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The zodiacal signs are sometimes supposed to have been connected with the rural occupation of the ancients. The cluster of stars among which the sun was passing in spring was called the Ram, because at that time the flocks were sent out into the fields. The Lion, too, has been considered symbolical of the intensity and power of the rays of the summer sun. The Balance tells of the period of equal day and night; the Scorpion of the unhealthiness of autumn; while the Waterbearer and the Fishes betoken the rains and floods of winter.

The names given to these twelve constellations are as follows:-Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces. Their order may, however, be more easily remembered by the following lines:The Ram, the Bull, the heavenly Twins, And next the Crab the Lion shines, The Virgin, and the Scales; The Scorpion, Archer, and He-Goat, The Man that bears the Watering Pot, And Fish with glittering scales.

Among the most important of the phenomena of the heavens are solar and lunar eclipses, and these of course attracted the attention of early astronomers, and at length the true cause of them was discovered. A careful record also appears to have been kept of them, so that the Saros, or Chaldean Period, was discovered. This is a period of eighteen years and eleven days, or 223 lunar months, at the expiration of which the moon enters again upon its former track in the heavens, and thus the same eclipses are, as it were, repeated.

The wonder and anxiety with which these remarkable events were witnessed can easily be imagined, and when the first astronomer ventured to predict an eclipse, and his prediction was found true, he must have been looked upon as little short of divine. The first instance we have on record in which this was actually done is in the year 610 B.C., when Thales, the father of astronomy among the Greeks, foretold an eclipse of the sun. It seems probable, however, that a similar thing had been previously done by the Chaldæans.

With Thales begins the true history of astronomy. The Greeks were not, however, distinguished by any great proficiency in the natural sciences. We find here and there shrewd guesses and faint gleams of truth; but it is always mixed up with fanciful speculations, instead of being supported by careful observation and reasoning. They seem, for the most part, to have started with certain principles (which had no existence except in their imaginations), as, for instance, that the earth must be in the centre of the universe, and that, since the circle was the perfection of shape, all the motions of the heavenly bodies must be in circles. They then observed the phenomena of the sky, and the apparent motions of the sun and stars, and formed cumbrous and complicated systems to try and reconcile these appearances with their theories.

Hence we find all the involved mysteries of transparent wheels revolving one within the other, and carrying with them the planets and stars, of cycles and epicycles, and of crystal spheres in ceaseless rotation, which the followers of Ptolemy were ever planning and altering. The true law of discovery-which is to make accurate observations first, and afterwards start a theory to explain the appearances-seems to have been quite lost sight of, and hence confusion prevailed.

We must, however, just glance at a few of the names which stand prominently forward in the history of the science. Anaxagoras and Pythagoras were two of the Greek philosophers who succeeded Thales, and they appear to have had much more accurate views than most in their day. The truth of the earth's motion round the sun seems to have been realised by them, though it does not appear to have been received by others, and was opposed by those in power as being impious. The former of the two was indeed sentenced to death on account of his philosophical views; but his sentence was afterwards, through the influence of a friend, commuted into banishment for life. The next we notice was the greatest of all the ancient astronomers, Hipparchus, who lived in the second century before the Christian era. He gave up all attempts to frame a system for the universe, and occupied himself by carefully watching and recording the motions of the sun and planets. The movements of the sun in particular occupied his persevering attention, and in this way he made a very near approximation to the true length of the year; and the accuracy of his observations is very

remarkable when we consider the imperfect nature of the instruments he had to employ. He also observed the irregularities in the rate of the sun's motion, and determined in what part of its course its speed was greatest, and thus ascertained that, if the motion of the sun was uniform, the earth was not situated in the centre of its orbit.

A

Fig. 1.

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Another thing for which the name of Hipparchus is memorable is a catalogue of fixed stars, which he formed in order that future astronomers might be able to detect any alteration in their position or number. He appears to have been led to undertake this task by the appearance of a new star, and though the work of carefully ascertaining and noting the position of each star was, especially with the imperfect instruments possessed in his time, a work requiring great labour and patience, he persevered, and completed a list which contained 1081 stars. In the progress of this work he made one very important discovery. On comparing the place assigned by him to a star in the constellation Virgo with that determined by some distinguished astronomers nearly two hundred years previously, he found a difference of two degrees in its longitude.

He then made similar comparisons, where it was possible, with respect to other stars, and found the same change in their position. It was thus evident that all the stars must have moved forward, or else that the point from which the measurements were taken had moved backwards. This phenomenon is known as the Precession of the Equinoxes, and will be fully explained in its place. The reason of it was discovered by the great Newton.

Another idea for which we are indebted to Hipparchus was that of representing the positions of the stars on an artificial globe, and of marking the position of places on the terrestrial globe by means of lines of latitude and longitude.

