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processes you must go over again and again, until you are per- In printed Greek books you will see several marks of accen. fectly master of the whole, and can from memory write down tuation over the letters. These I shall for the most part omit, the alphabet, with all its forms and parts, as here given. I as the study of them would embarrass the beginner, and as a advise you to take great pains in this matter, and not to pass knowledge of them is not necessary to either the understanding on until you have thoroughly accomplished this task. Your or the pronunciation of Greek. When you have mastered the attention to this recommendation will save you a world of trouble. real and inevitable difficulties of the language, you will readily

In the commencement, you will do well to confine yourself to acquire an acquaintance with these now almost useless signs. the small characters ; having acquired them, you will readily make yourself familiar with the capitals. In the small characters, you will at once discover similarities

LESSONS IN GEOGRAPHY-XIV. betweon the Greek and the English forms. The Greek a and

ASTRONOMICAL PRINCIPLES OF GEOGRAPHY. the English a are obviously the same. The English e and the SUPPOSE that you were elevated in the heavens, or in the vast short e in Greek are very nearly alike. The two b's differ little. space in which roll all the stars, to a point millions of miles above The two i's are identical; so are the two o's (o short); and the the sun; and that you were furnished with a telescopic eye so Greek o long (w) is nothing but two short o's (00) put together. powerful, that from that point you could observe the magni.

You will notice, in the Greek, two forms of the small letter s. tudes, motions, and distances of all the bodies in the Solar These two forms are o and s. Of these, the first occurs at the System-that is, the bodies or planets which revolve round the beginning and in the body of a word; the second stands at

sun in consequence of the laws of attraction and tangential the end of a word. This form of the sigma, namely, s, may also impulse—you would perceive among them a highly-favoured be used in the middle of compound words, when the first of the planet called the Earth, accompanied by a satellite (an attend. words of which the compound is formed ends in 9: for example :- ant) in its course, called the Moon. Ordinary Sigma. Sigma at the end. Sigma in Compounds. This earth and her satellite, like all the other planets and δουλωσω δρασμος

δυογενης

their satellites which you would behold in this bird's-eye view, receive both their light and their heat from the sun; the in

fluences of light and heat being invariably distributed to all σεισμος

προσφερω

the planets in the same ratio as the power of attraction which Gamma, y, has the sound of n before y, k, X, &; thus, keeps them rovolving in their orbits (tracks or paths); that is, Farms is pronounced gan'-ghees; Ovykorn is pronounced sune'- in the inverse ratio of the squares of their distances ; or, to ko-pe; Keyxplos, ken'-kri-os; and napuug, lar-unx.

express it more clearly, the power of the attraction, the light Chi, x, has a guttural sound, and so differs from kappa, k. and heat of the sun on one planet, is to that on another planet, The letter x is never pronounced like our ch in church, but always as the square of the distance of the latter is to the square of in a way resembling our k in kite, kitchen, kick.

the distance of the former. Over vowels, e in bēta, i in epsilon, etc., this mark · will be In your elevated position you would next perceive that the observed. It is used to denote a long vowel. The force of it planets, in their various revolutions, would at some times be you may give by throwing the stress of the voice on the vowel nearer to the sun than at other times ; and that if the orbit of or syllable over which it is placed. Thus omicron is to be pro- each were traced by a white line in space, it would appear to your nounced o-mi'-kron. The opposite of : is ", as in omega; the eye, if rightly placed, to have the form of an oval nearly, being marko denotes a short syllable; accordingly, oméga is pronounced in fact, what is called in mathematics, an ellipse. thus, o'-meg-a, with the stress on the o. A vowel of doubtful In order that you may understand the nature of this curve, we length is marked thus , as ă. When two vowels come together, shall explain it by means of a diagram. Thus, in Fig. 1, if you the former is generally short, as IXžov, '-li-on. Diphthongs, how

fix two pins on a board, at the points F and ever, are long; that is, on them you must throw the stress, as

F', and fasten a string F M F, of any conavšavw, au'd-a-no. Syllables are short or long, as they contain a

venient length, but greater than the disshort or long vowel. Syllables containing a diphthong are long.

tance between the two points, by its extraYou may ascertain whether you have mastered the letters, by

mities, at these points ; and if you take a practising yourself in the following

crayon or chalk pencil, and press it on the

string horizontally at m, so as to keep it EXERCISE FOR PRONUNCIATION.

