upon all the maps and charts now in use, it would have tended to produce confusion between those of the old and those of the new system. The ancient division of the sphere, and, consequently, of the circle, into 360, and therefore into quadrants of 90 degrees, originated in the coincidence of the daily rotations of the earth in its orbit round the sun, or the apparent motion of the sun in the ecliptic, which, as near as the approximation of numbers can bring it, is of one degree every day. The division of the day into twenty-four hours, each of sixty minutes, is founded on a similar coincidence of time in the rotation of the earth round its axis, and the apparent daily revolution of the firmament round the earth resulting from it; giving for the rising or setting of each sign of the zodiac a term of two hours, and for each degree of the circle described by the earth in its rotation a term of four minutes, or fifteen degrees to the hour. The adoption of the decimal divisions for the quadrant of the meridian, and for the circle, would have disturbed all these harmonies, as well as that of the sexagesimal division of the circle by the radius; a division not perfectly exact, since the radius is not exactly the sixth part of the circumference, but which, having been found the most convenient for practice, has been established from the remotest antiquity, and, being already used by all the civilized nations of the earth, could not, by being set aside, tend to uniformity, unless the method to supply its place could be alike secure of universal adoption.

The divisions of the barometer had always been marked in inches and lines. The application to it of the decimetre, its multiples and divisions, had for observation and calculation the usual conveniences of the decimal arithmetic. The graduation of the thermometer had always been arbitrary and various in different countries. The principle of the instrument was every where the same, that of marking the changes of heat and cold in the atmosphere, by the expansion and contraction which they produced upon mercury or alcohol. The range of temperature between boiling and freezing water was usually taken for the term of graduation, but, by some, it was graduated downwards from heat to cold, and by others upwards from cold to heat. By some the range between the two terminating points was divided into 80, 100, 150, or 212, degrees. One put the freezing, and another the boiling, point at 0. Reaumur's thermometer, used in France, began with 0 for the freezing point, and placed the boiling point at 80. Fahrenheit's, commonly used in England, and in this country, has the freezing point at 32, and the boiling point at 212. The centigrade thermometer, adopted by the new system, begins at the freezing point at 0, and places the boiling point at 100: its graduation, therefore, is decimal, and its degrees are to those of Reaumur as five to four, and to those of Fahrenheit as five to nine.

The application of the new metrology to the moneys and coins of France, has been made with considerable success; not, however, with so much of the principle of uniformity as might have been expected, had it originally formed a part of the same project. But the refor mation of the coins was separately pursued, as it has been with us :

and, as the subject is of great complication, it naturally followed that, from the separate construction of two intricate systems, the adaptation of each to the other was less correct than it would have been, had all the combinations of both been included in the formation of one great master-piece of machinery. It is to be regretted that, in the formation of a system of weights and measures, while such extreme importance was attached to the discovery and assumption of a national standard of long measure as the link of connection between them all, so little consideration was given to that primitive link of connection between them, which had existed in the identity of weights and of silver coins, and of which France, as well as every other nation in Europe, could still perceive the ruins in her monetary system then existing. Her livre tournois, like the pound sterling, was a degeneracy, and a much greater one, from a pound weight of silver, but it had scarcely a seventieth part of its original value. It was divided into twenty sols or shillings; and the sol was of twelve deniers or pence. It had become a mere money of account: but the ecu, or crown, was a silver coin of six livres, nearly equivalent to an ounce in weight, and there were half crowns, and other subdivisions of it, being coins of one-fourth, one-fifth, one-eighth, and one-tenth, of the crown. There were also coins of gold, of copper, and of mixed metal called billon, in the ordinary circulations of exchange. Shortly after the adoption of the provisional or temporary metre and kilogramme, a law of 16 Vendemaire 2, (7th October, 1793,) prescribed that the principal unit, both of gold and of silver coins, should be of the weight of ten grammes. The proportional value of gold to silver was retained as it had long before been established in France, at 154 for one: the alloy of both coins was fixed at one-tenth; and the silver franc of that coinage would have been worth about thirty-eight cents, and the gold franc a little short of six dollars. This law was never carried into execution. It was superseded by one of 15th August, 1794, (28 Thermidor S,) which reduced the silver franc to five grammes: and it was not until after a law of 7 Germinal 11, (28th March, 1803,) that gold pieces of twenty and forty francs were coined at 155 of the former to the kilogramme.

