The plane of the quadrant is fixed to the wall, and adjusted in any position by nearly the same number of holdfasts as there are little squares round about the quadrant, as in Fig. 2. Each holdfast consists of two separate parts, one of which is fixed to the wall and the other to the quadrant.
A transverse section of the wall a b is shown in Fig. 7. where c, c, Ste. are the holdfasts. Between the chops of each, shown at d e, there passes one end of a small brass plate, having its plane parallel to that of the quadrant, the other end being bent to a right angle, and rivetted to the perpendicular bars.of the quadrant. Each plate is, besides, pinched by two opposite screws r s, which work through the chops d e, made pretty wide for the purpose of adjusting the position of the plane of the quadrant. Another use of the screws in the chops was, in the event of the wall or quadrant swelling or shrinking, so to alter their proportions that the brass plates might slide without distending the instrument. As lead is apt to yield, the holdfasts are fastened in the wall with a composition of stone, dust, pitch, and brimstone, or rosin, such as stonecutters use for cementing broken stones.
The next point of importance is to balance the tele scope, so that it may have a free and easy motion round the centre of the quadrant. This is done by the me thod shown in Fig. 5. where a b is an iron axis laid across the top of..the wall, having two brass plates fixed perpendicular to the ends of it, with notches or holes cut in them for the axis to turn in, which points to the centre of the quadrant at right angles to its plane. To the end of the axis next the quadrant, is fixed an iron arm c d, having two brass plates c e, d f, almost per pendicular to it, and to them are rivetted two slender slips of fir, whose other ends meet at g, near the eye glass, being held together in a brass cap or socket.
Through a small plate fixed to one side of a collar, em bracing this lower end of the telescope, there passes a screw-pin at g, parallel to the telescope ; which pin being screwed into the cap at the end of the slips, keeps up the telescope tight against the centre work. The slips are strengthened by five or six cross braces of the same wood, as represented in the figure. To the other end of the axis a 1), another arm h i is fixed, parallel to the telescope, and in a contrary direction, carrying a weight i to counterpoise the weight of the telescope, and make it rest in any position. And for greater ease
and freedom of its motion, two small brass rollers are fixed to each side of it, at k and 1, which are held tight to the plane of the limb by a plate springing against its backside, which plate has also a roller at each end of it, When the telescope is pretty nearly directed to an object whose altitude is to be taken, a plate in n, which is carried by the telescope along the limb and lies across it, may be fixed to it by a screw, not here represented. Then by twisting the head o of a long screw o p, which is parallel to the limb, and which works through a female screw annexed to the plate m n, and whose neck at ft, turns round in a collar annexed to the telescope ; a very gradual motion is given to the telescope for bringing the cross hairs exactly to cover the object.
To avoid the trouble of subdividing the quadrantal arch into smaller parts, the telescope carries a small brass plate, which slides upon the limb, and is called is Xanius, from the name of its inventor. To understand the reason and use of this plate, it is convenient to premise the following theorem :—If a line , a f, be di vided into number of equal parts, a b, b c, c d, d e, and an equal line w be divided into other equal parts, a p, p 7, 7 e, whose number is one less than the number of parts in a f; then a (3, a y, a a E, will ex ceed a 1), a c, a d, a e, respectively, by one, two, three, four parts of a b, whose denominator is the number of parts in a e, or in a e. For, let. the lines a f, a E, be coincident at both ends, and since any equitnultiples of two a b, a p, are in the same ratio as the quantities, themselves, (Euclid, v. 15.)it will be as a b : al3=ac : cey=ad ca=ae ae, or af, and disjointly as ab : bp=ac: cy=ad e E, or ef. The conse quents b p, c d e E, are therefore in the same arith metical progression as the antecedents a b, a c, a d, a e, and the first of the consequents b f3, is the same part of its antecedent a b, as the last consequent e f is of its antecedent a e, or as ap is of ME, the number of parts in a e and a e being equal b) the first supposition. And it is manifest, that any two equal and coincident arches or a circle have the sane property.