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even a fraction of a mill. These eighths and sixteenths form a very considerable proportion of our metallic currency : and although the eighth dividing the cent only into halves adapts itself without inconvenience to the system, the fraction of the sixteenth is not so tractable; and in its circulation, as small change, it passes for six cents, though its value is six and a quarter, and there is a loss by its circulation of four per cent, between the buyer and the seller. For all the transactions of retail trade, the eighth and sixteenth of a dollar are among the most useful and convenient of our coins: and, although we have never coined them ourselves, we should have felt the want of them, if they had not been supplied to us from the coinage of Spain.

This illustration, from our own experience, of the modification with which decimal arithmetic is adaptable even to money, its most intimate and congenial natural relative, will disclose to our view the causes which limit the exclusive application of decimal arithmetic to numbers, and admit only a partial and qualified application of them to weight or measure.

It has already been remarked, that the only apparent advantage of substituting an aliquot part of the circumference of the earth, instead of a definite portion of the human body, for the natural unit of linear measure, is, that it forms a basis for a system embracing all the objects of human mensuration; and that its usefulness depends upon its application to geography and astronomy, and particularly to the division of the quadrant of the meridian into centesimal degrees. In the novelty of the system, this was attempted in France, as well as the decimal divisions of time, and of the rhumbs of the wind. A French navigator, suffering practically under the attempt thus to navigate, decimally, the ocean, recommended to the national assembly to decree, that the earth should perform four hundred revolutions in a year. The application of decimal divisions to time, the circle, and the sphere, arc abandoned even in France. And for all the ordinary purposes of mensuration, excepting itinerary measure, the metre is too long for a standard unit of nature. It was a unit most especially inconvenient as a substitute for the foot, a measure to which, with trifling variations of length, all the European nations and their descendants were accustomed. The foot rule has a property very inportant to all the mechanical professions, which have constant occasion for its use: it is light, and easily portable about the person. The metre, very suitable for a staff, or for measuring any portion of the earth, has not the property of being portable about the person : and, for all the professions concerned in ship or house building, and for all who have occasion to use mathematical instruments, it is quite unsuitable. It serves perfectly well as a substitute for the yard or ell, the fathom or perch; but not for the foot. This inconvenience, great in itself, is made irreparable when combined with the exclusive principle of decimal divisions. The union of the metre, and of decimal arithmetic, rejected all compromise with the foot. There was no legitimate extension of matter intermediate between the ell and the palm, between forty inches and four. This decimal despotism was found too arbitrary for endurance; not only the foot, but its duodecimal divisions, were found to be no arbitrary or capricious insti. tutions, but founded in the nature of the relations between man and things. The duodecimal division gives equal aliquot parts of the unit, of two, three, four, and six. By giving the third and the fourth, it indirectly gives the eighth and sixteenth, and gives facility for ascertaining the ninth, or third of the third. Decimal divi. sion, in giving the half, does not even give the quarter, but by multiplication of the subdivisions. It is incommensurable with the third, which unfortunately happened to be the foot, the universal standard unit of the old metrology. The choice of the kilogramme, or cubical decimetre of distilled water, as the single standard unit of weights, with the application to it of the decimal divisions, was followed by similar inconveniences. The pound weight should be a specific gravity easily portable about the person, not only for the convenience of using it as an instrument, but as the measure of quantities to be carried. To the common mass of the people, the use of weights is in the market, or the shop. The article weighed is to be carried home. It is an article of food for the daily subsistence of the individual or his family. As he has not the means of purchasing it in large quantities, it must often be sold in quantities represented by the pound weight, which, like the foot rule, with various modifications, is universally used throughout the European world. Subdivisions of that weight, the half, the quarter of a pound, are often necessary to conciliate the wants and the means of the neediest portion of the people; that portion to whom the justice of weight and measure is a necessary of life, and to whom it is one of the most sacred duties of the legislator to secure that justice, so far as it can be secured by the operation of human institutions. The half of the kilogramme was nearly equivalent to the ancient Paris pound. But there was in the new system no half, or quarter of a pound; because there was no quarter or eighth of a kilogramme. There was no intermediate weight between the pound, or half kilogramme, and the hectogramme, which was a fifth part of a pound.

