round the sun, consists of 365 24224 mean solar days. This is very nearly 365 days, and a year is made to consist of 365 days, while to every fourth year a whole day is added, and such year is termed a leap year. The average year 365 days is too long by the difference between 25 and 24224 or 00776 of a day; consequently if I day be divided by 00776, the quotient 128 87 is the number of years in which the error will amount to day, so that the error is 3 days in 3 times 128.87 years, or nearly 3 days 2 hours in 400 years. This error is corrected by allowing only one out of four of the years which terminate the centuries to be leap years. Every year whose date is divisible by 4 is a leap year, except that date be exactly a number of centuries, in which case that number must be divisible by 4, in order that it may be a leap year: thus 1600, 2000, 2400, etc., are leap years, whilst 1900, 2100, 2200, 2300, etc., are not accounted leap years, for 19, 21, 22, 23, etc., the numbers of the centuries, are not divisible by four. Hence in 400 years there are only 97 leap years and 303 common years.

The day is then the first measure that is obtained, and it is divided into 24 parts, each of which is called an hour; each hour is divided into 60 parts, called minutes, and each of these is divided into 60 parts which are termed seconds. Since 24 × 60 × 60 86400, it is obvious that 1 second (marked thus 1') is the 86400th part of a day.

A civil month consists of 4 weeks or 28 days. The 12 calendar months, and the number of days in each are as follow:-January 31, February 28 in common years, and 29 in leap years, March 31, April 30, May 31, June 30, July 31, August 31, September 30, October 31, November 30, and December 31. The mean solar year consists of 365 24224 days, or 365 days 5 hours 48 minutes and 49.5 seconds.

II. Standard of Lineal Measure.

139. It is an object of the first importance in a civilized state of society that standards of weights and measures shall remain without alteration, and that we should be able to replace them in the event of their being destroyed either by accident or design. With a view to this object the English Government has had reference to the length of the seconds' pendulum. It has been seen that the second of time is an unalterable period of duration, and by the application of very ingenious contrivances, and the known laws of mechanics, the actual length of the seconds' pendulum has been ascertained, in the latitude of London, at the level of the sea in a vacuum, and at a certain degree of the thermometer, so that in case our standard of length should be destroyed, it would always be possible, while the laws of Nature remain unchanged, to restore that standard without alteration. The seconds' pendulum is not the unit of our measure of length. By an Act of Parliament, passed on the 17th June, 1824, a certain brass rod is declared to be the standard yard of England; and that its length, as compared with that of the seconds' pendulum, determined as above, is in the proportion of 36 to 39 1393; it follows, therefore, that although the seconds' pendulum is not the unit of our measure of length, it furnishes the means of restoration if at any time hereafter the standard yard should be lost or destroyed. * The

*The standard yard was destroyed in the conflagration of the Houses of Parliament, in 1834, and has not yet been restored.

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measures of length are given in (34), and for particular purposes some other denominations are employed. Thus, for measuring cloth of all kinds, 2 inches = 1 nail, 4 nails = 1 quarter, 4 quarters 1 yard, and 5 quarters = 1 ell. For measuring the height of horses, 4 inches = 1 hand. For measuring depths, 6 feet 1 fathom. The chain for measuring land is 22 yards, or 66 feet, or 792 inches in length, and consists of 100 links, each of which is consequently 7.92 inches. Mechanics usually divide the inch into halves, quarters, and eighths. A degree of the equator is 69 156 miles, and a degree of the meridian is 69 044 miles.

Since a square inch is a square whose side is 1 inch, and a cubic inch is a cube whose side is 1 inch, it necessarily follows that a lineal inch is the foundation of the unit of square and cubic measure. In the superficial measurement of stone, brick or slate-work, 36 square yards are termed a rood, and 100 square feet of flooring a square.

III. Standard of Weight.

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140. By the Act of Parliament already referred to, and which came into operation on the 1st of January, 1826, a cubic inch of distilled water, weighed in air by brass weights, at the temperature of 62 degrees of Fahrenheit's thermometer, the barometer being at 30 inches, is equal to 252 458 grains." Of the grains thus determined 5760 are a troy pound, and 7000 are a pound avoirdupois. These pounds are divided, as in the tables of troy and avoirdupois weight, in (34). In troy weight, and that usually termed apothecaries' weight, the grain, ounce, and pound are the same. The former, or troy weight, is used for the precious metals and for jewels, as also in trying the strength of spirituous liquors, etc.; and the latter is employed in medical prescriptions. The carat, used for weighing diamonds, is 3 grains. The assay weights, which are only used to show the fineness of gold, are 4 grains = 1 carat, and 24 carats 1 pound. Avoirdupois weight is the general weight of commerce, and by it all articles are bought and sold, except precious metals and precious stones. The avoirdupois pound is larger than the troy pound, the former being to the latter as 7000 grains to 5760 grains, or as 175: 144. The troy ounce is to the avoirdupois ounce as 480 grains to 437 5 grains, or as 192: 175.

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IV. Standard of Capacity.

141. The standard unit of the measure of capacity is the imperial gallon, containing 10 pounds avoirdupois of distilled water at the temperature of 62 degrees Fahrenheit, the barometer 30 inches, and is equal to 277 274 cubic inches. The imperial bushel, consisting of 8 gallons, will consequently contain 2218 192 cubic inches, or 80 pounds avoirdupois of distilled water.

V. Standard of Value.

142. The usual coins of England are in copper, silver, and gold, of the value stated in the Table of Money, Art. 34. Of these, gold is the only legal tender above 40 shillings. A farthing is the coin of least value, and it is usual to denote farthings as fractions of a penny. From the Latin words libra, a pound; solidus, a shilling; and denarius, a penny; £. s. d. are made to represent pounds, shillings, and pence re

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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.

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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.

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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 = 771636 grains, of which 69 447 grains are fine silver and 7716 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 =1134 4804-25 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. :