Sir John Herschel claimed, first, that the metre was not exactly the ten-millionth of the terrestrial meridian passing through France, which was entirely correct, and that, therefore, it was not a good unit for international use, which does not at all follow. He further attempted to show that the polar radius of the earth, which could never be known except indirectly, was a better unit than the quadrant, a large part of which could be measured directly, and that this radius differed by only eighty-two yards from 500,500,000 English inches. He then proposed to increase the English standard by its one-thousandth part, so as to furnish what he declared would then be "a system of linear measurement the purest and most ideally perfect imaginable." It has always been a surprise that so able a mathematician and astronomer could have overlooked the inherent weakness in such an argument. To those who have followed the history of this subject it is unnecessary to say that for many years no metrologist has thought for a moment of relating the standard of length accurately to any terrestrial dimension. The precision of our knowledge of the figure and dimensions of the earth, now and for many years to come, is such as to forbid this, even if there were no other arguments against it. In the light of current geodesy Sir John's calculations themselves furnish a curiously interesting proof of this. The argument with which he opposed the metre may to-day be turned with equal force against his proposed "ideally perfect" inch. According to the latest determination of the polar radius of the earth, his eighty-four yards become more than one thousand yards, and if his scheme had been adopted when proposed it would have been as badly "out of joint" with Nature as is the metre.
The simple facts are that while in the beginning the metre was made to be as nearly as possible one ten-millionth of the meridian, no one imagined that it could be exactly so, or rather that we could ever know that it was exactly so. It is sufficiently near that value to be very convenient in calculations relating to terrestrial distances and areas, but it must always be considered as defined by a material standard, and no metrologist ever thinks of it in any other sense. Within a few years Michelson has devised a method of measuring light waves with an accuracy hitherto unthought of, and has measured the length of several such waves in terms of the international prototype metre at Paris, so that we have the metre related to what we may assume to be an invariable dimension in Nature, with a degree of accuracy extremely satisfactory at the present time. But this does not alter the fact that it is and must be regarded as an arbitrary unit represented by a material prototype. Keeping this fact in mind, it will not be necessary to point out the total irrelevancy of Herschel's argument.