Nicias, one of the followers of Hipparchus, is said to have gone even further than his master, and started an hypothesis that the apparent changes in the sky were caused by a daily revolution of the earth. The idea, however, was not supported by any arguments, and was lost sight of for ages.

The only other one of the ancient astronomers we shall refer to in this sketch is Ptolemy, who was a very learned scholar, not only in astronomy, but in mathematics and geography. Having carefully examined the observations of Hipparchus and others, he at length promulgated a system known as the Ptolemaic, which, though since proved to be quite erroneous, accounted so well for all known phenomena that its errors could not, with the instruments then in use, be discovered; and accordingly, it was universally received until the age of Copernicus, and even then it was long before it was entirely given up.

According to this system, the earth was the centre, with the planets revolving round it in the following order: The Moon. Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and, beyond all, the fixed stars. To account for the apparent irregularities in their motions, he introduced what he termed epicycles, which will be understood by reference to Fig. 1. E represents the earth, and A B C the orbit in which the planet should move; but, instead of this, he supposed that there was a point c moving in this orbit, and that the planet P moved round this point in a small circular orbit or epicycle. The combination of these two motions explained the irregularities. This system was afterwards rendered much more complicated by the ulterations introduced by his successors.

LESSONS IN ALGEBRA.-XIV. SIMPLE EQUATIONS. 151. Most of the investigations in algebra are carried on by means of equations. In the solution of problems, for example, we represent the unknown quantity, or numbers sought, by a certain letter; and then, in order to ascertain the value of this unknown quantity or letter, we form an algebraic expression from the conditions of the question, which is equal to some given quantity or number.

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@= 60, the number bought of each.

Here, the last expression is obtained from the preceding one by dividing each member by 14, the co-efficient of 14.

It will be perceived, in this example, that the unknown quantity, or number sought, is represented by the letter ; and from the conditions of the problem, we obtain tire quantity 14, which is equal to the given quantity 840 crowns. This whole algebraic expression, 14 840 crowns, is called an equation.

152. An EQUATION, therefore, is a proposition expressing in algebraic characters the equality between one quantity or set of quantities and another, or between different expressions for the same quantity.

This equality is denoted by the sign , which is read "is equal to." Thus +ab+c, and 5+8=174, are equations, in one of which the sum of a and a is equal to the sum of b and c; and in the other, the sum of 5 and 8 is equal to the difference of 17 and 4.

The quantities on the two sides of the sign are called members of the equation; the several terms on the left constituting the first member, and those on the right the second member.

When the unknown quantity is of the first power, the proposition is called a simple equation, or an equation of the first degree. 153. The reduction of an equation consists in bringing the unknown quantity by itself to one side of the sign of equality, and all the known quantities to the other side, without destroying the equality of the members.

To effect this, it is evident that one of the members must be as much increased or diminished as the other. If a quantity be added to one, and not to the other, the equality will be destroyed. But the members will remain equal

(1.) If the same or equal quantities be added to each. Ax. 1. (2.) If the same or equal quantities be subtracted from each. Ax. 2.

(3.) If each be multiplied by the same or equal quantities. Ax. 3.

(4.) If each be divided by the same or equal quantities. Ax. 4. The principal reductions in simple equations are those which are effected by transposition, multiplication, and division.

REDUCTION OF EQUATIONS BY TRANSPOSITION.

In the equation x-7=9, the number 7 being connected with the unknown quantity z by the sign, the one is subtracted from the other. To reduce the equation, let the 7 be added to both sides. It then becomes x- −7+7=9+7.

The equality of the members here is preserved, because one is increased as much as the other. But on one side we have -7 and +7. As these are equal, and have contrary signs, they balance each other, and may be cancelled. The equation will then be a 9 +7.

Here the value of x is found. It is shown to be equal to 97, that is, to 16. The equation is therefore reduced. unknown quantity is on one side by itself, and all the known quantities on the other side.

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+ x + a.

1. Reduce a + 2x
2. Reduce y + ab hm = a + 2y - ab + hm.
3. Reduce h +30 +7x=86h + 6x + b.

4. Reduce bh + 21 − 4x + d = 12 − 3x + d - 7bh. 5. Reduce 5x + 10+ a = 25 + 4x + c.

6. Reduce 5c + 2x + 12 - 3 = x + 20 + 5c. 7. Reduce a + b - 3x = 20 + a 4x + b.

8. Reduce x + 32e-434+3x-4-5x. 9. Reduce 4x 2 + 18 = 5 +8. 10. Reduce 24 11. Reduce 3+ 5x-18=6x-22. 12. Reduce 10x +60 +7x=28x + 64

23x8+ 2.

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EXERCISE 29.