Fig. 1.

always tense (i.e. stretched), and parallel to N.B.-Every vowel in Greek, whether at the end of a word or

the board, moving the pencil round and not, is pronounced as a separate syllable.

round at the same time, from one side to the other, you will Kα, κε, κη, κι, κο, κυ, κω. Γε, γο, γη, γω, γα, γι.

describe the curve A CBD, which is called an ellipse. It is

Xn, xw. evident that the limits of the form of this curve are the circle Tα, τε, το.

Δε, δη.

Θη, θι, θεα, θητα. Πι, πω, πας. Ballw. and the straight line. If the two points F and F' are brought close νι, φερω. Σα, σον, σιγη. Φυγη, φυγω. Ματερ, μελος. Yo together, the curve will be a circle; if they be separated as much Γασηα. Ζητα, ζητεω, ζητησις; Ξανθος ; Νυκτες ; Χθων.

as the string will allow, the curve will become a straight line. The Αλεξανδρος, Αυλις. Ωλην, Ωκεανος. Ωρωπος. Ψαυμις,

two points F and F' are called the foci (the plural of the Latin Ψαμμετοχος. Βιας. Γη, Γλαυκος, Γοργη. Χαρίτες, Χάριλαος.

word focus) of the curve; the straight line A B drawn through

them, and terminated both ways by tho curve, is called the Φωκευς, Φωκίων, Φρυγες. “Υδρα, Μπάνις, Υλλος. Aloy, major aris; and the straight line c D drawn at right angles to Διονύσος, Διοσκουροι. Ερις. Ζακυνθος, Ζευξις. Ηλεκτρα, Ηχω, | this axis from its middle point o, and terminated both ways by Hws.

Κιμβροι. Λυδια, Λυσιας, Λοκρις, Λακεδαιμων. Nikn. the curve, is called its minor axis. If a straight line be drawn Μινως. Ολυμπος. Πλαταια, Πιττάκος. Σαλαμις, Σακας, Σκυθια. | from F' to c, it will be equal to the straight lino Ao, or half the Τιτάνες. Ροδος, Ρωμη, Ρηγιον. Ξανθος.

major axis. The point o is called the centre of the ellipse, and

the ratio of ro to A 0—that is, of the distance between the You will find in the ensuing lessons these three marks or centre and the focus to half the major axis-is called the eccen. accents, namely,' above the letter (or to the left of it in capitals), tricity of the ellipse. The distance from the focus F to any point as in iva; i under the letter, as in oon; and ^ above the letter, m in the curve is called the radius vector of the ellipse ; it is as in ous. The first is called the spiritus asper, or rough breathing, least at A, and greatest at B. With these explanations, while being equivalent to our aspirated h; pronounce, then, as with an you are supposed to be looking at the orbit of a planet from h syllables before which this aspirate is placed, as 'Adns, Hades. your elevated position in space, you will now be able to com. The second mark is called iota subscript (i underwritten), so prehend the fundamental principles of Astronomy,-namely, termed because the letter i, instead of appearing at the end, as Kepler's Laws. in noywi, is written or placed under the w as in noya: this The eminent German astronomer just mentioned, who filon. mark is commonly disregarded in pronunciation. The third is rished at the close of the sixteenth century and the beginning of called the circumflex, being made up of the acute accent' and the seventeenth, discovered by laborious observations and calcuthe grave accent', from the union of which “ the circumflex “is lations, the following remarkable laws, which were afterwards produced The circumflex denotes & contraction, as in the mathematically demonstrated by Sir Isaac Newton :diphthong ous, an ear,

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

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planes passing throngh the centre of the sun; the sun itself hangeth the earth upon nothing” (Job xxvi. 7). This passage being placed in one of the foci of the ellipse.

is singularly true in regard to the first sentence as well as to the 2. That the radius vector, or straight line drawn from the second, for the axis of the earth is inclined to the plane of its centre of the sun to the centre of the planet, passes over equal orbit, at an angle of 66 degrees 32 minutes, that is, rather areas in equal times in every part of the orbit; that is, whether more than two-thirds of a right angle; so that literally and truly the planet be in its aphelion, or farthest from the sun, in its “the north is stretched over the empty place,” and not over the perihelion, or nearest to the sun, or at its mean distance from body of the earth itself, in either of its motions, whether axial

or orbitual. This inclination is preserved during the whole of its 3. That the squares of the periodic times of the planets—that motion in its orbit, and is the cause of the variation of the is of the times of a complete revolution in their orbits-are pro- seasons; the preservation of the inclination of this axis has been portional to the cubes of their mean distances from the sun ; in not inaptly called the parallelism of the earth's axis. other words, that the square of the periodic time of one planet is Before explaining the effect of this parallelism and inclination to the square of the periodic time of another planet, as the cube of the earth's axis in producing the seasons, it will be proper to of the mean distance of the former from the sun is to the cube of explain what is meant by tangential impulse. In Fig. 2, let A C B the mean distance of the latter from it.

