Sir George (Phil. Trans. for 1798) examined the errors of division in several of the old British standard measures,• and compared their length with his own, made by Trough ton in 1796. The first in his list is the standard yard of Henry VII. about the year 1490, which is said to have been taken from the length of the arm of that monarch; but as history is silent respecting this trait of his great ness, it may be presumed that the surveyors of his Ma jesty's person took for the purpose hall the distance be tween the extreme finger ends of out-stretched hands and arms. Upon this standard the greatest measured interval exceeds the least, by no less a quantity than .152 of an inch ; and the whole yard is .076 of an inch shorter than Sir George's. In the standard yard of Elizabeth, about 1588, the greatest interval exceeds the least by .185, and the entire yard is .015 longer. For the standard ell of Elizabeth, of the same date, the greatest difference of intervals is .072, and the whole length exceeds the mo dern standard by .016 of an inch.
Many of our Standard measures bear no subdivisions, being simply finished to the length. Of these, nothing but their whole extent could be examined ; and this was done by Graham in the four following instances. The yard-bed of Guildhall, about 1660, too long by .032. Ell bed of Guildhall, same date, .018 too long. A standard belonging to the clock-makers' company, about 1671, too short by .028 on 36 inches. And the standard of the tower of London, about 1720, made by P.owley, was .004 too long.
Graham's own standard, made by Sisson, in 1742, with which it is supposed the above comparisons were made, was itself examined by Sir George, and found to be as follows : line E, .0013 longer, and line Exch..0067 shorter, upon 36 inches, than his own.
Many of the above measures exhibit miserable work ; a neat hand, by doubling, tripling, &c. a string, and ma king notches with a file, would subdivide better. But it is likely, and indeed the list indicates as much, that great er attention was paid to the whole length, than was done to the intermediate parts; yet are the yard•bed of Guild hall, and the standard of the clock-makers company, ex ceptions, and differ from each other by no less than .06 of an inch. Indeed, it seems difficult to suppose that the makers of those measures did their very best. It is more probable, that, according to their own judgment, or that of the times in which they lived, they thought their works sufficiently correct for the purpose ; or, as the ancient as tronomers graduated their own instruments,—might not the magistrates of old make their own standard measures ? Hevelius, and the astronomers who preceded him, made their observations without the assistance of tele scopes, and the result of the well-known controversy be tween Hevelius and Dr Hook speaks highly in favour of the d;vision of his sector ; for men of science decided the dispute in favour of the Dantzig astronomer, from the superior accuracy of his observations; whereas, had the instruments of Hook been equal in other respects, the telescopic sights, as is now well known, must have given him the advantage.
Dr Hook, in his animadversions upon the Machine Calestis of Hevelius, published in 1674 the first method of graduation that has been described. It consisted of indenting the edge of an arc by the rotation of a screw about its axis, in the manner that has since been practised with success in the dividing engine ; the indentations them selves stood for the divisions of the instrument, the angu lar value of which were to be found by other means. A screw similar to that which cut the teeth, was connected with the telescope; and the number of teeth, and parts of a tooth, as shewn upon the micrometer head of the screw, gave the observed angle.
As the inventor of this method describes no means for correcting distant divisions, it may fairly be concluded, that he did not foresee the necessity of any. And his own Words bear out this supposition. Dr Hook entitles it, ?n explication of the new way of dividing : and says, that the perfection of his instrimzent is in the way of making the division ; that it excels all the common ways of divi sion ; and that it does not at a11 depend upon the care and diligence of the instrument-maker, in dividing, graving or numbering the divisicns, for the same screw makes it from end to end.
With such screws as may be supposed to have been in use at that time, their want of truth could have had no good effect upon the run from end to end of the arc ; yet as the same error would recur at every complete revolu tion, no material mischief might arise. But it is evident that the parts of a revolution would be affected by the whole amount of such error. The method was put in practice by Tompion, Sharp, Rowley, the Due dc Ghoul nes, and perhaps many others; but in every recorded in stance it completely failed ; and such instruments as bore this graduation, before they could be depended on to any uselul degree, were furnished with hand dividing.