ON THE ABBREVIATING HOOKS, ETC., IN LESSON VIII. To be written by the pupil in Phonography, and in longhand. N HOOK.

1. cone, town, deign, chin, Jane, pine, bean, run (upward r). 2. cones, towns, deigns, chins, Jane's, pines, beans, runs (upward r). 3. shine, then, fawn, vein, lawn, earn (downward r), known, moan. 4. shines, fawns, veins, lawns, leans, earns, man's, moons.

FOR V HOOK.

5. dove, devour (upward r), divide, above, approve, brave, chaff.

AM: 6. groove, rough, pave, scoff, serve, tough, turf, serf, surf, crave.

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7. rife, achieve, brevity, advent, advert, defer, derive, deprave. 8. divine, divinity, dovetail, defend, refer, reference, profit, mischief. -TION HOOK.

9. anction, addition, additional (downward 7), admission, admonition, 10. affliction, aggravation, animation, anticipation, approbation. 11. commendation, compassion, confession, confusion, consideration. 12. temptation, pension, nation, mansion, invention, intention.

HALVING PRINCIPLE, ADDING T OR D.

13. ask, asked; aim, aimed; attack, attacked; avail, availed.
14. bake, baked; bath, bathed; bawl, bawled; boil, boiled.
15. calm, calmed; cheer, cheered; chip, chipped; deem, deemed.
16. elope, eloped; envy, envied; fail, failed; fear, feared; fill, filled.
17. glue, glued; guide, guided; howl, howled; her, heard (tick ).
18. jump, jumped; keep, kept; knock, knocked; kneel, knelt.
19. leaf, left; loathe, loathed; lodge, lodged; laugh, laughed.
20. maim, maimed; move, moved; match, matched; nip, nipped.
21. ooze, oozed; pair, paired; pick, picked; pitch, pitched.
22. quill, quilt; reach, reached; rob, robbed; rock, rocked.
23. save, saved; shame, shamed; spare, spared; subdue, subdued.
24. touch, touched; thaw, thought; thatch, thatched; wage, waged.
ST AND STR LOOPS.

25. abased, abreast, attest, boast, bust, cast, chaste, crust, durst, dust.
26. fast, fist, ghost, grist, infest, inmost, jest, just, last, list, lost.

27. mast, mist, most, next, nest, oppressed, paste, pest, post, quest.
28. request, roast, stage, steal, steam, suggest, text, trust, utmost.
29. castor, Chester, faster, fluster, Leicester, Manchester, minister.
30. monster, muster, poster, punster, Ulster, Winchester, youngster.
S-TION HOOK.

31. decision, disposition. vexation, possession, position, opposition.
32. exposition, physician, compensation, organisation, transition.
(In the last three words, turn the ns circle on the left.)

LENGTHENED CURVE, ADDING THR, DER.

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Votre maître vous aime; donc, Your master loves you; therefore you
vous devez l'aimer.
should love him.

Je suis donc un témoin de leur I am, therefore, a witness of their
peu de puissance.
want of power.
Et d'où peut donc venir ce change- Whence, therefore, can this extreme
ment extrême ?
change proceed?

33. asunder, founder, slander, provender, thither, father, thunder. 34. adventure, mother, matter, September, November, December. 35. temper, neither, another, dissenter, laughter, rafter, letter. 36. latter, alter, fetter, fender, order, salter, smatter, weather, wither. Si ce n'est toi, c'est donc ton frère. If it is not you, then it is your

EXERCISE 30.

When you feel angry, it
Try to do that which is
There is a time for play,

-Je n'en ai pas.-C'est donc
quelqu'un des tiens.
"Allons done!" répondit-on, et la
transaction n'eut pas lieu.

brother.-I have none.-Then it must be some one of your family. "Well done!" replied they, and the affair did not take place. QUE.

DE MÊME De même que le soleil brille sur la terre, de même le juste brillera dans les cieux.

As the sun shines upon earth, so will the just shine in heaven.

(To be written in Shorthand.) Do as you wish others to do to you. is well to think long before you speak. right, and avoid that which is wrong. and there is a time for work; a time to think, and a time to talk; a time to keep silence, and a time to speak. When you speak, think to whom you speak, of whom you speak, and say only that C'est être faible et timide que To be inaccessible and proud is to be which you know to be just and right.

The pupil should now test his progress, by submitting his work to the examination of a competent phonographer. He is recommended to send a shorthand transcript of Exercise No. 30, (with interlined longhand, leaving a blank line under every two lines thus filled, for corrections,) to some first-class member of the Phonetic Society for examination, and correction if necessary. His request will be cheerfully complied with, and he will be invited to forward other exercises for correction. The lesson should be accompanied by a stamped and directed envelope for its return. A List of the Society for the current year may be obtained through any bookseller, of Mr. F. Pitman, 20, Paternoster Row, London, or of Mr. Isaac Pitman, Bath, by post,

price 2d.