represent the orbit of the earth, which is nearly Into the full explanation of these laws we cannot enter until circular ; let D represent the place of the sun, ma trcat of astronomy; in the meantime it is necessary to give and a the place of the earth at the moment 2 houe explanation of the law which we have marked first, though when it began its revolution in its orbit. At B 1. His generally accounted the second, in order to clear up some this moment the force of the sun's attraction

points connected with phenomena relating to the earth, and the would begin to act on the earth in the direction ...croles drawn on the globe, which is the only true representation A D, and had this alone been allowed to ope

Fig. 2. of the earth's surface. Supposing, then, the ellipse in Fig. 1 to rate, would have drawn it rapidly towards the Depresent the earth's annual orbit round the sun, and the focus sun in a straight line, until it had come finally in contact with 1' the place of the sun's centre; then the point A will represent the sun itself; but at the same moment an original impulse the position of the earth's centre at mid-winter, when it is was, or is supposed to have been given to the earth in the direcberrest the sun, or in its perihelion ; B will represent its posi- tion A E, which is that of a tangent, or straight line touching

tion at mid-summer when it is farthest from the sun, or in its the circle at the point a; so that the earth, which under the 3. Siluelion ; C will represent its position at the spring or vernal action of the former force would in a certain time have been

squinOr, when it is at its mean distance from the sun; and d its found at some point in A D, and under that of the latter force position at the harvest or autumnal equinox, when it is also at would, in the same time, have been found at the point F in A E, its mean distance from the sun.

would, by the combined action of both forces, be found near the We think we hear some of our readers exclaiming, notwith point c in the curvilinear orbit A c B. This original impulse, tanding the elevated position in which we have supposed them the effect of which remains to this day unaltered by the action of o be placed, “What? Will you tell us that the sun is the cause attraction (seeing it has met with no resistance in empty space, I light and heat on the earth's surface, and yet you assert that and has been so balanced against the force of attraction as to be earth is nearer to the sun in winter than in summer? How retain the earth in its orbit), is called the tangential impulse or in this be ?" Paradoxical as this may seem, it is nevertheless force, which was imparted to it when it began its orbitual revose; and the reason we shall now give. As you are supposed lution. Young, in his “ Night Thoughts," alluding to this tenet be looking from a great distance, and to be able to discern of the Newtonian philosophy, asks I the motions of the

planets, if you look narrowly at the earth, “ Who rounded in his palm those spacious orbs ? Fill perceive that besides its orbitual or annual motion round Who bowled them framing through the dark profound ?" sun, it has a revolving or diurnal motion on its own axis.

Night IX. eris here is meant that imaginary straight line passing Let us now consider the effect of the inclination of the earth's wongh the globe of the earth, on which its rotation is supposed axis to the plane of its orbit. In Fig. 1 we have supposed the take place, and which is aptly represented in artificial globes sun to be at the focus F, while the earth is at the point A in the strong wire passing from one side to the other, at the mid-winter. Now, at this point, you would see from your sup. ats called the poles (that is, pivots), which are the extremities posed 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 This revolving motion on its own axis may be likened to the 28 minutes, the supplement of its angle of inclination to the aning of a top, a motion which continues while the top is plane of the orbit; so that the North Pole, with the space on Ren forward in any direction from one place to another. In the earth's surface around it to a considerable extent, is pre

the analogy would be so far complete independently of the vented from receiving the rays of the sun, and consequently the ses of the motion, if the top, while it is spinning or revolving heat of those rays; while the South Pole, with the space aronnd were on its own axis, were made to run regularly round in it to the same extent, is made to receive these rays and to enjoy oral ring on the ground, under the lash of the whip. Thus, their heat. Hence, while it is winter in the northern or arctic bearth has two motions ; one on its own axis, performed once regions of the earth, it is summer in the southern or antarctic

twenty-four hours; and one its orbit, performed once regions. While the earth is still in this position, the rays of

365 days 6 hours. We have stated these periods in round the sun fall more obliquely upon the illuminated portions of the abers, in order that they may be easily remembered; but northern hemisphere than they do upon the southern hemisphere, exact period of the earth's daily revolution on its axis is and thus have less power to produce heat than if they fell perboars, 56 minutos, 4 seconds, and 9 hundredth parts of a pendicularly; just as a person sitting at the side of a fire-place and; and the exact period of the earth's annual revolution in with a good fire in it, feels less heat than a person who sits bebit is 365 days, 5 hours, 48 minutes, 49 seconds.

