fracting light; and hence, as from so many minute prisms, the unfolded rays of the sun are sent up to the eye in similar brilliant colours to those of the rainbow. The deposition of dew was first satisfactorily explained by Dr. Wells, in 1814. When the sun is below the horizon, and for a short period before his setting, bodies upon the surface of the earth, exposed to the aspect of a clear sky, cool by the radiation of the particles of heat absorbed, and at a more rapid rate than the atmosphere. The air, in immediate contact with these bodies, replete with humidity, in the form of transparent aqueous vapour, is chilled by their cold embrace; and, owing to the increase of its density, it becomes incapable of holding in suspension the moisture with which it is charged in the same quantity as before. The surplus is therefore disengaged, and appears upon the surface of the refrigerating object in globules of dew. It is essential to this process that the night should not be a cloudy one; because, when the sky is overcast, the radiant caloric proceeding from the surface of the earth, and which otherwise would go off into free space, is intercepted by the clouds, and returned by them in sufficient quantity to prevent the decrease of temperature necessary to compel the atmosphere to surrender a portion of its hoard of aqueous particles. On nights that are perfectly cloudless, therefore, the deposition of dew is greater than when the sky is partially screened; on those that are both cloudy and windy there is none whatever formed; but a gentle motion in the air on a clear night is favourable to its production in the greatest copiousness, by bringing fresh portions of the atmosphere, laden with moisture, into contact with the surfaces of colder bodies. Wind prevents the deposition of dew, by constantly renewing the air lying upon the earth before it has had its temperature sufficiently reduced to cause condensation of moisture. The theory of the dewing process at once explains the rationale of the practice adopted by gardeners, to protect tender plants and fruit trees in blossom on clear nights from cold, by spreading over them a mat or awning. The cover performs the same office as the clouds. It returns the heat radiated from the plants to them, and thus a temperature is preserved which prevents refrigeration. It is observable that substances exposed at night to the action of the same circumstances differ greatly in the amount of dew deposited on them, some being thickly coated with its pearls, while others are without a single globule. This arises from the varying capacity of bodies for the radiation of heat. Light downy substances part with it more freely than the solids; so that the former cool down to the dew-point, or to that degree of the thermometer at which its disengagement from the atmosphere commences; while the latter, remaining above it, receive no deposition. To the following substances dew has been observed more particularly to cling: swans-down, fine raw silk, fine unwrought cotton, flax, wool, grass, hair, low plants and vegetables, both dead and living; glass and animal substances. As the temperature of substances must be reduced below that of the atmosphere, in order to the formation of dew, it is never observed, in temperate climates, upon the naked parts of a living and healthy human body. The following substances shew a marked inaptitude to receive dew: rocks, bare earth, considerable masses of water, iron, steel, and the other metals. When dew is frozen, the moment it falls it becomes hoar frost.

ABBREVIATIONS.

The shortest way to multiply by 5, is to annex a cipher to the multiplicand and divide by 2. This is equivalent to taking the half of 10 times.

To divide by 5; multiply by 2, and strike off the last figure. Half the last figure is the true remainder.

To multiply by 25; annex two ciphers to the multiplicand, and divide by 4.

To divide by 25; multiply by 4, and strike off the last two figures. One-fourth of these two figures, taken as one number, will give the true remainder.

To multiply any number by 9; annex a cipher to the multiplicand, and subtract the number. This is equivalent to taking the number 10 times, and deducting it once.

To multiply by 99; annex two ciphers to the multiplicand, and subtract the number.

To multiply by 999; annex three ciphers to the multiplicand, and subtract the number.

To divide by any number of nines; from the right of the dividend point off as many figures as there are nines in the divisor; then write the figures not cut off below these, striking off as many nines as before; again, write below the figures not cut off; and repeat the operation until all the figures are thus cut off, then plus 1 and add up. The figures not cut off will form the quotient, and those struck off will constitute the remainder.