LESSONS IN FRENCH.-L.

SECTION XCIX.-EXAMPLES ILLUSTRATING THE VARIOUS
USES OF THE PRINCIPAL CONJUNCTIONS.

À MOINS QUE.

Il n'en fera rien, à moins que vous He will do nothing of the kind, unless ne lui parliez.

À moins que vous ne preniez bien

votre temps, vous n'en viendrez pas à bout.

Quel indigne plaisir peut avoir

Et

l'avarice?

you speak to him.

d'être inaccessible et fier.
Une famille vertueuse est un vais-
seau tenu pendant la tempête par
deux ancres, la religion et les

mœurs,

ET.

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Quel carnage de toutes parts!
On égorge à la fois les enfants, les They murder at once the children and
Et la sœur et le frère,

vieillards,

Et la fille et la mère,
Le fils dans les bras de son père.

the old men, the sister and the brother, the daughter and the mother, the son in the arms of his father.

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Unless you choose your time well, C'était déjà la puissance impériale It was already the imperial power of

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que sert d'amasser, à meins What is the use of hoarding up unless qu'on en jouisse? we enjoy ?

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Jamais on ne vit an si grand ex-
emple, que le courage n'est point
incompatible avec la mollesse.
Nous n'avons que peu de temps à
vivre, et loin d'en profiter, nous
ne cherchons qu'à le perdre.
A quoi vous servira d'avoir de

l'esprit, si vous ne l'employez
pas, et que vous ne vous appli-
quiez pas ?

Never was such a striking example

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Soit la hardiesse de l'entreprise,

Soit qu'il le fasse, soit qu'il ne le Whether he does it, whether he does it
fasse pas.
not.
Be it the boldness of the enterprise,
be it the presence alone of this great
man, be it the visible protection of
heaven, he astonishes by his reso-
lution.

soit la seule présence de ce grand
homme, soit la protection visible
du ciel, il étonne par sa résolu-
tion.

Soit en bien, soit en mal, mon ami,
la prudence dit, qu'il faut rare-
ment juger sur l'apparence.
Vous le voulez ? ainsi soit-il!
Un mal funeste et contagieux se
répandit dans les principales
villes de la Normandie; soit que
l'intempérie des saisons eût
laissé dans les airs quelque ma-
ligne impression, soit qu'un com-
merce fatal eût apporté des pays
éloignés, avec de fragiles rich-
esses, des semences de maladie
et de mort, soit que l'ange de
Dieu eût étendu la main pour
frapper cette malheureuse pro-
vince.

Be it for good, be it for evil, my
friend, prudence says that we must
rarely judge from appearances.
You will have it so? So be it!
A fatal and contagious disease spread
in the principal cities of Nor-
mandy; be it that the inclemency
of the season had left in the air
some malignant impression, be it
that a fatal commerce had brought
from distant countries, with perish
able riches, the seeds of disease and
death, be it that the angel of God
had stretched forth his hand to
smite that unfortunate province.

PLOYED IN FRENCH.

seen, that courage is not incom- SECTION C.-A LIST OF THE USUAL ABBREVIATIONS EMpatible with effeminacy. We have but little time to live, and instead of improving it, we only seek to waste it.

Of what use will be your wit, if
you do not employ it, and do not
apply yourselves?

The following is a list of the most usual abbreviations employed in French

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ABBREVIATIONS.

A. P. A protester.

A. S. P. Accepté sous protêt.

Toutefois, que sert-il de me justi. However, what is the use of justifying A. S. P. C. Accepté sous protèt

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pour à compte.

Bon. Baron.

Qu'il

Let him do what he pleases.
How great is the world!
nificent!

Cer.

How mag

Cte.

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Chevalier.
Comte.

Ctesse. Comtesse.

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MEANINGS.

To be protested.
Accepted under protest.

Accepted under protest on account.

Baron.

Chevalier, knight, sir.

Count.

Countess.

Doctor.

Doctor of medicine.

East.

Jesus Christ.

LL. AA. II. Lears Altesses Im. Their Imperial Highnesses.

périales.

LL. AA. RR. Leurs Altesses Their Royal Highnesses.
Royales.

LL. AA. SS. Leurs Altesses Séré- Their Most Serene Highnesses.
nissimes.

LL. Em. Leurs Eminences.
LL. Ex. Leurs Excellences.
LL. HH. Leurs Hautesses.
LL. MM. Leurs Majestés.
LL. MM. II.
Impériales.

LL. MM. RR.
Royales.

Leurs Majestés

Their Eminences.

Their Excellencies.

Their Highnesses.

Their Majesties.

Their Imperial Majesties.

Leurs Majestés Their Royal Majesties.

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