exactly in the front of it. the analogy of the motions of the top, however, to the mo- On the other hand, if you consider the earth from your

of the earth, as thus described, is incomplete in respect of elevated position, when it is at the point B in mid-summer, the position of their axes. The axis of the spinning top is in reverse of all this takes place. The northern half of the earth's tral upright or perpendicular to the ground, which may be axis is inclined to the major axis (or line of apsides, as it is led the plane of its orbit, that is, of the oval ring in which it sometimes called ; that is, the line of junction of the two opposupposed to move; but the axis of the earth in its daily motion site points A and B) at an angle of 66 degrees 32 minutes, which let perpendicular to the plane of its orbit, or the ellipse in which is its angle of inclination to the plane of its orbit; so that the annual motion is performed. In speaking of the plane of the North Pole, with the space on the earth's surface around it, l's orbit our analogy fails, for there is nothing to represent above-mentioned, is made to receive the sun's rays, and conseground on which the motion of the spinning top takes place. quently their heat; while the South Pole, with the similar space incre attraction of the sun, coupled with the effect of an origi. around it, is prevented from receiving those rays and enjoying timpulse in the direction of a tangent to its orbit, is sufficient their heat. Hence, while it is summer in the northern or arctic perve the earth in its orbitual motion in empty space. Hence regions, it is winter in the southern or antarctic regions. While e sublimity and truth of the ancient passage in the book of the earth remains in this position, the rays of the sun fall more bo: " He stretcheth out the north over the empty place, and directly upon the northern hemisphere than they do upon the

the axis.

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20

100 + 2 = 102s.

12

southern hemisphere, and thus have more power to produce heat LESSONS IN ARITHMETIC.-XXIV. than if they fell obliquely, according to the illustration given above. Now, as we in this country are inhabitants of the 1. From the tables given in Lessons XXI., XXII., XXIII. (VoL northern hemisphere, and of that part which is within the circle I., pp. 366, 379, 304), it is evident that any compound quantity of illumination all the year round, we experience the vicissitudes could be expressed in a variety of ways, according as we use of the seasons just described as belonging to it, and we are con- one or other of the various units, or denominations, as they sequently colder in winter than in summer, although the earth are cailed, which are employed. Thus the compound quantity be actually noarer the sun in winter than in summer.

£2 3s. 6d. could be indicated as here written, or by 522 pence, But we must explain more fully what we mean by the circle or again, by 43 shillings, etc. The process of expressing a of illumination. It is plain that the rays of light falling from compound quantity given in any one denomination in another, the sun upon the opaque or dark body of the earth in straight is called reducing the quantity to a given denomination. The lines, can never illuminate more than one-half of its surface at a process is termed time; as may be seen by the very simple experiment of making

REDUCTION. the light of a candle fall upon a ball at a distance from it. Now, as the earth revolves on its axis once every 24 hours, it is

2. EXAMPLE 1.-Reduce £5 28. 77d. to farthings. evident that the illuminated half, and consequently the circle of

Since there are 20 shillings in a pound, in 5 pounds there aza illumination which is the boundary of that half, is perpetually 5 X 20, or 100 shillings; and therefore, in £5 28., 100 + 2, ar changing, so that almost all parts of the globe receive light for 102 shillings. Since there are 12 pence in a shilling, in 108 several hours in succession, and that they are also enveloped in shillings there are 102 X 12, or 1224 pence; and therefore, in darkness for several hours in the same manner. If the axis of £5 28.7d., 1224 + 7, or 1231 pence. Since there are the earth, instead of being inclined at a certain angle to the farthings in a penny, in 1231 pence there are 1231 x 4 plane of its orbit, which we shall hereafter call the Ecliptic, 4924 farthings; and therefore, in £5 28. 7.d. there are were at right angles to that plane, and preserved its parallelism, + 3, or 4927 farthings. then the circle of illumination would continually extend from The process may be thus arranged : polo to pole, and all places on the earth's surface would enjoy

£5 25. 70. light for 12 hours in succession, and would be enveloped in darkness for exactly the same period the whole year round.