In the new system, the name of livre, or pound, as applied to money or coins, was discarded: but the franc was made the unit both of coins and moneys of account. The franc was a name which had before been in common use as a synonymous denomination of the livre. The new franc was of intrinsic value more than the livre. The franc is decimally divided into decimes of, centimes of, and millimes of, of the unit; but the smallest copper coin in common use is of five centimes, equivalent to about one of our cents. The silver coins are of one-fourth, one-half, one and two francs, and of five francs; the gold pieces, of twenty and forty francs. The proportional value of copper to silver is of one to forty, and that of billon to silver of one to four: so that the kilogramme should weigh 5 francs of copper coin, 50 of the billon, 200 of the silver, and 3100 of the gold coins: and the decime of billon should weigh precisely

two grammes. The allowances, known by the name of remedy for errors in the weight and purity of the coins, are of

upon copper,

which is only for excess: those upon the weight of billon are of upon silver for one-quarter francs, for one-half francs, and of or one per cent. on one and two franc pieces, and of Too for five franc pieces. That of the gold coins is of; all, excepting the copper, allowances either for excess or deficiency. But the practice of the mint never transgresses in excess; and the deficiency is always nearly the whole allowed by law. The remedy of alloy is of either of excess or defect, for billon; of To for silver; and of 1 for gold. It is said that the actual purity of the coins, both of gold and of silver, is within To less than the standard. The conveniences of this system are,

First, The establishment of the same proportion of alloy to both gold and silver coins, and that proportion decimal.

Secondly, The established proportions of value between gold, silver, mixed metal, and copper coins.

Thirdly, The adaptation of all the coins to the weights in such manner as to be checks upon and tests of each other. Thus the decime of billon should weigh two grammes, the franc of silver five, the two franc piece of silver and the five centime piece of copper each ten, and the five franc piece fifty. The allowances of remedy disturb partially these proportions. These are practices continued in all the European mints, after the reasons upon which they were originally founded have in a great measure ceased. In the imperfection of the art, the mixture of the metals used in coining, and the striking of the coins, could not be effected with entire accuracy. There would be some variety in the mixture of metals made at different times, though in the same intended proportions, and in different pieces of coin, though struck by the same process and from the same die. But the art of coining metals has now attained a perfection, that such allowances have become, if not altogether, in a great measure unnecessary. Our laws make none for the deficiencies of weight: and they consider every deficiency of purity as an error, for which the officers of the mint shall be excused only in case of its being within part, or about To; for if it should exceed that, they are disqualified from holding their offices. Where the penalty is so severe, it is proper that the allowance should be large; but, as obligatory duty upon the officers of the mint, an allowance of ToOO would be amply sufficient for each single piece, and no allowance should be made upon the average.

Among the difficulties attending all innovations upon established usages relative to weights and measures, are their application to the tonnage of ships and boats, and to the form and size of casks. We have seen, in the review of the history of English weights and measures, how Henry the Seventh's change of the Rochelle for the troy pound affected the barrels of herring fishers, the hogshead of claret, and the butts of Alicant wine. The tonnage of ships, on the old established metrologies, was founded, like their weights and measures

