The decimal scale is made easy of use by the happy system of notation borrowed from the Hindoos, which might be applied equally well to an octaval scale; but at this time it would be vain to propose a change in the radix of the numerical scale. The number ten is the recognized starting-point, and gives its name to the scale. It only remains for us at present to follow other nations in applying it to an improved system of weights and measures.
A system of weights and measures born of philosophy, rather than of chance, is what we now seek. To this end old systems must be abandoned. A chance system cannot be universal: science is universal; therefore what is produced by science may find a home everywhere. If we consider the proper elements or characteristics of such a system, we find at least three essential conditions. First, the new system must have in itself the assurance of unvarying stability, and, to this end, it should be derived from some standard in Nature by which to correct errors creeping into the weights and measures from time or imperfect manufacture. Secondly, the parts should be divided decimally, as nearly as practice will warrant, in conformity with our arithmetic. Thirdly, it should be such as to disturb national prejudices as little as possible.
To a common observer the difficulties of finding an unvarying standard are not readily apparent. But philosophy shows that all things in Nature are undergoing change; so that there would seem to be no invariable magnitude, the same in all countries and in all times, as Cicero pictured the great principles of Natural Law,[56] by which a lost standard on an inaccessible island might be reproduced with mathematical certainty. There is but one magnitude in Nature which, so far as we know, approximates to these requisites. I refer to the length of the pendulum vibrating seconds, which in our latitude is about 39.1 inches. This length, however, varies in travelling from the equator to the pole, and it also varies slightly under different meridians and the same latitude; but the law of variation has been determined with considerable accuracy. One element in this variation is the difference of temperature. In his report on weights and measures, Mr. Jefferson proposed that we should find our standard in the pendulum. At the same time, the French Government, just struggling to throw off ancestral institutions, conceived the idea of a new system, which, founded in science, should be common to the civilized world.
The French began not only by discarding old systems, but also by discarding a measure derived from the pendulum. They conceived the idea of measuring an arc of the earth’s meridian, and finding a new unit in a subdivision of this immense span. The work was undertaken. An arc of the meridian, embracing upward of nine degrees of latitude, and extending from Dunkirk, in France, to the Mediterranean, near Barcelona, in Spain, was measured with scientific care. Illustrious names in French science, Méchain and Delambre, were engaged in the work, which proceeded, notwithstanding domestic convulsion and foreign war. The Reign of Terror at home and invasion from abroad did not arrest it. Seven years elapsed before the measurements were completed, when other nations were invited to coöperate in the establishment of the new system.
The unit of measure was one ten-millionth part of the distance between the equator and the north pole thus measured. It received the name of metre, from the Greek, signifying measure. A bar of platinum, representing this length, was prepared with all possible accuracy. This bar was deposited in the archives of France as the perpetual standard. Other bars have been copied from it and distributed throughout France and in foreign countries.
There is something transcendental in the idea of this measurement of the earth in order to find a measure for daily life. It was an immense undertaking. But the conception seems to have been vast rather than practical. There is reason to believe, from later labors, that there was a serious error in the work. Thus, the distance of 10,000,000 metres from the equator to the north pole, established by the French observers, is too small by 935 yards, according to Bessel,—by 1,410 yards, according to Puissant,—and by 1,967 yards, according to Chazallon. Sir John Herschell also testifies with the authority of his great name against the accuracy of this result. If there be an error such as is supposed, then the metre ceases to be what it was called originally, one ten-millionth part of the distance from the equator to the north pole.
Even assuming that there is no error, and that the metre is precisely what it purports to be, yet it is not easy to see how the artificial standard can be corrected by recurrence to the standard in Nature. The massive work originally undertaken will not be repeated. The astronomers of France will not verify the accuracy of the bar of platinum, which is the artificial standard, by another scientific enterprise, requiring years for completion. Therefore, for all practical purposes, the metre is really nothing else than a bar of platinum with a certain length preserved in the archives of France. It is not less arbitrary as a standard than the yard or foot, and it can be perpetuated in practice only by distribution of exact copies from the original bar, which is the assumed metre.
I have thus explained the origin and character of the metre, because I desire that the admirable system founded on it should be seen actually as it is. To my mind, it gains nothing from the theory which presided at its origin. Its unit is not to be regarded as a certain portion of the distance between the equator and the north pole, but as an artificial measure determined with peculiar care. Had the same or any other unit been selected without measurement of the earth, the metric system would not have been less beautiful or perfect.