Mr Smeaton seems to ascribe the failure of Hook's method to the different resistance which the different hard ness in parts of the metal presented to the action of the screw ; and undoubtedly this afforded one source of error. But we are of opinion, that much greater errors arose from the screw not being so sharp at the end of the arc as it was at the beginning ; and that notching the screw, in or der to produce the full tooth, made it cut sharper with the preceding edge of the threads in some parts, and the following edge in others ; a fact which is mentioned by Troughton as having embarrassed him in racking his en gine.
Both Hook and Hevelius, in their controversy, pretend ed, in measuring an angle, to come at the exactness of a single second ; but as they flourished upon the verge of an age when most things relative to science were taken upon credit, perhaps their works should not be too se verely criticised by those who live at a time when every thing is tried by the test of experiment.
The polar sector of Flamstead, made by Tompion, with which he made so many observations from 1676 to 1689, bore the screw division ; but its gross errors obliged Mr Flamstead himself to perform an original diagonal gradua tion upon its limb. It was about the latter date that a mural arc was completed for the royal observatory, which, under the direction of Flamstead, was altogether constructed by his assistant Mr Sharp. This also had the division of Hook, but it does not appear to have succeeded better than that executed by Tompion : however, Sharp's instru ment was at first furnished with a diagonal graduation more accurate than any that had preceded it.
The celebrated astronomer of Denmark, Olaus Roemer, about the year 1715, finished a mural arc. Probably know ing of the failure of the screw method in England, he per formed his graduation in a very different way. Mr Smea ton, in the paper before alluded to, introduces his account of Roemer's method with the following remark : " Though it is a very simple problem, by which geometricians teach how to divide a given right line into any number of pal ts required, yet it is still a much more simple thing to set off upon a given right line, from a point given, any num ber of equal parts required, where the total length is not exactly limited ; for this amounts to nothing more than as suming a convenient opening of the compasses, and be ginning at the given point, to set off the opening of the compasses as many times in succession as there are equal parts required ; which process is as applicable to the arch of a circle, as it is to a right line. Of this simple princi
ple Roemer endeavoured to avail himself." To this end he took two finely pointed pieces of steel, and bound them firmly together at a which, as nearly as he could calculate, would give him divisions upon his arc of 10' each. This contrivance was to avoid the spring of long-legged compasses, and was, for the purpose intended, much bet ter than the best spring-dividers of the present day. With this distance between the points of the tool, set off in suc cession 450 times, Roemer divided his arc of 75°. This way of dividing has appropriately been denominated sten ping, and Hook's can be considered in no other light. Nei ther of them could give exactness in the total arc, even within moderate limits ; but this defect, great as it is, would have been amply compensated for, had they secured the grand desideratum of equal parts. Smeaton is of opi nion, that of those two methods, Hook's is the best, because the screw, in making the teeth, has hold of several at a time ; and, as far as neighbouring divisions are concerned, it certainly is so : but with respect to distant ones, as well as general accuracy, we feel inclined to give the preference to Roemer's. The astronomer of Uramburg was the first who read off the angles observed with instruments, by means of a double microscope ; not indeed by a wire put in motion by a micrometer screw, as is now done. Instead of this, 10 equidistant parallel lines of single silk were stretch ed across the field of view, and being adjusted so as to fill the space between two of his dots, gave him single mi nutes : the seconds were obtained only by estimation.
Soon after the death of Flamstead, the royal observatory was unfurnished. It has been said, that his executors de manded a higher price for the instruments than govern ment thought it right to pay. This was the more excusa ble in the latter, as it is probable that it was in contempla tion to procure new ones, in which case the old ones were intrinsically of no more value than the materials of which they were composed ; yet it is a pity that those venerable and solid records of art should have left the spot where they had been so useful in their day.