=

=

spectively; hence one farthing = td., two farthings d., and threefarthings d. The English pound is generally called a pound sterling, to distinguish it from a pound weight, as well as from stock or foreign coins.

The standard gold coin is made of a metal composed of 22 parts of pure or fine gold, and 2 parts of copper. The standard silver coin is made of a metal composed of 37 parts of pure silver and 3 parts of copper. These compositions are better fitted for the purposes of a circulating medium than either pure gold or silver, which are too soft and flexible. Of these standard metals, a pound troy of gold is coined in'o £46. 14s. 6d., and a pound troy of silver into 66 shillings; hence the mint price of standard gold, or gold of a fineness, is £3. 17s. 10 d. per ounce; and of our silver coinage of a fineness 27, or nearly, is 3s. 6d. per ounce.

37

The weight of a sovereign, or pound sterling, is consequently 5 dwts. 3 grains, and the weight of a shilling is 3 dwts. 15 grains. An avoirdupois pound of copper is coined into 24 pence, each of which weighs 10 drams avoirdupois, or 291 grains troy. The weight of the silver florin is double that of the shilling, or 7 dwts. 6 grains.

COMPARISON OF ENGLISH AND FOREIGN MEASURES,
COINS, ETC.

143. It is explained (139) that the standard of English lineal measure is a brass rod preserved in the Exchequer of a certain length called a yard, and that in order to the recovery of this measure or standard if it should be accidentally destroyed, a comparison has been made between it and the length of the seconds' pendulum vibrating under certain conditions. The standard lineal measure of France is in like manner a certain fixed length called a metre. This length has been obtained as follows:-About 9 degrees of the meridian of Paris were carefully measured by some of the most distinguished mathematicians and astronomers of France and Spain, in terms of a certain assumed mètre, and by means of the length of the whole of this measured terrestrial arc, and the lengths of separate parts of the same, the figure of the earth, and the entire measure of the quadrant from the Equator to the Pole, was computed in terms of the assumed mètre, and then the ten-millionth part of this arc was adopted as the standard mètre of France. Several comparisons have been made by the most carefully-conducted experiments to ascertain the ratio of the length of this mètre to that of the English standard yard, and the result considered the most accurate, makes the metre 39 370079 English inches. This ratio being thus established, we easily arrive at the standards of lineal measure of the several European nations, which are generally founded on either the English or French system.

=

It is shown also (139) that the unit of lineal measure becomes necessarily the foundation of the unit of square and cubic measure, as also of the measures of solidity and capacity. And by availing ourselves of the unalterable condition of water at a fixed temperature and barometrical pressure, it furnishes also the means of determining a fixed unit of weight, or rather for fixing a means of comparison of different units of weight. Thus a certain brass weight in the Exchequer is determined to be the English troy pound, and the 5760th part of this is one

grain; and by the means of careful experiments, it has been ascertained that a cubic inch of water under the conditions above referred to weighs 252 458 grains. These grains thus become a sort of universal term of comparison of the weights of different nations. Some discrepancy is found to exist in the results as obtained by different philosophers, but they are very inconsiderable; and we believe the numbers in the following tables are those which are generally considered as the most

correct.

144. The metrical system of weights, measures, and coins, adopted in France, both as regards the multiples and submultiples of the unit, proceed according to the decimal scale, the units of the different measures being denominated as follows:

1. The unit of length is the mètre.

2. The unit of surface is the are, which is a square whose side is ten mètres.

3. The unit of volume is the stère, which is a cube whose side is a mètre.

4. The unit of capacity is the litre, which is a cube whose side is a tenth part of a mètre, and

5. The unit of weight is the gramme, which is the weight in vacuo of a cubic centimètre (the hundredth part of a metre) of water at the temperature of 4 degrees of the centigrade thermometer (39.2' Fahrenheit), being the temperature of water when its density is a maximum.

The Latin derivatives déci to denote the tenth part, centi, the hundredth, and milli, the thousandth part, being prefixed to any of the preceding units, serve to denominate its decimal submultiples; whilst the Greek prefixes, deca to denote ten times, hecto a hundred, kilo a thousand, and myria ten thousand times, will express the decimal multiples. Thus a décimètre signifies the tenth of a mètre, and a decamètre is 10 mètres. Taking the length of the mètre to be 39 370079 inches, the following tables of comparison of French and English measures will be easily understood.

Comparison of English and French Coinage.

145. In England the only legal tender above 40 shillings is the pound sterling or sovereign, a gold coin of the standard fineness of, viz., eleven parts of fine gold with one of alloy. In France either gold or silver may be legally tendered to any amount. The coins of France are

of fineness, viz., nine parts of fine metal with one of alloy, and the gold coins are considered to have a variable value with respect to the silver coins; the 20 and 40 franc gold coin being commonly at a premium in respect of 20 or 40 silver francs. The silver franc is the unit of French money, which is subdivided and multiplied, like their weights and measures, according to the decimal scale. The subdivisions are stated in centimes or hundredths of a franc.

=

The weight of a silver franc is the 200th part of a kilogramme, or of 15432 72 grains 77 1636 grains, of which 69.447 grains are fine silver and 7.716 grains alloy. A franc in gold is the 3100th part of a kilogramme; its weight in standard gold is therefore 4.9783 grains, of which 4 48047 are fine gold and ⚫49783 alloy.

Now (135) it is shown that the English pound sterling or sovereign contains 113 grains of fine gold; therefore, estimating the value of the two coins by their respective weights of pure gold, the English sovereign =113÷4·480425 22 gold francs, whatever may be the price of gold, the exchange being made in the same place, and at the same time; but other conditions must be considered under the general question of exchange between the two countries, as is shown in (135). From the above are obtained the following comparative intrinsic values of the French and English coinage, viz. :

COMPARATIVE TABLES of ENGLISH, FRENCH, and GERMAN MEASURES and WEIGHTS.

ALGEBRA.

DEFINITIONS AND ELEMENTARY PRINCIPLES.

ART. 1. ALGEBRA is the science of computation by general symbols, or it is a general method of reasoning on quantity by means of symbolical characters.

In algebra, quantities are represented by the symbols a, b, c, x, y, z, etc., and by employing this concise notation, the steps and results of algebraic investigations can be expressed not only in simple and intelligible forms, but free from that prolixity of which common language could never divest them. These very convenient symbols are made the arbitrary representatives of the quantities under consideration, and by the fundamental principles and operations of algebra, which are the same as those of common arithmetic, results are deduced exhibiting in what manner the various quantities are combined, and showing their relations to each other, even before particular values have been assigned to these quantities. In arithmetic each question requires a separate investigation, but in algebra all questions of the same class are considered together, and included in the same investigation, and the result of the reasoning with general symbols is expressed in a general form that applies with equal facility to every question of the same kind.

Thus, suppose that a represents the number of days in which a person, A, can perform a certain piece of work, and that b denotes the number of days in which another person, B, can perform the same, or an equal piece of work; then, by the principles of algebra it can easily be shown that the time in which A and B, working in conjunction, can perform the specified piece of work, is expressed in symbols by

a x b a + b Now, to apply this to an example or two, let us suppose that A can do a piece of work in 10 days, and that B can do it in 15 days, then a will denote 10 and b will denote 15; hence ахь 10 x 15 150

a+b

=

10 + 15 25

6 days, the time in which A and B

jointly can perform the piece of work.

Again, suppose A takes 12 days to perform a piece of work, and B takes 20 days, in what time will A and B jointly perform the piece of work?

that A and B jointly would take to perform the work.