On the other hand, if the axis of the earth were coincident with the plane, and preserved its parallelism, this would happen only twice a year; and each hemisphere would at opposite periods be in total darkness for a whole day, while the

1224 + 7 = 1231d. variations between these extremes would be both inconvenient and injurious. In the former case the seasons would be all the

4924 + 3 = 4927 farthings. same, that is, there would be perpetual sameness of season all the year round; in the latter case, the seasons, instead of being EXAMPLE 2.-In 4927 farthings how many pounds, shilling four only, would be innumerable, that is, there would be per pence, and farthings are there ? petual change.

4927 divided by 4 gives a quotient 1231, and a remainder 31 Here, then, creative wisdom shines unexpectedly forth. The hence 4927 farthings are 1231 ponce and 3 farthings. 1931 inclination of the earth's axis is such as to produce the four divided by 12 gives a quotient 102, and a remainder 7: bener seasons in a remarkable manner, and to permit sufficient time 1231 penco are 102 shillings and 7 pence.

102 divided by 2 for the earth to bring her fruits to perfection, as well to let her gives a quotient of 5, and a remainder 2; hence 102 shilling lie fallow for a period that she may renew her fruitfulness. are 5 pounds and 2 shillings. Therefore 4927 farthings

In Fig. 1, when the earth is supposed to be at the point c, she 1231 pence, which is 102s. 77d., which is £5 2s. 7d. is at her mean distance from the sun at the vernal equinox, which The operation may be thus arranged :is the first time of the year when day and night are equal, which happens on or about the 21st of March. Now, at this point the

4 ) 4927 inclination of the earth's axis to the minor axis of the ellipse is a right angle, and as the focus F', in the case of the earth,

12) 1231 ... St. nearly coincides with the centre o, the rays of light proceeding

20 ) 102 ...7d. from the sun nearly in the straight line o c, fall upon that axis nearly perpendioularly, and illuminate the globe from pole to

£5 28.730. pole, so that the circle of illumination passes through the poles, and the days and nights are equal all over the globe, each con- In dividing by 20, note the remark (Lesson VII., Art. 7). sisting of 12 hours, while the earth is in this position. In the The same method would apply to compound quantities of opposite position at D, the earth is again at her mean distance other kind. from the sun at the autumnal equinox, which is the second time Hence we get the following of the year when day and night are equal, which happens on or Rule for the Reduction of Compound Quantities. about the 22nd of September. At point the circumstances (1.) To reduce quantities in given denominations to equita of the globe and the circle of illumination are exactly the same quantities of lower denominations. as we have just described. At these four points, A, C, B, and D, Multiply the quantity of the highest denomination by in the orbit of the earth, are found the middle points of the four number which it takes of the next lower denomination to seasons of the year, viz., at A, mid-winter; at c, mid-spring; at one of the higher; and to the product add the number of B, mid-summer; and at d, mid-autumn. At the point A, or mid- tities of that lower denomination, if there are any. Proced winter, which is on or about the 21st of December, we have the like manner with the quantity thus obtained, and those c shortest day in the northern hemisphere and the longest day in successive denomination, until the required denominatin! the southern hemisphere; and at the point B, or mid-summer, arrived at. which is on or about the 22nd of June, we have the longest day (2.) To reduce quantities of given denominations to em in the northern hemisphere and the shortest in the southern lent quantities of higher denominations. hemisphere.

Divide the number of quantities of the given denomination de “ Thus is primeval prophecy fulfilled :

that number which it takes of quantities of this denomirano While earth continues, and the ground is tilled ;

to make one of the next higher. Proceed in the same man Spring time shall come, when seeds put in the soil

with this and each successive denomination, until the reques Shall yield in harvest full reward for toil ;

denomination is arrived at. The last quotient, with the set Heat follow cold, and fructify the ground,

remainders, will be the answer required.
Winter and summer in alternate round;
And night and day in close succession rise,

Obs.—It is manifest that the correctness of an operation was
While each is regulated by the skies.

formed in accordance with either of the foregoing rules mas Supreme o'er all, at first, Jehovah stood,

tested by reversing the operation—that is, by reducing And, with creative voice, pronounced it good."

result to the original denomination.