The litre, or unit of measures of capacity in the new system, had one great advantage over the linear and weight units, by its near equivalence to the old Paris pint, of which it was to take the place. But, on the other hand, decimal divisions are still more inapplicable to measures of capacity for liquids, than to linear measures or weights. The substance in nature best suited for a retail measure of liquids, is tin: and the best form, in which the measure can be moulded, is a slight approach from the cylinder to the cone. Our quart and gallon wine and beer measures are accordingly of that form, as are all the most ordinary vessels used for drinking. In the new French system, the form of all the measures of capacity is cyJindrical; and the litre is a measure, the diameter of which is half its depth. It is, therefore, casily divisible into halves, quarters, and eighths; for it needs only thus to divide the depth, retaining the same diameter. But all conveniences of proportion are lost, by taking one-tenth of the depth and retaining the same diameter: and, if the diameter be reduced, there is no means, other than complicated cal. culation, squarings of the circle, and extractions of cube roots, that will give one liquid measure which shall be the tenth part of another.

In the promiscuous use of the old weights and measures and the new, which was unavoidable in the transition from the one to the other, the approximation to each other of the quarter and the fifth parts of the unit became a frequent source of the most pernicious frauds; frauds upon the scanty pittance of the poor. The small dealers in groceries and liquors, and marketmen, gave the people the fifth of a kilogramme for a half pound, and the fifth of the litre for a half setier. The most easy and natural divisions of liquids are in continual halvings : and the Paris pint was thus divided into halves, quarters, eighths, sixteenths, and thirty-second parts, by the name of chopines, half setiers, possons, half possons, and roquilles. The half setier, just equivalent to our half pint, was the measure in most common use for supplying the daily necessities of the poor; and thus the decimal divisions of the law became snares to the honesty of the seller, and cheats upon the wants of the buyer.

Thus then it has been proved, by the test of experience, that the principle of decimal divisions can be applied only with many qualifications to any general system of metrology; that its natural application is only to numbers; and that time, space, gravity, and extension, inflexibly reject its sway. The new metrology of France, after trying it in its most universal theoretical application, has been compelled to renounce it for all the measures of astronomy, geography, navi. gation, time, the circle, and the sphere; to modify it even for superficial and cubical linear measure, and to compound with vulgar fractions, in the most ordinary and daily uses of all its weights and all its measures. It has restored the foot, the pound, and the pint, with all their old subdivisions, though not exactly with their old dimensions. The foot, with its duodecimal divisions into thumbs and lines, returns in the form the most irreconcileable possible, with the deci. mals of the metre; for it comes in the proportion of three to ten, and consists of 3331 millimetres. This indulgence to linear measure is without qualification, and may be used in all commerce, whether of wholesale or retail. The restoration of the pound, the boisseau, * and the pint, is limited to retail trade. The fractions of the pound are as averse to decimal combinations as those of the foot. The eighth of a pound, for instance, is 625 decigrammes, each of about 13

• One of the most abundant sources of error and confusion, in relation to weights and measures, arises from mistranslation of those of one country into the language of another. Thus, to call the pinte of Paris, a pint, is to give an incorrect idea of its contents. The Paris pinte corresponded with our wine quart, containing 46.95 French, or 58.08 English cubic inches. To call the boisseau a bushel, is a still greater incongruity between the word and the idea connected with it. The boisseau contained 655 French cubic inches, and was less than 1) peck English. The minot, or three boisseaus, was the measure corresponding with the English bushel.

grain troy weight. The half of this eighth is an ounce, to form which decimally requires a recourse to another fractional stage, and to say 31.25 milligrammes. But the milligramme, being equivalent to less than 1 of a grain troy weight, is too minute for accurate application; so that it is called, and marked upon the weight itself as 31.3deci. grammes. The half ounce, instead of 15.625 decimilligrammes, is marked for 15.6 decigrammes. The quarter of an ounce, instead of 7.8125, passes for 7.8 decigrammes, and the gros, or groat, instead of 3.90625, is abridged to 3.9. The ounce and all the smaller weights, therefore, reject the coalition of subdivision by decimal and vulgar fractions : and the weights for account are different from the weights for trade.