It is required to divide 4378635278 by 999.

4378635 278

4378 635
4378

Quotient 4383018 296 Remainder.

SOME OF THE PROPERTIES OF NUMBERS,

The product of two even numbers is even.

The product of two odd numbers is odd.

The sum or difference of any two odd numbers is even.

The sum of any two consecutive odd numbers may be divided by 4.

The product of two consecutive numbers is even, and may be divided by 1 x 2, and if they be even consecutive numbers, their product will be divisible by 8.

The product of three, of four, or of five consecutive numbers, may be divided by 1 × 2 × 3, by 1 × 2 × 3 × 4, and by 1 × 2 × 3 × 4 × 5, as the case may be.

If an even number can be divided by an odd number, its half can also be divided by it.

The difference of the squares of two odd numbers may be divided by 8.

Any number divided by 6 has the same remainder as its cube divided by 6.

The product of any two odd numbers is less than the square of the middle number between them, by the square of half their difference.

No number can be a square which has either 2, 3, 7, or 8, for its last digit.

No square number can terminate with two figures the same, except they be two ciphers, or two 4's.

The product of two different primes cannot be a square.

MISCELLANEOUS EXAMPLES.

1. The following Alphabets contain the number of letters indicated below: the English alphabet has 26 letters; the French, 23; the Italian, 20; the Spanish, 25; the German, 26; the Sclavonic, 27; the Muscovite, 43; the Latin, 22; the Greek, 24; the Hebrew, 22; the Arabic, 28; the Persian, 31; the Turkish, 33; the Georgian, 36; the Coptic, 32; the Sanscrit, 50; and the Ethiopic no fewer than 202. Add these together, and divide the difference between the square and the cube of their sum by the sum?

The Chinese have no Alphabet, but have characters, which are the signs not of words, but of ideas, and are in number about 80000.-Imp. Dict.

An Alphabet (Alpha, Beta, the first and second letters of the Greek Alphabet) is the customary arranged series of the several letters forming the elements of a language. By means of this important invention, sounds are represented by symbols, and language made visible to the eye. The books of Moses are the earliest specimens of alphabetical writing. The first letter of the Phænician and Hebrew alphabet was aleph, called by the Greeks alpha, and afterwards abbreviated to A. Cadmus, about 1493 B.C., introduced the Phænician letters, about 15 in number, into Greece, and the forms of these were gradually changed till they became the ground of the Roman letters now used all over Europe. The origin of alphabetical writing belongs to a period long antecedent to the date of any historical testimony which has reached our times. Phænician inscriptions, and numerous ancient coins have, however, preserved the earliest form of that alphabet, from which all others have been derived. The Phænician mode of writing was continuously from right to left. This primitive alphabet underwent various changes in its transmission to alien nations. The ancient Greek alphabet was an immediate descendant of the Phænician, with which its letters corresponded in name, figure, and order; but in process of time they were changed both in sound and form. The same may be said of the Latin. Polybius, the earliest extant writer of Roman history says, that the Roman language of the first treaty with the Carthaginians (B. C. 509) engraved on brass, and extant at the time he wrote (about 360 years afterwards), could hardly be understood by the best antiquarians. The primitive alphabet of the Romans consisted only of 16 letters; A B C D E J K L M N O P Q R S T.

2. In 1848 the bank note circulation of the United Kingdom was as follows:-Bank of England, £17505718; private banks, £3681544; joint-stock banks, £2666749; Scotland, £3136516; and of Ireland, £4506421. The money coined in the same year consisted of 110400 lbs. of gold, yielding 5158400 sovereigns; of 38100 lbs. of silver, yielding £125730; and of copper 40 tons, yielding £4960. Which was the greater-the paper currency; or the gold, silver, and copper coined; and by how much?

