Graham undertook, about the year 1725, to construct for our national establishment an eight feet mural quadrant. This magnificent instrument still occupies its place ; and though great part of a century has elapsed since its erec tion, it seems not to have suffered at all from either use or time. Its frame is made of iron : the arc which bears the graduation, as also the telescope and centre work, are of brass. The contrivance and execution of the whole are admirable ; but it should be remembered, that its division alone is applicable to our present article.
To Graham, in the graduation of this quadrant,has been ascribed the rejection of the diagonal method ; but certain ly he was not the first ; for Hook and Roemer did the same. He has also the credit of being the first who discontinued the practice of cutting the divisions by the edge of a ruler with the dividing-knife, instead of which he substituted the beam-compass. His strokes cut in this way, of course, were circular arcs ; but as they were short in comparison with the length of the beam, the bend was scarcely per ceptible ; and as the resting point was set in a line that made a tangent to the arc where the strokes were cut, the latter would stand nearly in the direction of the radius. With respect to making divisions with the beam-compass, it may be doubted whether it was not a practice among in strument makers, particularly upon chamfered edges, be fore the time that the Greenwich quadrant was finished ; and we have seen old works that indicated it. But there was another improvement of much more importance than either of the above, which was indisputably the invention of Graham ; that is, the division of the quadrant into 96, which precludes altogether the practice of stepping, and has ren dered essential service to astronomy.
Graham's quadrant is described at length in Smith's Optics, and we have availed ourselves of the process pur sued in its graduation, by copying the following account from that celebrated work.
are 2 arches struck upon the brass limb ; one with a radius of 8 feet, or more exactly of 96.85 inches; and the other with a radius of 95.8 inches. This inner arch is divided into degrees, and 12th parts of a degree ; and the outward arch into 96 equal parts, which are severally sub divided into 16 equal parts. The beam of the compass which struck these arches, was secured from bending, by several braces fastened to it ; and when an arch was struck, 60 degrees of it was determined, by placing one point of the compass at a, (Fig. 1. Plate CCLXXXII.) and by
making a strobe with the other at b. This arch a b, was bisected in c, by drawing two small arches upon the cen tres a and b, with such a radius as to cross the arch a c b, in two points as near together as possible, without touching each other ; then the small interval between them was bi sected at c, by estimation of the eye, assisted by a magnify ing glass. After this, the interval between the points a and c, or c and b, was taken with the beam compass, and was transferred from b to d, which determined the length of the quadrantal arch a c b d. Every one of the three arches being bisected in the same manner, the quadrant became divided into six equal parts, containing 15 degrees apiece ; and every one of these was divided into three equal parts, as follows. To avoid making any false or superfluous points in the quadrantal arch, with its radius unaltered, but upon any other centre, there was struck another faint arch, upon which the chord of 15 degrees, already found, was transferred from the quadrantal arch ; and the third part of 15 degrees, being determined by trials upon the faint arch, was transferred hack again upon the quadrantal arch ; which then was divided into 18 equal parts, containing 5 degrees apiece ; and the 5th part of these was found by trials, as before, in dividing a separate arch, drawn upon a new centre for this purpose only. The subdivisions of the degrees into 12 equal parts, were made by bisections and trisections, as before. Thus was the whole quadrant di vided without any false or superfluous points.
The outward quadrantal arch was divided into 96 equal parts, by no other method than that of bisection, till 60 de grees, or two thirds of the quadrant, became divided into 64, and the remaining third into 32 equal parts, which make 96 in the whole. And every one of these was also divided into 16 equal parts by continual bisections. These two sorts of divisions are a check upon each other, being in ef fect two different quadrants ; and the divisions in one being reduced into the divisions of the other, by a table made for that purpose, they are never found to differ above five or six seconds in any place of the limb, and when they do, the preference ought to be given to the bisected divisions, as being determined by a simpler operation.