284 QUADRANT. 



gether, is two inches and two-tenths, the brass limb of a ruler, the following method was adopted : In or- Quadrant. 

 being an inch and two-tenths more remote from the der to divide any other concentric arch fh t by cross >--Y"' 

 centre than the iron one. In order to reduce the limb strokes into parts similar to those in the given arch 

 l ' to a true plane, the quadrant a b d o, Fig. 3. was placed acgebd, take a small beam compass, and having fix- 

 firmly on a level plane with its brass limb upwards, ed its points at any convenient interval, upon the 

 To a vertical axis / m, pointing to the centre o, was centres e, g, being the given points of the divided 

 fixed an iron arm mn, carrying an iron scraper p, which, arch, strike the small arches^/*', h k, &c. cutting the un- 

 when turned round the axis I m, scraped the brass divided arch in f, h t then will the intercepted arches 

 to a perfect plane, the edge of the scraper being cor- as//t be similar to the arches eg ; that is, they will sub- 

 rectly perpendicular to the axis of motion. tend the same angles at their common centre o. For 

 Two arches were struck upon a brass limb, one with joining ef, g h, and also of,oh,oe,og, the triangles 

 a radius of t)6.85 inches, and the other with a radius of e of,g o h will be similar and equal to each other ; every 

 95.8 inches. side in the one being respectively equal to every side 

 The outward arch is divided into ninety-six equal in the other. Taking away, therefore, the common 

 parts each, which are again divided into sixteen equal angle eoh from the equal angles eof,goh, the re- 

 parts, and the inner arch is divided into degrees and maining angles eog, foh will also be equal. If the 

 twelfth parts of a degree.* triangles efo,gh o be right angled at/ ami h, the di- 

 The beam of the compass, by which these arches viding strokes fi, h k, &c. will cut the quadrantal arch 

 were struck, was prevented from bending by several fht, at right angles also at^'and h. 



braces, and when an arch was struck, 60 degrees of it 

 was determined by placing one point of the compass at 

 a, and making a stroke with the other at b. The arch 

 a b was then bisected in c, by drawing two small arches 

 upon a and b as centres, and with such a radius, as to 

 cross the arch a c b in two points, as near together as 

 possible without touching. The small interval between 

 these points was then bisected at c by the estimation of 

 the eye, aided by a magnifier. After this, the intervals 

 o c or c b was taken with the beam compass, and trans- 

 ferred from b to d, which determined the length of the 

 quadrantal arch a d. Each of the three arches being 

 bisected in the same manner, the quadrant was divided 

 into six equal parts, containing fifteen degrees each, 

 and every one of these was divided into three equal 

 parts, in the following manner. To avoid making any 

 superfluous points in the quadrantal arch, with its ra- 

 dius unaltered, but upon any other centre there was 



In Fig. 4. a b c d represents a square piece of brass Fig. 4. 

 (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 mn 

 represents a thick circular plate of brass, with a hollow 

 pipejg fixed perpendicular to the middle of it. This 

 plate was turned exactly circular in a Jathe upon a 

 brass arbor oi, turned tapering, and a little hollow in 

 the middle, so as to fit the cavity of the pipe f%, and 

 to bear against it chiefly at both ends. When the hol- 

 low pipe fg is put through the holes (exactly fitted 

 for it) in the middle of the square abed, the brass 

 circle k I m n is fixed to the plane of the square abed, 

 with screws and steady pins. The point o in the pole 

 of the arbor o t is not only the centre of the circular 

 neck klmn, 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 



struck a faint arch, upon which the chord of fifteen de- of the telescope which holds the object glass lies across 



grees, already found, was transferred from the qua- 

 drantal arch, and the third part of fifteen degrees being 

 determined by trials on the faint arch, was transferred 

 back again upon the quadrantal arch, which was thus 

 divided into eighteen equal parts, containing five de- 

 grees each, and the fifth part of these was found by 

 trials as before, in dividing a separate arch, drawn up- 

 on a new centre, for this purpose only, the subdivi- 

 sions of the degrees into twelve equal parts were made 

 by bisections and trisections as before, so that the whole 

 quadrant was thus divided without using any superflu- 

 ous point. 



The outward arch of the quadrant was divided by 

 bisections into ninety-six equal parts, till sixty degrees 

 or two-thirds of the quadrant became divided into six- 

 ty-four, and the other third into thirty-two equal parts, 

 making in the whole ninety-six. Every one of these 

 was likewise divided into sixteen equal parts by con- 

 tinued bisections. These two sorts of divisions form a 

 check upon each other, 'being in reality two different 

 quadrants; and the divisions of the one being reduced 

 to those of the other by a table. (See ASTRONOMY, 

 Vol. II. p. 724.) They never differed above five or 

 six seconds in any part of the limb, the preference 

 being always given to the bisected divisions, as having 

 been determined by a simple operation. 



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 



one end of an oblong plate of brass s /, 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 s t, there is a round hole lined 

 with a steel collar p q r, to be put over the brass neck 

 klmn, and to turn round upon it. The section of 

 this collar, taken at right angles to its plane, is shown 

 at z, the broader of the two rings being under the plate 

 st, and contiguous to the square plate abed. Over 

 this neck and collar there is fixed a brass spring shown 

 at v, and screwed to the neck klmn, to keep the collar 

 from slipping from it ; and over all these is screwed a 

 cap, shown at x, to cover the centre work, and to keep 

 off the dust, which is also prevented from coming be- 

 tween the plates abed and s t to the neck and collar, 

 by means of a brass hoop surrounding the broad rim 

 or base of the collar p r, and screwed to the backside 

 of the plate s t ; which hoop is received into a circu- 

 lar groove 1, 2, 3, 4, formed in the square plate with- 

 out touching any part of it. 



The superiority of this centre work consists in pre- 

 serving the place of the central point of the quadrantal 

 arch in the pole of the arbor oi. For whenever an 

 unsteady motion of the telescope round the centre of 

 the quadrant shall arise from the wearing of the neck 

 plate him n, a new neck plate and pipe may 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. 



* A part of this process of dividing the limb has already been given under GKADUATION ; but we have repeated it here, in order 

 that the complete description of this quadrant may be read at once. 



