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= (which is read by) is the sign of division: a divided by b is written a = b, or even as a fraction,

6. The sign – between two quantities shows that their difference is to be taken, it being immaterial which of them is the greater: thus, a = b indicates the difference between the quantities a and b; and if a be greater than b, a ~b is equivalent to ab, if b be greater than a, a ~b is equivalent to b-a.

The sign (which is read equals) shows that the quantities are equal to each other : thus, 7a + 3a=10a, 7a--3a=4a, 7 x 3=21, and so on.

The sign > signifies that the former quantity is greater than the latter: thus, 7a > 3a. But < signifies the reverse : as, 3a <70.

Brackets, ( ), { }, [ ], show that the quantities included between them are to be taken collectively, or as one quantity: they are very useful in the higher operations of algebra, but may be simply illustrated here : {3a + 4a + 6a} +86 = 13a + 86.

The sign ... signifies therefore: .. signifies because.

The signs , Ý, Ý, &c., V, are used to express the square root, the cube root, the biquadrate, &c., nth root respectively of the quantity before which they are placed : thus signifies the square root of 4, that is to say 2; in like manner j8 is 2; and (/64 is the nth root of 64, where n may have any value: for if we make 2 to be the value of n, %64 will be 8; if n be 3, "/64 is 764, that is to

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These explanations presuppose some acquaintance with the principles of arithmetic; and, if they be studied during the month, some lessons in following Numbers will be easily understood.

M. L. R.

ASTRONOMICAL PHENOMENA.

JANUARY, 1855. By A. GRAHAM, Esq., Markree Observatory, Collooney. THE EARTH will be at its least distance from the Sun on the 1st, Mars on the 25th. Mercury will be at his greatest distance on the 5th, VENUS on the 12th.

Mars and JUPITER may be seen very close together, near the horizon, in the south-west, shortly after sunset, on the 1st. VENUS will be close to JUPITER on the 18th, and MERCURY on the 25th : but these phenomena will occur too near the Sun to be seen by the

naked eye.

MERCURY will be in superior conjunction with the Sun on the 20th, JUPITER on the 30th.

Saturn is the only one of the primary planets which will arrest the attention during this month. Situate amid a fine array of fixed stars, Aldebaran very near, the Pleiades to the right above, Orion to the left below, he shines conspicuous, infinitely heightened in interest by the revelations of the telescope. His rings, seen by us obliquely, are projected into concentric and similar ellipses, of which the outer axes, on the lst, are 46" and 20% respectively.

RISING AND SETTING OF THE SUN, FOR THE PARALLELS OF THE

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Jan.

Rises. Sets. Rises. Sets. Rises. Sets. Rises. Sets. Rises. Sets. h. m. h. m. h. m. h.m. h, m. h. m. h. m. h. m. h. m. h. m. 17 59 4 98 8 3 59 8 19 3 48 8 32 3 36 8 46 3 22 117 56 4 218 6 4 12 8 15 4 2 8 26 3 518 39 3 38 217 48 4 36.7 56 4 28,8 5 4 19 8 14 4 9 8 26 3 58 317 36 4 52 7 43 4 467 50 4 38 7 58 4 30 8 7 4 21

SUN AND PLANETS AT GREENWICH.

Sun.

MERCURY. Venus. Mars. JUPITER. Saturx. UKANUS.

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Rises. Sets. Rises.
h. m. h. m. h. m.
8 6 4 2 7 26m.
8 3 4 14 7 56
7 54 4 30 8 12
7 41 4 47 8 13

Sets. Sets.
h. m.

n. m.
4 17a. 5 49a.
4 43 5 55
5 14
5 46 6 7

5 54a.
5 28
5 2
4 36

Sets. Sets, h. m. 6 50m. 3 26m. 6 7 2 46 4 26

27

1 3 46 1 28

PHASES OF THE MOON.

Full

3d day, 8h. 19m, morn. Last Quarter 11th day, Oh. 13m. aftern. " New

13th day, 8h. 37m. morn.. First Quarter . 25th day, lh. 39m. morn.

H. T. & J. Roche, Printers, 25, Hoxton-square, London.

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YOUTH'S INSTRUCTER

AND

GUARDIAN.

FEBRUARY, 1855.

a

CLAUDE OF LORRAINE.

(With a Portrait.) Born in an obscure village of Lorraine, in the year 1600, of very humble parents. At a very early age the boy was bound apprentice to a pastrycook, and seemed doomed to creep through life amidst steam and sweetmeats. For this kind of existence he had no relish; and when his parents died, the period of apprenticeship being past, he left the pastrycook, and went to Fribourg, where a brother of his followed the calling of engraver on wood. Here he gave the earliest indications of artistic genius; and here a relative, setting out for Rome, invited him to be his companion. But they had not been long in Rome, when the relative deserted him : he was obliged to seek subsistence in the capacity of domestic servant, and became cook and colour-grinder to Agostino Tassi, a landscape-painter.

His love of the pencil now displayed itself in efforts to copy some of this person's pictures, who rewarded it by giving him lessons in the mechanical branch of the art. As yet he was no more than a copyist, and gave little indication of originality; but having seen some landscapes by Giofredi Wals, then painting at Naples, he became so enamoured with the style of that artist, that he resolved to visit him; and, although destitute of means for travelling, he boldly left Rome, and was brought safely by Providence

VOL. XIX. Second Series,

D

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