286 



QUADRANT. 



Quadrant. f rom the index, that a division line of the Nonius, which 

 V^y**' lies between the numbers 3 and 4, is exactly opposite 

 PLATE to a division line upon the adjoining arch, which shows 

 CCCCLXXVI. that 31 minutes is to be added to the 50 minutes. For 

 1 'S- 9. since a degree is divided into 12 equal parts, each con- 

 taining 5 minutes, and since the length of the Nonius 

 is made equal to 11 of these parts, and divided into 10 

 equal parts, it appears by the preceding Theorem, in 

 counting back again from the coincident division lines 

 to the index, that the first part of the Nonius exceeds 

 the first upon the limb by l-10th of this latter part, 

 that is by 1-1 Oth of 5 minutes, which is half a minute, 

 and consequently that seven parts of the Nonius, from 

 the coincident division lines to the index, exceed the 

 seven corresponding parts of the arch by seven half 

 minutes or 3' 30". 



When no one division line upon the limb is exactly 

 opposite to a division line upon the Nonius, then we 

 must look for that single part of the limb which is so 

 opposed to a single part upon the Nonius, as to be ex- 

 ceeded by it at both ends, as shown in the parts G, H, 

 Fig. 9. Then if that part of the Nonius appears to the 

 eye to exceed the part of the limb equally at each end, 

 15" more must be allowed than if they had coincided 

 at their ends next the index ; and according as the ex- 

 cess next the index is judged to be one-third, one-half, 

 double, or treble, of the other excess, we must allow 

 7", 10", 20", 22^", respectively. For as the sum of 

 the two excesses is always the same, and is equal to 

 SO", (as is obvious when one of them is diminished to 

 nothing,) the number of seconds to be added will al- 

 ways be to 30", as the excess next the index is to the 

 aum of the two excesses. 



The lower arch of the Nonius is divided into 16 equal 

 parts, and is equal in length to 17 equal parts upon the 

 opposite arch, and therefore will determine l6'th parts 

 ot' every one of them, by the theorem and method 

 above mentioned. In Fig. 9, the opposite division lines 

 of the Nonius and the lower arch are supposed to coin- 

 cide at the end of the 9th part upon the Nonius, which 

 shows that the index cuts off 9-16ths of the opposite 

 part of the arch. And so the length of the arch from the 

 beginning of a 96th part of the quadrant, is thus denot- 

 ed 15.9, the lower pointer being past the 15th stroke. 

 This way of subdividing by a Nonius, is preferable 

 to the common method of drawing diagonals, both be- 

 cause the trouble of drawing so many diagonals is en- 

 tirely avoided, and also because they cannot be drawn 

 so exactly by the edge of a ruler, as the lines upon the 

 Nonius ; and lastly, because the intersection of these 

 diagonals with the index or fiducial edge, (as they call 

 it,) by reason of the great obliquity to each other, can- 

 not be determined so exactly by the eye as the coinci- 

 dence of two division lines in the Nonius, and the arch, 

 which stand directly opposite to each other. 



The object-glass being firmly and permanently fixed 

 in the telescope, the Nonius plate c d, and the collar 

 piate s t, were both screwed fast to the telescope when 

 taken off from the quadrant, and then the line of sight 

 was brought to be parallel to the line c o, drawn through 

 o the centre of the collar pqtoc, the beginning of the 

 divisions on the Nonius, in the following manner : The 

 lines sot and ecf being drawn upon these plates both 

 perpendicular to o c, any distances o t and cf were ta- 

 ken equal to each other, on one side of oc, and any other 

 distances o s and c e (long enough to go beyond the te- 

 lescope, ) were also taken equal to each other on the op- 

 posite side of o c. Through the four points e, s, t,f, the 

 nds of the two plates were filed exactly parallel to 



oc. Then placing the points tfupon two points in n Quadrant. 

 of an horizontal line, drawn upon a firm plane, a point ^s^y^*' 

 of a remote object covered by the cross hair?, was 

 marked. The telescope being then turned half round, 

 its axis a b, and the opposite points es of the plates be- 

 ing placed upon the same points m n, another point of 

 a remote object now covered by the cross hairs, was 

 also marked ; and the telescope remaining fixed, the 

 cross hairs were moved in its focus, till after several re- 

 petitions of the operation, the same point of the object 

 was covered by them in both positions of the telescope ; 

 and then the line of sight was exactly parallel to the 

 line o c, supposing the object to be remote. But be- 

 cause smaller marks upon a nearer object are better 

 discerned, the hairs were so adjusted, till in each posi- 

 tion of the telescope they covered a separate mark, the 

 interval of the marks being taken equal to the diffe- 

 rence of the heights of the axis of the telescope above 

 the fixed line m n, as near as could be measured. 



The object glass being well centred, the line of 

 sight was first of all made parallel to the plane of the 

 quadrant, as near as it need be, by the measures of 

 the brass work annexed to the telescope ; and then 

 the plane described by the line of sight, turned about 

 the centre of the quadrant, was brought into the 

 plane of the meridian, by observing whether the fix- 

 ed stars passed over the cross hairs at the same in- 

 stant of time, as they passed over a meridian tele- 

 scope, adjusted as above described, and placed so near 

 the quadrant that the two observers would hear each 

 other calling out at the times of the transits. And 

 by the coincidence of these observations upon stars 

 at various altitudes, it appeared that the plane of 

 the quadrant was wrought very true. For it is cer- 

 tain that the meridian plane described by the meridian 

 telescope as turning upon a transverse axis, must be 

 truer than that described by the quadrantal telescope, 

 as guided by the rollers upon the limb. 



When the quadrant was thus reduced into the plane 

 of the meridian by the holdfasts above described, that 

 radius of it which terminates 90 degrees, was placed 

 exactly vertical (by the movement above mentioned,) 

 with a plumb line of very fine silver wire ; so suspend- 

 ed as to play exactly over the middle of the central 

 point o (in the pole of the arbor oz,) and also over the 

 stroke at 90 degrees upon the limb below. This posi- 

 tion of the quadrant being once found, another plumb- 

 line was suspended by the side of the quadrant, quite 

 clear of the centre work, so as to play exactly over the 

 middle of a fine point made in the limb below, in or- 

 der to examine afterwards with more expedition, whe- 

 ther the quadrant has kept its place. For this purpose 

 an oblong piece of brass ab, laid flat upon the square 

 plate at the centre of the quadrant, was gradually mov- 

 ed to the right or left by two screws c, d, working 

 against the ends of it : a slit a b being cut lengthwise 

 through the plate to slide along two other screw-pins, 

 e,f, fixed in the back plate. The wire of the plummet 

 was hung by a loop upon a pin g, and lay in a very 

 fine angular nick, filed in the edge of a little plate h, 

 which projected a little farther than the loop for the 

 wire to bear upon it. This plate h, and the pin g, 

 were both fixed to the oblong plate a b ; by whose 

 gradual motion, above described, the wire h i was 

 brought to play exactly over the middle of the hole i 

 in the limb ; and then the plate a b was pressed to the 

 quadrant by the screws e,f. Smith's Optics, Vol. II. 

 p. 332-341. 



In the year 1753 a quadrantal arc of 96, with its 