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planes passing through the centre of the sun; the sun itself hangeth the earth upon nothing” (Job uvi. 7). This passage being placed in one of the foci of the ellipse.

is singularly true in regard to the first sentence as well as to the 2. That the radius vector, or straight line drawn from the second, for the axis of the earth is inclined to the plane of its centre of the son to the centre of the planet, passes over equal orbit, at an angle of 66 degrees 32 minutes, that is, rather areas in equal times in every part of the orbit; that is, whether more than two-thirds of a right angle; so that literally and truly the planet be in its aphelion, or farthest from the sun, in its “the north is stretched over the empty place,” and not over the perihelion, or nearest to the sun, or at its mean distance from body of the earth itself, in either of its motions, whether axial the sun.

or orbitual. This inclination is preserved during the whole of its 3. That the squares of the periodic times of the planets—that motion in its orbit, and is the cause of the variation of the is, of the times of a complete revolution in their orbits--are pro- seasons; the preservation of the inclination of this axis has been portional to the cubes of their mean distances from the sun ; in not inaptly called the parallelism of the earth's axis. other words, that the square of the periodic time of one planet is Before explaining the effoct of this parallelism and inclination to the square of the periodic time of another planet, as the cube of the earth's axis in producing the seasons, it will be proper to of the mean distance of the former from the sun is to the cube of explain what is meant by tangential impulse. In Fig. 2, let AC B the mean distance of the latter from it.

represent the orbit of the earth, which is nearly Into the full explanation of these laws we cannot enter until circular ; let o represent the place of the sun, we treat of astronomy; in the meantime it is necessary to give and A the place of the earth at the moment come explanation of the law which we have marked first, though when it began its revolution in its orbit. At Bi it is generally accounted the second, in order to clear up some this moment the force of the sun's attraction points connected with phenomena relating to the earth, and the would begin to act on the earth in the direction circles drawn on the globe, which is the only true representation A D, and had this alone been allowed to ope

Fig. 2. of the earth's surface. Supposing, then, the ellipse in Fig. 1 to rate, would have drawn it rapidly towards the represent the earth's annual orbit round the sun, and the focus sun in a straight line, until it had come finally in contact with 1' the place of the sun's centre; then the point A will represent the sun itself; but at the same moment an original impulso the position of the earth's centre at mid-winter, when it is was, or is supposed to have been given to the earth in the direcnearest the sun, or in its perihelion ; B will represent its posi- tion A E, which is that of a tangent, or straight line touching tion at mid-summer when it is farthest from the sun, or in its the circle at the point a; so that the earth, which under the uphelion; c will represent its position at the spring or vernal action of the former force would in a certain time have been egninor, when it is at its mean distance from the sun; and p its found at some point in a D, and under that of the latter forco position at the harvest or autumnal equinox, when it is also at would, in the same time, have been found at the point F in A E, its mean distance from the sun.

would, by the combined action of both forces, be found near the 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 the effect of which remains to this day unaltered by the action of to be placed, “ What! Will you tell us that the sun is the cause attraction (seeing it has met with no resistance in empty space, of light and heat on the earth's surface, and yet you assert that and has been so balanced against the force of attraction as to the earth is nearer to the sun in winter than in summer? How retain the earth in its orbit), is called the tangential impulse or can this be ?” Paradoxical as this may seem, it is nevertheless force, which was imparted to it when it began its orbitual revo. true; and the reason we shall now give. As you are supposed lution. Young, in his “Night Thoughts," alluding to this tenet to be looking from a great distance, and to be able to discern of the Newtonian philosophy, asksall the motions of the planets, if you look narrowly at the earth, “ Who rounded in his palm those spacious orbs ? son will perceive that besides its orbitual or annual motion round Who bowled them framing through the dark profound ?" the sun, it has a revolving or diurnal motion on its own axis.

Night IX. By aris here is meant that imaginary straight line passing Let us now consider the effect of the inclination of the earth's through the globe of the earth, on which its rotation is supposed axis to the plane of its orbit. In Fig. 1 we have supposed the to take place, and which is aptly represented in artificial globes sun to be at the focus F', while the earth is at the point A in by the strong wire passing from one side to the other, at the mid-winter. Now, at this point, you would see from your suproints called the poles (that is, pivots), which are the extremities posed elevated position, that the northern half of the earth's of the axis.

axis is inclined to the major axis A B at an angle of 113 degrees This revolving motion on its own axis may be likened to the 28 minutes, the supplement of its angle of inclination to the spinning of a top, a motion which continues while the top is plane of the orbit; so that the North Pole, with the space on driven forward in any direction from one place to another. In the earth's surface around it to a considerable extent, is prefact, the analogy would be so far complete independently of the vented from receiving the rays of the sun, and consequently the causes of the motion, if the top, while it is spinning or revolving heat of those rays; while the South Pole, with the space around as it were on its own axis, were made to run regularly round in it to the same extent, is made to receive these rays and to enjoy an oval ring on the ground, under the lash of the whip. Thus, their heat. Hence, while it is winter in the northern or arctic the earth has two motions ; one on its own axis, performed once regions of the earth, it is summer in the southern or antarctic every twenty-four hours; and one in its orbit, performed once regions. While the earth is still in this position, the rays of every 365 days 6 hours. We have stated these periods in round the sun fall more obliquely upon the illuminated portions of the aumbers, in order that they may be easily remembered; but northern hemisphere than they do upon the sonthern hemisphere, the exact period of the earth's daily revolution on its axis is and

