή, φύγω. Ματερ, μέλος. V. Γασης. Ζητα, ζητεω, ζήτησις; Ξανθος; Νυκτες; Χθων. Αλέξανδρος, Αυλις. Ωλην, Ωκεανος. Ωρωπος. Ψαύμις, YOUMETIXOS. Bias.

In, гλaukos, гopyn. Xapites, Xápiλaos. Φωκευς, Φωκίων, Φρύγες. Ύδρα, Ὑπάνις, Ύλλος. Δόλοψ, Διόνυσος, Διοσκουροι. Ερις. Ζακυνθος, Ζεύξις. HAEKтpa, Hyw, Hus. Κίμβροι. Λυδία, Λυσίας, Λοκρίς, Λακεδαίμων. Nikn. Μίνως, Ολυμπος. Πλαταια, Πιττάκος. Σαλαμις, Σακας, Σκυθία. Τιτάνες, Ρόδος, Ρωμη, Ρήγιον. Ξανθος.

You will find in the ensuing lessons these three marks or accents, namely, above the letter (or to the left of it in capitals), as in iva; under the letter, as in won; and above the letter, asin ots. The first is called the spiritus asper, or rough breathing, being equivalent to our aspirated h; pronounce, then, as with an Fyllables before which this aspirate is placed, as 'Adns, Hades. The second mark is called iota subscript (i underwritten), so termed because the letter i, instead of appearing at the end, as at, is written or placed under the was in Aoy: this monly disregarded in pronunciation. The third is mflex, being made up of the acute accent and from the union of which the circumflex is iumflex denotes a contraction, as in the

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In printed Greek books you will see several marks of accentuation over the letters. These I shall for the most part omit, as the study of them would embarrass the beginner, and as a knowledge of them is not necessary to either the understanding or the pronunciation of Greek. When you have mastered the real and inevitable difficulties of the language, you will readily acquire an acquaintance with these now almost useless signs.

LESSONS IN GEOGRAPHY.-XIV.

ASTRONOMICAL PRINCIPLES OF GEOGRAPHY.

SUPPOSE that you were elevated in the heavens, or in the vast space in which roll all the stars, to a point millions of miles above the sun; and that you were furnished with a telescopic eye so powerful, that from that point you could observe the magnitudes, motions, and distances of all the bodies in the Solar System-that is, the bodies or planets which revolve round the sun in consequence of the laws of attraction and tangential impulse-you would perceive among them a highly-favoured planet called the Earth, accompanied by a satellite (an attendant) in its course, called the Moon.

This earth and her satellite, like all the other planets and their satellites which you would behold in this bird's-eye view, receive both their light and their heat from the sun; the influences of light and heat being invariably distributed to all the planets in the same ratio as the power of attraction which keeps them revolving in their orbits (tracks or paths); that is, in the inverse ratio of the squares of their distances; or, to express it more clearly, the power of the attraction, the light and heat of the sun on one planet, is to that on another planet, as the square of the distance of the latter is to the square of the distance of the former.

In your elevated position you would next perceive that the planets, in their various revolutions, would at some times be nearer to the sun than at other times; and that if the orbit of each were traced by a white line in space, it would appear to your eye, if rightly placed, to have the form of an oval nearly, being in fact, what is called in mathematics, an ellipse.

In order that you may understand the nature of this curve, we shall explain it by means of a diagram. Thus, in Fig. 1, if you fix two pins on a board, at the points F and

A

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CM

D

Fig. 1.

B

F, and fasten a string F M F, of any convenient length, but greater than the distance between the two points, by its extre mities, at these points; and if you take s crayon or chalk pencil, and press it on the string horizontally at M, so as to keep it always tense (i.e. stretched), and parallel to the board, moving the pencil round and round at the same time, from one side to the other, you will describe the curve A C B D, which is called an ellipse. It is evident that the limits of the form of this curve are the circle and the straight line. If the two points F and F are brought close together, the curve will be a circle; if they be separated as much as the string will allow, the curve will become a straight line. The two points F and F' are called the foci (the plural of the Latin word focus) of the curve; the straight line A B drawn through them, and terminated both ways by the curve, is called the major aris; and the straight line C D drawn at right angles to this axis from its middle point o, and terminated both ways by the curve, is called its minor axis. If a straight line be drawn from r' to c, it will be equal to the straight line A o, or half the major axis. The point o is called the centre of the ellipse, and the ratio of Fo to A O-that is, of the distance between the centre and the focus to half the major axis-is called the ecces tricity of the ellipse. The distance from the focus F to any point M in the curve is called the radius vector of the ellipse; it is least at A, and greatest at B. With these explanations, while you are supposed to be looking at the orbit of a planet from your elevated position in space, you will now be able to com prehend the fundamental principles of Astronomy,-namely, Kepler's Laws.