Banks are commercial establishments, intended for the safe custody of money, and to facilitate its payment by one individual to another. A Bank-Note is a substitute for a metallic currency, and is a promissory note issued by a banking company, signed by their president, and countersigned by the cashier, payable to the bearer in gold or silver on demand. By the use of a paper currency mercantile men and others can effect payments at all distances with great facility and safety, when, by employing gold and silver coin, risk and delay would be incurred. Previously to 1759, the Bank of England did not issue any notes for less than £20; £10 notes being then first issued. £5 notes were first issued in 1794, and £1 and £2 notes (since discontinued) in 1797. The bank never re-issues the same notes, even if they are returned the same day they are sent out. A Bank of England note, apparently so slight, is nevertheless so strong, that before it is sized it will support a weight of 36 lbs., and with the addition of one grain of size, it will sustain half a hundred weight without tearing. The first forgery of a bank-note occurred in 1756, when the person who forged it was convicted and executed.

Money is the standard representation of property, or the medium which serves as a universal equivalent for all commodities. This is usually, among modern commercial nations, of gold, silver, or copper, stamped by public authority with the name and arms of the prince or state in which it is made to pass current at a certain value. Gold and silver are the most convenient metals for this purpose, as they represent great value in a small compass, and are also durable and little liable to diminution by use. In very early times all commerce was managed by way of barter. Afterwards bits of leather were used to express the value of commodities. Money is mentioned as a medium of commerce in the 23rd chap. of Genesis, when Abraham purchased a field as a sepulchre for Sarah. The money of Scripture is all mentioned by weight, and the Jewish shekel was impressed simply with the almond rod and pot of manna. The first coined money among the Jews was in the time of Judas Maccabæus. Before this, payments had always been made by weight; hence the correspondence between the names of their sums and their weights. Homer speaks of brass money as existing 1184 B.C. Money was first coined at Rome, according to Pliny, under Servius Tullius, about 550 B.C.; and brass money only was in use there previously to 269 B.C., when Fabius Picton coined silver. Gold was coined 206 B.C. The etymology of the Latin word pecunia (money) affords evidence that cattle (pecus) were the first money among the Romans. In the earlier and simpler days of Rome, the likeness of no living personage appeared upon their coins; the heads were those of their deities, or of those heroes who had received divine honors. Julius Cæsar, after consolidating the Roman empire, was the first who obtained the express permission of the senate to stamp his portrait on the coin. Iron money was used in Sparta; iron and tin in Britain; and even so late as 1574 money was made of pasteboard by the Hollanders. The first coinage in England was under the Romans at Camalodunum (Colchester.) English coins were of different shapes, as square, oblong, and round, until the middle ages. Our word money is derived from the Latin moneta, the Roman name for money, as they coined their silver money in the temple of Juno-Moneta.

3. What is the area in feet and inches of a room, for the paving of which 25088 bricks have been used, at the rate of 32 for every square yard?

4. The British House of Lords is composed of the following Princes and Lords Spiritual and Temporal: 3 princes of the blood-royal, 20 dukes, 21 marquesses, 115 earls, 22 viscounts, 26 English bishops, 4 bishops of Ireland, 201 barons, 16 representative peers of Scotland, and 28 of Ireland. How many members constitute the House of Lords?

The origin of Parliament has been carried back to the assembly of the Druids, the Saxon Gemots, Folkmotes, Wittenagemots, or assemblies of the wise men in the great council of the nation. The very first meeting of the inhabitants to agree upon a form of government would constitute a parliament, which Coke explains to be a place where every one spoke his mind. The American Indians call the same assemblage a Great Talk. The early members of the Parliaments of England consisted solely of the barons, or lords of manors, summoned by the king; and in after ages, when Christianity had become the religion of the land, the bishops and mitred abbots were added to the assembly, for they were still richer than the Lords, had larger landed possessions, and infinitely greater knowledge. These national councils, previous to the conquest, were rude and uncertain in their formation, governed by no settled rules, subject to no authority, save the law of the strongest,