of capacity, upon a principle of combining specific gravity and occupied space. The ton of shipping was adapted both for a weight and a measure. The capacity of a ship as a measure is ascertained by its internal cubical dimensions, which, before the change of system in France, gave 42 royal cubic feet to a ton. The mode of admeasurement was, like ours, a complicated multiplication and division of length, breadth, and thickness, with given deductions and estimates, all finally divided by the standing number, 94, as ours is by 95, and the quotient of which gives the number of what may be called custom house tons. But the French ordinances, like our law, did not indicate by what specific measure this length, breadth, and thickness, were to be taken. It was always perfectly understood here, that it is in feet, and tenths of feet; and in France, that it was in royal feet and their tenths. Nothing can afford a more striking illustration of the construction which long established usage can give to law, than this admeasurement in feet and tenth parts of a foot; differing from that used in all other cases of feet and inches or twelfth parts; not expressly directed by law, and yet practised for these thirty years, probably without a question upon the meaning of the law. The attempt in France to apply it to the admeasurement by the metre, without changing the final common divisor 95, signally shows how cautiously complications of weights, measures, numbers, and coins, must be dealt with. The law of the 12th Nivose 2, (1st January, 1794,) directed those measures to be taken in the new metre and divisions, without changing the final divisor, 95, to produce a number of tons. The consequence would have been, that the cubic numbers divided by 95 would have been metres and their decimal parts, instead of feet and their decimal parts; and the quotient would have reduced the tonnage to about one third of its proper dimensions. To have produced a quotient of a number of tons, their final divisor should have been 30 instead of 95. This mistake was precisely the same as that of the British parliament of 1496, when, thinking to reenact the law of 1266, they prescribed a bushel to be made from sixty-four gallons troy weight of wheat of thirty-two kernels to the troy pennyweight, instead of a bushel of sixty-four pounds sterling at fifteen ounces to the pound, of wheat, thirty-two kernels of which weighed the penny sterling of Henry the Third. It was the same mistake which the Greek Church yearly repeats in celebrating Easter, by the Julian calendar of 365 days 6 hours to the year, and the lunar cycle of nineteen years. And, to come nearer home to ourselves, it was the same mistake which our own statute book discloses, in estimating the British pound sterling four dollars forty-four cents, because one hundred and ten years ago Sir Isaac Newton found the Spanish Mexican piece of eight to be of the intrinsic value of four shillings and six pence sterling.

The burden of a ship, as a weight, is ascertained by the depth of the water that she draws. On the principles of hydrostatics, the weight of any floating object is equal to that of the mass of water displaced by it: and the weight of a ship's burden is the difference

between the column of water drawn by her when in ballast, and when laden. The draft of water, therefore, measured by the metre and its divisions, gives of itself the result, in tons of 1000 kilogrammes, by the mere multiplication of the dimensions of the vessels; the result giving cubic metres of water, each of which, saving the difference between the specific gravity of river or sea, and distilled water, will of course be of 1000 kilogrammes.

The size of casks was among the objects intended to be included in the reformed system: and regulations were adopted prescribing, first, that their dimensions should be of uniform proportions, the diameter of the two ends, that of the centre, and the length of the barrels, being as 8, 9, and 104 to each other; and, secondly, that their contents should be in decimal or subdecimal divisions of litres. Tables were published prescribing the dimension in millimetres of the length and diametres of each cask, from the contents of 50 to those of 1000 litres. But the forms and proportions of casks are different in different countries, and in different places of the same country. These differences may arise from the nature of the substance, liquid or dry, which they are to contain; from the materials of which they are made or with which they are bound; from laws or usages long established, to which the cooper, the vintner, or brewer, the merchant, the miller, and other numerous professions dealing in articles which are packed in barrels, have accommodated themselves from time immemorial. With regard to articles of exportation, the laws of other countries also interpose, by prohibiting their admission in casks of other dimensions than those which have been used: and the instruction of 2 Frimaire 11, (23d November, 1802) revoked the regulation of Pluviose 7, (January, 1799) requiring only thenceforth, according to the proclamation of 11 Thermidor 7, (29th July, 1799,) that no wines or other liquors should be exposed to sale, unless branded with the mark of their contents in litres; with a recommendation, however, that casks should be made as much as possible in the dimensions and proportions which had been ordained in January, 1799.

The intentions of reformation upon the principles of uniformity and of decimal divisions were, in the novelty of the system, extended to the mariner's compass, which it was proposed to divide into forty rhumbs of wind, instead of thirty-two; to the log-line, the usual divisions of which are proportioned to the marine mile of sixty to a degree; to the sounding line, which had usually been divided by French mariners, not into their fathoms of six, but into brasses of five royal feet; and to the cable's length, which was of 100 toises. Some of these were consequences of the project for dividing decimally time, and the quadrant of the circle: and the others followed from the substitution of the metre for the foot and toise.

The lapidaries and dealers in precious stones, throughout Europe, have a weight peculiar to themselves, under the denomination of the carat, which is nearly of the weight of three grains troy, and which they divide into halves, quarters, eighths, and sixteenths. As this trade is of extremely limited extent, even in Europe, it was to