From the verdict of experience, therefore, it is doubtful whether the advantage to be obtained by any attempt to apply decimal arithmetic to weights and measures, would ever compensate for the increase of diversity which is the unavoidable consequence of change. Decimal arithmetic is a contrivance of man for computing numbers; and not a property of time, space, or matter. Nature has no partial. ities for the number ten : and the attempt to shackle her freedom with them, will for ever prove abortive.

The imperial decree of March, 1812, by the reservation of a purpose to revise the whole system of the new metrology, after a further interval of ten years of experience, seems to indicate a doubt, whether the system itself can be maintained. Ten years from 1812, was a period far beyond that which Providence had allotted to the continuance of the imperial government itself. The royal government of France, which has since succeeded, has hitherto made no change in the system. Whether, at the expiration of the ten years, limited in the decree, the proposed revisal of it will be accomplished by the present government, is not ascertained. In the mean time, the whole system must be considered as an experiment upon trial even in France: and should it ultimately prove, by its fruits, worthy of the adoption of other nations, it will at least be expedient to postpone engrafting the scion, until the character of the tree shall have been tested, in its native soil, by its fruits.

4. The fourth advantage of the French metrology over that which we possess, consists in the convenient proportions, by which the coins and moneys of account are adjusted to each other, and to the weights.

This is believed to be a great and solid advantage; not possessed exclusively by the French system, for it was, in high perfection, a part of the original English system of weights and measures, as has already been shown. It was more perfect in that system, because the silver coins and weights were not merely proportioned to each other, but the same. This is not the case with the French coins : and even their proportions to the weights are disturbed and unhinged by the mint allowance, or what they call toleration of inaccuracy, both of weight and alloy. This toleration, which is also technically called the remedy, ought every where to be exploded. It is in no casc necessary. The toleration is injustice: the remedy is disease. If it were the duty of this report to present a system of weights, measures, and coins, all referable to a single standard, combining with it, as far as possible, the decimal arithmetic, and of which uniformity should be the pervading principle, without regard to existing usages, it would propose a silver coin of nine parts pure and one of alloy : of thickness equal to one-tenth part of its diameter; the diameter to be one-tenth part of a foot, and the foot one-fourth part of the French metre. This dollar should be the unit of weights as well as of coins and of accounts; and all its divisions and multiples should be decimal. The unit of measures of capacity should be a vessel containing the weight of ten dollars of distilled water, at the temperature of ten degrees of the centigrade thermometer: and the cubical dimensions of this vessel should be ascertained by the weight of its contents; the decimal arithmetic should apply to its weight, and convenient vulgar fractions to its cubical measure. This system once established, the standard weight and purity of the coin should be made an article of the constitution, and declared unalterable by the legislature. The advantage of such a system would be to embrace and establish a principle of uniformity with reference to time, which the French metrology does not possess. The weight would be a perpetual guard upon the purity and value of the coin. No second weight would be necessary or desirable. The coin and the weight would be mutual standards for each other; accessible, at all times, to every individual. Should the effect of such a system only be, as its tendency certainly would be, to deprive the legislative authority of the power to debase the coins, it would cut up by the roots one of the most pernicious practices that ever afflicted man in civil society. By its connection of the linear standard with the French metre, it would possess all the advantages of having that for a unit of its measures of length, and a link of the most useful uniformity with the whole French metrology.

But the consideration of the coins is beyond the scope of the resolutions of the two Houses ; nor is their relation to the weights and measures of the country viewed, by the constitution and laws of the United States, as that of parts of une entire system. Excepting the application of decimal divisions to our money of account, and the establishment of the dollar as the unit both of the money of account and of the silver coins, our moneys have no uniform or convenient adjustment to our weights. The proportion of alloy is not the same in our coins of silver, as in those of gold: and the only connection between our monetary system and our weights and measures is, that the gravity and proportional purity of the coins is prescribed in troy weight grains. To obtain, therefore, the advantage existing in the French metrology, of easy proportions between the weights and coins, or the still greater advantage of identity between them which belonged to the old English system, an entire change would be necessary in the fabrication of our coins, and in our moneys of account.

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