QUADRANT. 



Quadrant. We have represented in Fig. 5. the quadrant fixed 



y""*'^* to the eastern side of a freestone wall, built on pur- 

 LX vi P ose ' n l ' le P' anv * l ' lc * '"tridian. The whole weight 



F.c 5. ' * tne quadrant is sustained by two strong iron pins 

 fixed to the wall, as afterwards described, and pro- 

 jecting through two holes, made in two square plates 

 i iron ri vetted to the quadrant at a and li in Fig. 1. 

 Tiu- pin at a, which hears the greater part of the 

 weight, is immoveably fixed in the wall, but the pin 

 at 6 can be screwed up or down by a strong screw 

 in order to bring one side of the quadrant to a hori- 

 zontal, and the other to a vertical position. 



Fig. 6. Fig- C. shows the method in which the pin l> is moved. 



An oblong plate of iron / m n o 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 c, f, g, ft, having the shanks 

 going through four long slits made in another iron 

 plate, shown by the smaller parallelogram, and screw- 

 ed into the fixed plate / in n o. 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 bot- 

 tom of the pin be at d, being turned round in a strong 

 concave screw fixed to the bottom of the larger plate 

 at p q. The key for turning the long screw k i is a 

 sector of a circular plate shown at r st, the square hole 

 in its centre t being put upon the shank k. The radius 

 of the key is just so big as to move in the space be- 

 tween 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. 



The plane of the quadrant is fixed to the wall, and 

 adjusted in any position by nearly the same number 

 ot 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. 



Fie. 7. ^ transverse section of the wall a b is shown in Fig. 7. 



where c, c, &c. 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 

 tor 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, df, 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* Quadrant. 



bracing this lower end of the telescope, there passes a **~' r~-* 



crew-pin at g, parallel to the telescope ; which pin 



being screwed into the cap at theind of the ulipt, 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 It, 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 /, 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 m 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 op, which 

 is parallel to the limb, and which works through a fe- 

 male screw annexed to the plate m n, and whose neck 

 at p 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 a 

 Nonius, 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 af be di- 

 vided into any number of equal parts, a b, b c, cd, df, 

 and an equal line t be divided into other equal parts, 

 /S, 0y, y2, it, whose number is one less than the 

 number of parts in aj ; then &, * y, , i, will ex- 

 ceed a f), a c, ad, a e, respectively, by one, two, three, 

 four parts of a b, whose denominator is the number of 

 parts in a e, or in * e. For, let the lines a f, t, be 

 coincident at both ends, and since any equimultiples of 

 two quantities, a b, * p, are in the same ratio as the 

 quantities themselves, (Euclid, v. 15,) it will be as ab: 

 ft=ac : *v=arf : *3=oc : *, or of, and disjointly as 

 ab : bfizzac : cy=.ad : d%^=.ae : et, or ef. The conse- 

 quents b ft, c y, d 3, ei, are therefore in the same arith- 

 metical progression as the antecedents a b, a c, n d, a e, 

 and the first of the consequents b /3, is the same part of 

 its antecedent a b, as the last consequent ef is of its 

 antecedent a e, or as is of i, the number of parts in 

 a e and * i being equal by the first supposition. And it 

 is manifest, that any two equal and coincident arches 

 of a circle have the same property. 



The upper arch AB, Fig. 9, represents a degree di. Fig. 9. 

 vided into 12 equal parts, each containing five mi- 

 nutes ; and the under arch, CD, a 96th part of the 

 quadrant divided into 16 equal parts ; and EF, the 

 Nonius or subdividing plate fixed to the telescope, and 

 sliding with it in the space between the arches AB and 

 CD. Both these divisions are numbered from left to 

 right, commencing from the intersection of the vertical 

 radius, in order to measure the distanc.es of objects from 

 the zenith ; but the parts on the Nonius, are number- 

 ed the contrary way, beginning from the line 00, pro- 

 duced through the centre of the quadrant. In the fi- 

 gure the Nonius EF is so situated, that the upper end 

 of the index 00 is not opposite to any one line upon the 

 adjacent arch, but to some point of a 12th part of a de- 

 gree intercepted between 50 and 55 minutes. To find 

 the excess above 50, it will be seen by looking back 