The eminent German astronomer just mentioned, who flou rished at the close of the sixteenth century and the beginning of the seventeenth, discovered by laborious observations and calenlations, the following remarkable laws, which were afterwards mathematically demonstrated by Sir Isaac Newton:

1. That the planets all revolve in elliptic orbits, situated in

planes passing through the centre of the sun; the sun itself being placed in one of the foci of the ellipse.

2. That the radius vector, or straight line drawn from the centre of the sun to the centre of the planet, passes over equal areas in equal times in every part of the orbit; that is, whether the planet be in its aphelion, or farthest from the sun, in its perihelion, or nearest to the sun, or at its mean distance from

the sun.

3. That the squares of the periodic times of the planets-that is, of the times of a complete revolution in their orbits-are proportional to the cubes of their mean distances from the sun; in other words, that the square of the periodic time of one planet is to the square of the periodic time of another planet, as the cube of the mean distance of the former from the sun is to the cube of the mean distance of the latter from it.

Into the full explanation of these laws we cannot enter until we treat of astronomy; in the meantime it is necessary to give some explanation of the law which we have marked first, though it is generally accounted the second, in order to clear up some points connected with phenomena relating to the earth, and the circles drawn on the globe, which is the only true representation of the earth's surface. Supposing, then, the ellipse in Fig. 1 to represent the earth's annual orbit round the sun, and the focus the place of the sun's centre; then the point A will represent the position of the earth's centre at mid-winter, when it is nearest the sun, or in its perihelion; B will represent its position at mid-summer when it is farthest from the sun, or in its aphelion; c will represent its position at the spring or vernal equinox, when it is at its mean distance from the sun; and D its position at the harvest or autumnal equinox, when it is also at its mean distance from the sun.

hangeth the earth upon nothing" (Job xxvi. 7). This passage is singularly true in regard to the first sentence as well as to the second, for the axis of the earth is inclined to the plane of its orbit, at an angle of 66 degrees 32 minutes, that is, rather more than two-thirds of a right angle; so that literally and truly "the north is stretched over the empty place," and not over the body of the earth itself, in either of its motions, whether axial or orbitual. This inclination is preserved during the whole of its motion in its orbit, and is the cause of the variation of the seasons; the preservation of the inclination of this axis has been not inaptly called the parallelism of the earth's axis.

Fig. 2.

E F

Before explaining the effect of this parallelism and inclination of the earth's axis in producing the seasons, it will be proper to explain what is meant by tangential impulse. In Fig. 2, let A C B represent the orbit of the earth, which is nearly circular; let D represent the place of the sun, and a the place of the earth at the moment when it began its revolution in its orbit. At B this moment the force of the sun's attraction would begin to act on the earth in the direction A D, and had this alone been allowed to operate, would have drawn it rapidly towards the sun in a straight line, until it had come finally in contact with the sun itself; but at the same moment an original impulse was, or is supposed to have been given to the earth in the direction A E, which is that of a tangent, or straight line touching the circle at the point A; so that the earth, which under the action of the former force would in a certain time have been found at some point in A D, and under that of the latter force would, in the same time, have been found at the point F in A E, would, by the combined action of both forces, be found near the the effect of which remains to this day unaltered by the action of attraction (seeing it has met with no resistance in empty space, and has been so balanced against the force of attraction as to retain the earth in its orbit), is called the tangential impulse or force, which was imparted to it when it began its orbitual revolution. Young, in his "Night Thoughts," alluding to this tenet of the Newtonian philosophy, asks