thus have less power to produce heat than if they fell per 23 hours, 56 minutos, 4 seconds, and 9 hundredth parts of a pendicularly; just as a person sitting at the side of a fire-place second ; and the exact period of the earth's annual revolution in with

a good fire in it, feels less heat than a person who sits its orbit is 365 days, 5 hours, 48 minutes, 49 seconds.

exactly in the front of it. The analogy of the motions of the top, however, to the mo- On the other hand, if you consider the earth from your tions of the carth, as thus described, is incomplete in respect of elevated position, when it is at the point B in mid-summer, the the position of their axes. The axis of the spinning top is in reverse of all this takes place. The northern half of the earth's general upright or perpendicular to the ground, which may be axis is inclined to the major axis (or line of apsides, as it is called the plane of its orbit, that is, of the oval ring in which it sometimes called ; that is, the line of junction of the two oppois supposed to move; but the axis of the earth in its daily motion site points A and B) at an angle of 66 degrees 32 minutes, which is not perpendicular to the plane of its orbit, or the ellipse in which is its angle of inclination to the plane of its orbit ; so that the its annnal motion is performed. In speaking of the plane of the North Pole, with the space on the earth's surface around it, rarth's orbit our analogy fails, for there is nothing to represent above-mentioned, is made to receive the sun's rays, and consethe ground on which the motion of the spinning top takes place. quently their heat; while the South Pole, with the similar space The mere attraction of the sun, conpled with the effect of an origi. around it, is prevented from receiving those rays and enjoying nal impulse in the direction of a tangent to its orbit, is sufficient their heat. Hence, while it is summer in the northern or arctic to preserve the earth in its orbitual motion in empty space. Hence regions, it is winter in the southern or antarctic regions. While the sublimity and truth of the ancient passage in the book of the earth remains in this position, the rays of the sun fall more Job: " He stretcheth out the north over the empty place, and directly upon the northern hemisphere than they do apon the

522 pence,

20

12

4

southern hemisphere, and thus have more power to produce heat LESSONS IN ARITHMETIC.-XXIV, than if they fell obliquely, according to the illustration given above. Now, as we in this country are inhabitants of the 1. From the tables given in Lessons XXI., XXII., XXIII. (VOL northern hemisphere, and of that part which is within the circle I., pp. 366, 379, 304), it is evident that any compound quantity of illumination all the year round, we experience the vicissitudes could be expressed in a variety of ways, according as we use of the seasons just described as belonging to it, and we are con- ono or other of the various units, or denominations, as they sequently colder in winter than in summer, although the earth are called, which are employed. Thus the compound quantity be actually nearer the sun in winter than in summer.

£2 3s. 6d. could be indicated as here written, or But we must explain more fully what we mean by the circle or again, by 43) shillings, etc. The process of expressing & of iUumination. It is plain that the rays of light falling from compound quantity given in any one denomination in another, the sun upon the opaque or dark body of the earth in straight is called reducing the quantity to a given denomination. The lines, can never illuminate more than one-half of its surface at a process is termed time; as may be seen by the very simple experiment of making

REDUCTION. the light of a candle fall upon a ball at a distance from it. Now, as the earth revolves on its axis once every 24 hours, it is

2. EXAMPLE 1.-Reduce £5 25. 77d. to farthings. evident that the illuminated half, and consequently the circle of

Since there are 20 shillings in a pound, in 5 pounds there are illumination which is the boundary of that half, is perpetually 5 X 20, or 100 shillings; and therefore, in £5 2s., 100 + 2, or changing, so that almost all parts of the globe receive light for 102 shillings. Since there are 12 ponce in a shilling, in 102 several hours in succession, and that they are also enveloped in shillings there are 102 X 12, or 1224 pence; and therefore, in darkness for several hours in the same manner. If the axis of £5 28. 7d., 1224 + 7, or 1231 pence. Since there are 4 the earth, instead of being inclined at a certain angle to the farthings in a penny, in 1231 pence there are 1231 x 4, or plane of its orbit, which we shall hereafter call the Ecliptic, 4924 farthings; and therefore, in £5 28. 79d. there are 4924 were at right angles to that plane, and preserved its parallelism, 1 + 3, or 4927 farthings. then the circle of illumination would continually extend from The process may be thus arranged: pole to pole, and all places on the earth's surface would enjoy

