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3. Given 3 12 x 12, to find x."

To bring this equation to the form of a quadratic,

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Simplifying this expression, and collecting like quantities, we have,

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Completing the square, 26-12 + 36 = 64 + 36

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Taking the former of these, and extracting the cube

root, we have the approximate value of ≈,

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Taking the minus value of z, and performing the same operation, we find x = ·9324 +, which (singular to say), is identical with the previous value thus far, and doubtless to infinity, were the decimal places continued.

QUESTIONS IN GEOGRAPHY.

1. "What fixes the limits of the polar circles?" The circles, which are 43° from the Tropic of Cancer and of Capricorn respectively, are limited in position by the combined effects of three circumstances; the obliquity of the earth's axis to its orbit, the earth's motion in that orbit, and the impossibility of a round body, such as the earth, being illuminated over more than one-half of its surface at the same time by the direct rays of a single luminary such as the sun. The amount of obliquity is 2310, whatever position the earth may hold in its orbit.

Now, to show that these 23° transferred to length upon the surface of the earth, constitute the breadth of the Frigid Zone-the distance from the pole to the Arctic or Antarctic circle-and therefore define the limit of those circles, let us suppose an artificial globe to be placed before us, and a candle to be raised to the exact height of the wooden horizon, to represent the sun. Elevate the north pole 234°, and at the same time place the globe so that the pole may point to the actual pole of the heavens; this is done by means of the compass

attached to the globe. Next place the candle due east, or due west, as indicated by that instrument. The former will represent the relative position of the earth at the vernal, and the latter at the autumnal equinox. In either of these positions the sun would be directly perpendicular to the equator, and his light would, consequently, during the twenty-four hours, remain an equal time (12 hours) upon every portion of the earth's surface; hence the application of the term Equinoxequus, equal; nox, night.

But let us represent the earth moving through the south-western quarter of its orbit, by moving our globe round till its north pole is directed towards the candle. This done, we shall have the relative positions of the earth and sun at the summer solstice. Mark, now, the change that has been gradually made by the circle of illumination. Previously, the candle shone perpendicularly to the equator, but now, in consequence of the inclination of the north pole towards the candle, it is perpendicular to a place the same number of degrees. north of the equator as indicated by the elevation of the pole (23). The illuminated circle extends, therefore, 231° beyond the north pole, and not so far as the south pole by the same distance. Now, while the globe and candle are thus placed, turn the former upon its axis, to represent the diurnal motion, and it will be seen that no part, within 234° of the north pole, will, during the revolution, be placed in the shade; and with the south pole vice versa, a distance 23° from it only will be in the shade during the whole revolution. The same appearances would take place at the winter solstice, the only difference being that the south pole would be illuminated and the north in the shade. Now these circles of light and darkness transferred to the artificial globe define the extent or breadth of the frigid zones, and are termed Arctic and Antarctic respectively. (See

Sullivan's Geography Generalised, in which this and other phenomena are very logically treated.)

2. Give a list of the great mountain ranges of Europe, and the elevation of their highest peaks." 3." What are the chief productions of mountains?" 4. "Where are the chief pine forests in Europe, and what do they produce?"

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5. Give a sketch of the physical geography of Spain."

6. "Give a list of the rivers which run into the Mediterranean, as they are naturally grouped, with their sources and the chief towns upon them."

7. "What manufactures are Rome, Berlin, Dresden, Florence, Naples, Leghorn, Birmingham, Northampton, and Nottingham famous for?"

8. "Give a sketch of the political geography of Austria."

QUESTIONS ON THE SCRIPTURES.

1. "What were the tenets of the Pharisees, and what Scriptures did they acknowledge?"

The Pharisees, who in numbers, apparent sanctity, and standing in society, constituted the principal of the various sects of the Jews, appear, according to Josephus, to have acquired considerable weight as a separate body by the time at which John Hyrcanus was high priest, a century prior to the birth of our Saviour. The etymological import of their name (from "pharash," denoting separation), indicates, although but faintly, the supercilious contempt in which they held not only neighbouring heathen, but even the poor and unprivileged of their own people. With their overweening estimation of their privileges, as descendants of the faithful Abraham, and of their deserts as strict observers of the law, were closely connected many of their tenets: thus, they held

that it was obligatory upon God to bestow his peculiar favour on the Jews, because they were the children of Abraham; and farther, that their great progenitor, through regard for his offspring, sat close by the gates of hell, and prevented even the most deserving of a place in that abode of darkness, to descend thither. They believed in the immortality of the soul, in opposition to the Sadducees; and that it would be either happy or miserable eternally; that there are angels and demons, and that the Divine blessings belonged to the

Jews alone..

In addition to the Old Testament they held a number of traditions, as of equal and even greater importance than the Scriptures themselves. These traditions they pretended had their origin in Moses, and were transmitted through Aaron, Eleazer, Joshua, and the prophets, to the great sanhedrim. They were ultimately committed to writing at about the close of the second century; and then termed the Misna, which, with the Gemaras, or commentaries, made up the Talmud or Jewish code of doctrine.

A confused admixture of the doctrine of absolute predestination with free-will, ranked among the tenets of the Pharisees, as appears from Josephus, book xiii. chap. ix. of the Antiquities.

2. What did the great Jewish feasts commemorate? 3, Do any of the feasts of our Church correspond with them?

4. Show how the time, place, and manner of our Saviour's birth were limited by prophecy.

5. Give a concise account of the progress of Christianity during the fifty years after the ascension.

6. Give a concise history of the Book of Common Prayer.

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