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country town goes round to try the measures, they find some new measures too small, or perhaps too large : there are frequent complaints of this, and certainly it is very absurd that this should be the case, when it may be remedied so easily.
“ The following measures are wanting at the Exchequer, to make a complete set: Half-gallon, Winchester measure.) Peck ...... Ditto. Quarter-peck Ditto. Half-pint ... Ditto.
Some tradesmen have set the Half-gallon, Wine measure, magistrate at defiance, there Quart.. Ditto.
being no legal standards for these Pint. Ditto.
“ There is some inaccuracy in the weights at the Exchequer : they have one of each, 4 lb., 2 lb., and 1 lb. weight, bell fashion; and the same number of flat weights : but, strange to tell, the bell weights and flat weights differ in weight from each other, except the 2 lb.; and some of the small
weights are not in proportion with the larger ones." “ I am convinced that many weights and measures that are correct are taken away in consequence of these inaccuracies at the fountain head, the Exchequer, and innocent people censured.”
The Committee of the House of Commons on Weights and Measures, in 1758, had the standards of capacity at the Exchequer measured by Mr. Bird and Mr. Harris, then Assay master of the Mint, in their presence. It was found that,
The standard bushel, of the time of Queen Elizabeth, dated 1601, contained 2124 cubic inches.
The standard gallon, dated also 1601, marked with an E and a crown, contained 271 cubic inches.
The standard quart, same date, contained 70 cubic inches. The standard pint, dated 1602, contained 34 cubic inches.
The standard wine-gallon, dated 1707, contained 231} cubie inches.
Here are four standards of capacity, besides that for wine, all legal, and yet differing from each other. If the bushel bé assumed as correct, then the Winchester bushel (whose dimensions are fixed by 13 Will. III. c. 5. § 28) contains too much by 1. of a pint, and the gallon, quart, and pint, should contain 2651, 66, and 331 cubic inches respectively. If the gallon be deemed correct, then the pint should contain 331 inches, the quart 67%, and the bushel 2168. But, if the quart be regarded as correct, the pint should contain 35 inches, the gallon 280, and the bushel 2240, exceeding the actual standard bushel by more than 3 pints! If the gallon be assumed as the basis
of the reduction, other discrepancies will appear: and yet, say the Committee of 1758, as the law now stands, each of these different measures must be understood to contain the like
quantities, to be equally lawful, and may be indiscriminately used.”
In the Report of this Committee of 1758, there is a brief de scription of the then existing standards of length ; namely, a yard supposed to be of the time of Henry VÕI., and a yard and an ell both of the time of Elizabeth. These, say the Committee, s are all very coarsely made, and the divisions that are upon them not exact, and the rods appear to be bent, and are therefore very bad standards.” A more minute description of these standards, as well as of the one that was made by Mr. Bird for the Committee of 1758, and of various other standards and scales, has been published in a most interesting memoir by the late Sir George Shuckburgh Evelyn.* The comparative lengths of these, as referred to one and the same measure, Mr. Troughton's scale of 1796, are as below:
36 inches, on a mean of Hen. VII, standard of
}35-994 1490, are equal to
.03 of standard yard of Eliz, of 1588.
04 of standard ell of ditto ditto.
- 36.0013 + .0013
all made pro- ) 36.00036 of Gen. Roy's (Bird's)scale
+00036 0003 of Mr. Aubert's ditto
35.99880 -00120 0006
the years 17450 of Royal Soc. ditto
35.99955 --00045 +0004
of Mr. Troughton's scale, in 1796........ 36:00000 •00000 .0001 Hence it appears that the standards of length are much nearer to equality than those of weight and capacity; and that, of the most accurately constructed scales, those made or divided by Mr. Bird, for the Royal Society, for the House of Commons and for General Roy, are nearly of equal correctness: the probable error in the divisions, however, being smallest in General Roy's scale. Still, though there be this general accordance, within certain limits, of all the standards and scales for lineal measure, it must not be imagined that there is a similar conformity between the measures in actual use for different
purposes. On the contrary, we have known land-surveyors' chains, of twenty-two yards in length, to differ from each other by more than half a foot; yard-wands to differ by full half an inch; and carpenters' two-feet rules to differ, even when new, by a-fifth of an inch. Nay, we have known carpenters' rules, adjusted to the same standard, and bought of the same maker, to bave a permanent difference in length of an eighth of an inch, occasioned by the different capacities for contraction and expansion of the variously-seasoned wood from which they were made.
* See Phil. Trans, vol. 87, or New Abridgment, vol. xviii. p. 312.
Here, then, are many extraordinary diversities and irregularities, of which, notwithstanding the space devoted to them, we have only presented a condensed account. On the one hand, there are several legislative provisions, from the time of Magna Charta downwards, enacting that “there shall be, throughout the realm, one measure of wine, one of ale, and one of corn; and that it shall be of weights as of measures.” On the other hand, we find, in the several parts of the kingdom, extremely different measures of length, weight, and capacity, called by the same names; an office in the metropolis appointed by law for the prevention of error and irregularity, in which measures are stamped, to evince their correctness, without any examination; and another, in which are preserved standards for reference in all cases of dispute, which, though they are related to each other by the simplest and most obvious proportions, exhibit such gross anomalies as it might have been imagined would never be tolerated but in the rudest states of society. These are evils which, doubtless, call for legislative interference; but the principles by which such interference must be directed are chiefly scientific, and may therefore be exhibited by reviewers, as promoters of literature and science, without wandering from their peculiar province.