£5 28.740. light for 12 hours in succession, and would be enveloped in darknoss for exactly the same period the whole year round. On the other hand, if the axis of the earth were coincident

100 + 2 = 1028. with the plane, and preserved its parallelism, this would happen only twice a year; and each hemisphere would at opposite periods be in total darknoss for a whole day, while the

1224 + 7 = 1231d. variations between these extremes would be both inconvenient and injurious. In the former case the seasons would be all the

4924 + 3 = 4927 farthings. same, that is, there would be perpetual sameness of season all the year round; in the latter case, the seasons, instead of being EXAMPLE 2.-In 4927 farthings how many pounds, shillings, four only, would be innumerable, that is, there would be per- pence, and farthings are there? petual change.

4927 divided by 4 gives a quotient 1231, and a remainder 3; Here, thon, creative wisdom shines unexpectedly forth. The hence 4927 farthings are 1231 pence and 3 farthings. 1231 inclination of the earth's axis is such as to produce the four divided by 12 gives a quotient 102, and a remainder 7; hence seasons in a remarkable manner, and to permit sufficient time 1231 pence are 102 shillings and 7 pence. 102 divided by 20 for the earth to bring her fruits to perfection, as well to let her gives a quotient of 5, and a remainder 2; hence 102 shillings lie fallow for a period that she may renew her fruitfulness. are 5 pounds and 2 shillings. Therefore 4927 farthings are

In Fig. 1, when the earth is supposed to be at the point c, she 12314 pence, which is 102s. 77d., which is £5 2s. 7 d. is at her mean distance from the sun at the vernal equinox, which The operation may be thus arranged :is the first time of the year when day and night are equal, which happens on or about the 21st of March. Now, at this point the

4 ) 4927 inclination of the earth's axis to the minor axis of the ellipse is a right angle, and as the focus F', in the case of the earth,

12 ) 1231 ... 3. nearly coincides with the centre o, the rays of light proceeding

20 ) 102...70. from the sun nearly in the straight line o c, fall upon that axis nearly perpendicularly, and illuminate the globe from pole to

£5 28. 7fd. pole, so that the circle of illumination passes through the poles, and the days and nights are equal all over the globe, each con- In dividing by 20, note the remark (Lesson VII., Art. 7). sisting of 12 hours, while the earth is in this position. In the The same method would apply to compound quantities of any opposito position at D, the earth is again at her mean distance other kind. from the sun at the autumnal equinox, which is the second time Hence we get the following of the year when day and night are equal, which happens on or Rule for the Reduction of Compound Quantities. about the 22nd of September. At this point the circumstances (1.) To reduce quantities in given denominations to equivalent of the globe and the circle of illumination are exactly the same quantities of lower denominations. as we have just described. At these four points, A, C, B, and D, Multiply the quantity of the highest denomination by that in the orbit of the earth, are found the middle points of the four number which it takes of the next lower denomination to make seasons of the year, viz., at A, mid-winter; at c, mid-spring; at one of the higher; and to the product add the number of quan B, mid-summor; and at d, mid-autumn. At the point A, or mid- tities of that lower denomination, if there are any. Proceed in winter, which is on or about the 21st of December, we have the like manner with the quantity thus obtained, and those of each shortest day in the northern hemisphere and the longest day in successive denomination, until the required denomination is the southern hemisphere; and at the point B, or mid-summer, arrived at. which is on or about the 22nd of June, we have the longest day (2.) To reduce quantities of given denominations to equira in the northern hemisphere and the shortest in the southern lent quantities of higher denominations. hemisphere.

Divide the number of quantities of the given denomination by Thus is primeval prophecy fulfilled :

that number which it takes of quantities of this denomination While earth continues, and the ground is tilled ;

to make one of the next higher. Proceed in the same manner Spring time shall come, when seeds put in the soil

with this and each successive denomination, until the required Shall yield in harvest full reward for toil;

denomination is arrived at. The last quotient, with the several Heat follow cold, and fructify the ground, Winter and summer in alternate round;

remainders, will be the answer required.

Obs.—It is manifest that the correctness of an operation por
And night and day in close succession rise,
While ench is regulated by the skies.

formed in accordance with either of the foregoing rules may be Supreme o'er all, at first, Jehovah stood,

tested by reversing the operation—that is, by reducing the And, with creative voice, pronounced it good."

result to the original denomination.

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