We think we hear some of our readers exclaiming, notwith-point c in the curvilinear orbit A C B. This original impulse, standing the elevated position in which we have supposed them to be placed, "What! Will you tell us that the sun is the cause of light and heat on the earth's surface, and yet you assert that the earth is nearer to the sun in winter than in summer? How can this be ?" Paradoxical as this may seem, it is nevertheless true; and the reason we shall now give. As you are supposed to be looking from a great distance, and to be able to discern all the motions of the planets, if you look narrowly at the earth, you will perceive that besides its orbitual or annual motion round the sun, it has a revolving or diurnal motion on its own axis. By aris here is meant that imaginary straight line passing through the globe of the earth, on which its rotation is supposed to take place, and which is aptly represented in artificial globes by the strong wire passing from one side to the other, at the points called the poles (that is, pivots), which are the extremities of the axis.

This revolving motion on its own axis may be likened to the spinning of a top, a motion which continues while the top is driven forward in any direction from one place to another. In fact, the analogy would be so far complete independently of the causes of the motion, if the top, while it is spinning or revolving as it were on its own axis, were made to run regularly round in an oval ring on the ground, under the lash of the whip. Thus, the earth has two motions; one on its own axis, performed once every twenty-four hours; and one in its orbit, performed once every 365 days 6 hours. We have stated these periods in round numbers, in order that they may be easily remembered; but the exact period of the earth's daily revolution on its axis is 23 hours, 56 minutes, 4 seconds, and 9 hundredth parts of a second; and the exact period of the earth's annual revolution in its orbit is 365 days, 5 hours, 48 minutes, 49 seconds.

The analogy of the motions of the top, however, to the motions of the earth, as thus described, is incomplete in respect of the position of their axes. The axis of the spinning top is in general upright or perpendicular to the ground, which may be called the plane of its orbit, that is, of the oval ring in which it i3 supposed to move; but the axis of the earth in its daily motion is not perpendicular to the plane of its orbit, or the ellipse in which its annual motion is performed. In speaking of the plane of the earth's orbit our analogy fails, for there is nothing to represent the ground on which the motion of the spinning top takes place. The mere attraction of the sun, coupled with the effect of an original impulse in the direction of a tangent to its orbit, is sufficient to preserve the earth in its orbitual motion in empty space. Hence the sublimity and truth of the ancient passage in the book of Job: "He stretcheth out the north over the empty place, and

"Who rounded in his palm those spacious orbs ?
Who bowled them flaming through the dark profound ?"

Night IX.

Let us now consider the effect of the inclination of the earth's axis to the plane of its orbit. In Fig. 1 we have supposed the sun to be at the focus F', while the earth is at the point a in mid-winter. Now, at this point, you would see from your supposed elevated position, that the northern half of the earth's axis is inclined to the major axis A B at an angle of 113 degrees 28 minutes, the supplement of its angle of inclination to the plane of the orbit; so that the North Pole, with the space on the earth's surface around it to a considerable extent, is prevented from receiving the rays of the sun, and consequently the heat of those rays; while the South Pole, with the space around it to the same extent, is made to receive these rays and to enjoy their heat. Hence, while it is winter in the northern or arctic regions of the earth, it is summer in the southern or antarctic regions. While the earth is still in this position, the rays of the sun fall more obliquely upon the illuminated portions of the northern hemisphere than they do upon the southern hemisphere, and thus have less power to produce heat than if they fell perpendicularly; just as a person sitting at the side of a fire-place with a good fire in it, feels less heat than a person who sits exactly in the front of it.

On the other hand, if you consider the earth from your elevated position, when it is at the point B in mid-summer, the reverse of all this takes place. The northern half of the earth's axis is inclined to the major axis (or line of apsides, as it is sometimes called; that is, the line of junction of the two opposite points A and B) at an angle of 66 degrees 32 minutes, which is its angle of inclination to the plane of its orbit; so that the North Pole, with the space on the earth's surface around it, above-mentioned, is made to receive the sun's rays, and conse quently their heat; while the South Pole, with the similar space around it, is prevented from receiving those rays and enjoying their heat. Hence, while it is summer in the northern or arctic regions, it is winter in the southern or antarctic regions. While the earth remains in this position, the rays of the sun fall more directly upon the northern hemisphere than they do upon the

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