On a comparison of the different modes of deducing standards of length, weight, and capacity, and of causing them to flow one from the other, it has, we believe, been long agreed by theorists that the basis should be the standard of length. The grand question, then, is to determine, among the principal means which present themselves to the mind, that which furnishes the simplest and most accurate method of assigning a unit of lineal measure; one that shall be invariable, that shall be founded upon nature, and that shall be easily recoverable supposing the standard to be lost? If, besides these qualities, it recommend itself to people of all countries, by suggesting the means of bringing their several measures to agree, within practically narrow limits, it will be so much the more worthy of adoption.
Now, this important question has been answered by selecting from one or other of the following means, furnished by nature, an invariable standard,
1. From the length which must be given to an open tube or pipe, that it may yield a determinate musical sound.
2. From the altitude to which a person must ascend vertically, to cause the mercury in the barometer to sink a proportional part of its height.
3. From the length of a degree of a meridian in a given latitude, or from the length of a quadrant of such meridian.
4. From the length of a pendulum that shall vibrate in a given interval, in a given latitude.
3. From the space through which a body, falling freely from quiescence, will descend in a given time at a given place.
Of these methods, the first two are elegant in theory, but do not admit of sufficient precision in practice, to require a deliberate examination.
The third method, by the magnitude of the operations on which it depends, and the variety and utility of the scientific researches which it has tended to improve and perfect, has seduced many into its adoption. Among the various projects for reforming the world recommended by the French National Assembly soon after the revolution in that country, this of deducing the measures of length, and thence of capacity and weight, from a quadrant of ameridian, was proposed and strongly enforced. The most eminent members of the Paris Academy of Sciences, Lagrange, Laplace, Lalande, Borda, &c. recommended it warmly; and two skilful astronomers both in theory and practice, MM. Mechain and Delambre, were appointed to conduct the grand geodesic operations which were to issue in this momentous. result. Their part of the task was executed with astonishing perseverance and talent, and the work in which their operations are detailed (Base du Système métrique) is a valuable repository of principles and formulæ which must stand high in the estimation of men of science so long as mathematical genius is duly appreciated. The system of weights and measures founded upon this admeasurement, was adopted by the law of the 1st of August, 1793. Its nature and its nomenclature are so well known, that we need say no more of them in this place than that the unit of lineal measure, called the metre, is the ten millionth part of a quadrant of a meridian, that all the parts and multiples of this are regulated solely according to the decimal progression, and that the names by which they, as well as the several measures of weight and capacity, are distinguished, are peculiarly forced and pedantic. It appears from some recent decrees that attempts will be made to introduce a similar system in Holland, and we cannot but suspect that the nobleman who has been devoting himself to the reformation of English weights and measures, has directed his thoughts in the same channel. Yet it is now well known * that the system has failed in France; and we are decidedly of opinion that it ought to fail.
Let it be recollected that the proposition which affirms the ellipticity of the terrestrial meridians is a mere hypothetical assumption. Certain theoretic principles being granted, we know that the earth must be an ellipsoid of revolution. But we know that these principles do not accord with the physical constitution of the earth. And so far as actual measurements justify us in making any conclusions, they are that the meridians are not ellipses, that they are not alike, and that the two portions of any one meridian on different sides of the equator are neither similar nor equal. Upon what authority, then, can any one of these meridians, or rather, can a quarter of any one of them, be assumed as that which shall furnish the standard ?
But, farther, suppose the choice of a meridian to be satisfactorily made, how is it to be measured? That the entire amplitude of even a quarter of the meridian cannot be actually measured is evident. Its length, then, must be inferred; and from what? From the measure of a certain portion; and on the choice of that portion will depend the computed length of the meridian, and thence the inferred length of the metre. Thus it happens that different philosophers have deduced various lengths of the metre, according to the way in which they have applied the results of tlie geodesic operations. What is technically called the compression of the earth has been variously assigned, between iso and to; and consequent varieties of the metre between 443.24487 lines of the old Paris foot, and 443.31225 lines. The metre adopted by the commission was 443.295936 lines (equivalent to 39.3702 of our inches); but Delambre informs us that “his. advice has always been that the metre should be 443.31, or 443 1. lines, in round numbers."
Here, then, we have diversity of results from the same operations. Let us inquire a little farther, on what does the accuracy of these operations depend? Obviously, on the correctness of the angles observed, and on that of the measured base or bases of verification. If the original base be inaccurately measured, the computed lengths of the sides in the chain of triangles, and ultimately the length of the quadrant of the meridian, become proportionally wrong. Why, then, is not the standard of lineal measure at once connected with a convenient base of verification, at home? one whose bounds are marked by fixed points, and
* Dr. Kelly has published in his Metrology, a letter from a French merchant,
Imperial decrees” of 1812, from which it appears that men of business, may employ, instead of the metre and its multiples and parts, those of the aune; instead of those of the gramme and the litre, corresponding measures of the livre usuelle and the boisseau.