As the divisions now made were only fine points on the arch a d, it was necessary to draw lines through each of them. But as it was both difficult and tedious to draw lines exactly through every point by the edge of a ruler, the following method was adopted ;—In or der to (bride any other concentric arch f k t by cross strokes into parts similar to those in the given arch a cg r b d, take a small beam compass, and having fix ed its points at any convenient interval, upon the centres.', g, being the given points of the divided arch, strike the small arches i k. &c. cutting the undi vided arch in", h, then will the intercepted arches as! h be similar to the arches e g ; that is, they will subtend the sante angles as their common centre o. For joining rj;g h, and also of; o h,o e, o g, the triangles e v f;g 9 h will be similar and equal to each other ; every side in the one being respectively equal to every side in the other. Taking away, therefore, the common angle e o h from the equal angles o g o h, the remaining angles will also be equal. If the triangles r o, g h o be right angled atf and h, the dividing strokes/a h k, 84.c. will cut the quadrantal arch f h t, at right angles also atf and h.
In Fig 4. abed represents a square piece of brass (with several steady pins in it) screwed to the flat bars at the centre of the quadrant, the screw holes be ing so large as not to touch the screws ; and k I at n represents a thick circular plate of brass, with a hollow pipe/ g fixed perpendicular to the middle of it. This plate was turned exactly circular in a lathe upon a brass arbor o i, turned tapering, and a little hollow in the middle, no as to fit the cavity of the pipe f g, and to bear against it chiefly at both ends. When the hol low pipe f g is pet through the holes (exactly fitted for it) in the middle of the square it b c d, the brass circle k I in a, is fixed to the plane of the square a b c d, with screws and steady pins. The point o in the pole of the arbor a i is not only the centre of the circular neck k I ni n, about which the telescope must turn, but also the very centre upon which the divided arches were struck upon the limb of the quadrant. The end of the telescope whit]) holds the object glass lies across one end of an oblong plate of brass a r, at right angles to its sides, and is fixed to the plate by a brace capable of being widened and narrowed with a screw. Near the other end of the plate a I, there is a round hole lined with a steel collar p y r, to be put over the brass neck k I In a, and to turn round upon it The section of this collar taken at right angles to its plane, is shown at a, the broader of the two rings being under the plate 8 t, and contiguous to the square plate a b c d. Over this neck and collar there is fixed a brass spring shown at v, and screwed to the neck k l to n, to keep the collar front slipping from it ; and over all these is screwed a cap, shown at .r, to cover the centre work, and to keep
off the dust, which is also prevented from coming be tween the plates abcd and a t to the neck and collar, by means of a brass hoe surrounding the broad rim or base of the r, and screwed to the backside of the plate a r; which hoop is received into a circular groove 1,2, 3, 4, formed in the square plate without touching any part of it.
The superiority of this centre work consists in pre serving tbe place of the central point of the quadrantal arch in the pole of the arbor a 2. For whenever an unsteady motion of the telescope round the centre of the quadrant shall arise from the wearing of the neck plate A- l ni a, a Ilea neck plate and pipe 'nay be cast, well hammered, and turned upon the poles of the same arbor o i, to fit the hole and collar, and then it will move the telescope round the centre of the limb as correctly as when it was new.
NVe have represented in Fig, 5. the quadrant fixed to the eastern side of a freestone wall, built on purpose in the plane of the meridian. The whole weight of the quadrant is sustained by two strong iron pins fi .cd to the wall, as afterwards described, and projecting through two holes, made in two square plates of iron rivetted to the quadrant at a and b in Fig. 1. The pin at a, which bears the greater part of the weight, is immoveably fixed in the wall, but the pin at b can be screwed up or down by a strong screw in order to bring one side of the quadrant to a horizontal, and the other to a vertical po sition.
Fig. 6. shows the method in which the pin b is moved. An oblong plate of iron lin n a is let into the freestone wall, and fastened to it by bolts of iron, which pass through the wall, and through another plate let into the opposite side of it, the bottom of each plate being bent square and bedded in the stone. The heads of four iron screws are shown at e, f, g, Ii, having the shanks going through four long slits made in another iron plate, shown by the smaller parallelogram, and screwed into the fixed plate 1 n a. The moveable pin b c is fixed to the lesser plate, which is raised or depressed by means of a long screw k i working against the bottom of the pin b c at d, heing turned round in a strong concave screw fixed to the bottom of the larger plate at p ry. The key for turning the long screw k i, is a sector of a circular plate shown at r s t, the square hole in its centre t be ing put upon the shank k. The radius of the key is just so big as to move in the space between the wall and the bars of the quadrant, and a chisel v is inserted into the teeth, upon the arch of the key, to increase the power of moving it.