IV. .4 Quadrant, for a description of which, and its several uses, we refer to the article QUADRANT. We may, how ever, observe, that besides Hadley's quadrant, which is described there, we have the mural quadrant, which is reck oned one of the most useful and valuable of all the astronomical instruments, and is generally fixed to the side of a stone or brick wall, and the plane of it is erect ed exactly in the plane of the meridian. There is also a portable astronomical quadrant, which is in high estimation, on account of its being capable of being serried to any part of the world, and pa up for the purposes of observation by al most any common workman.
V. Astronomical or Equatorial Sector. This is an instrument for finding the dif ferencein right ascension and declina tion between two objects, the distance of which is too great to be observed by the micrometer. Let A B (Plate Observato ry, fig. 1.) represent an arch of a circle containing ten, or twelve degrees well di vided, having a strong plate, CD, for its radius, fixed to the middle Of the arch at D. Let this radius be applied to the side of an axis; H F I, and be moveable about a joint fixed to it at F, so that the plane of the sector may be always parallel to the axis H I, which being parallel to the axis of the earth, the plane of the sector will always be parallel to the plane of some hour circle. Let a telescope, C E, be moveable about the centre, C, of the arch, A B, from one end of it to the other, by turning a screw at G, and let the line of sight be parallel to the plane of the sector. Now, by turning the whole instrument about the axis, H I, till the plane of it be successively directed, first to one of the stars, and then to an other, it is easy to move the sector about the joint F, into such a position, that the arch, A B, when fixed, shall take in both the stars in their passage, by the plane of it, provided the difference of their de clinations does not exceed the arch, A B. Then, having fixed the plane of the sec tor a little to the westward of both the stars, move the telescope, C E, by the screw, G, and observe by a clock the time of each transit over the cross hairs, and also the degrees and minutes upon the arch, A B, cut by the index at each transit ; then in the difference of the arches, the difference of the declina tions, and by the difference of the times, we have the difference of the right ascen sions of the stars. The dimensions of this instrument are these ; the length of the telescope, or the radius of the -sec tor, is two feet and a half: the breadth of the radius, near the end C, is an inch and a half, and at the end, If, two inches : the breadth of the limb, A B, is one inch and a half, and its length six inches, con taining ten degrees, divided into quar ters, and numbered from either end to the other.
The telescope carries a nonius, or sub dividing plate, whose length being equal to sixteen quarters of a degree, is divided into fifteen equal parts, which, in effect, divides the limb into minutes, and, by es timation, into smaller parts. The length
of the square axis, H I F, is eighteen inches, and of the part, Ii I, twelve inches ; and its thickness is about a quar ter of an inch. The diameters of the cir cles are each five inches ; the thickness of the plates, and the other measures, may be taken at the direction of a work man. This instrument may be rectified for making observations in this manner : By placing the intersection of the cross hairs at the same distance from the plane of the sector as the centre of the object glass, the plane described by the line of sight, during the circular motion of the telescope upon the limb, will be suffi ciently true, or free from conical curvity, which may be examined by suspending a long plumb-line at a convenient distance from the instrument, and by the plane of the sector in a vertical position ; and then by observing, while the tele scope is moved by the screw along the limb, whether the cross-hairs appear to move along the plumb-line. The axis, h f o, may be elevated nearly parallel to the axis of the earth, by means of a small common quadrant, and its error may be corrected by making the line of sight fol low the circular motion of any of the cir cumpolar stars, while the whole instru ment is moved about its axis, h f o, the telescope being fixed to the limb ; for this purpose, let the telescope, k l a, be directed to the star a, when it passes over the highest point of its diurnal cir cle, and let the division cut by the nonius be noted ; then, after twelve hours, when the star comes to the lowest point of its circle, having turned the instrument half round its axis, to bring the telescope into the position in it, if the cross hairs cover the same star supposed at b, the eleva tion of the axis, h f o, is exactly right ; hut if it be necessary to move the tele scope into the position, uf c, in order to point to this star at c, the arch in ze, which measures the angle in fu, or bf c, will be known ; and then the axis, hf o, must be depressed half the quantity of this given angle if the star passed below b, or must be raised so much higher if above it ; and then the trial must be repeated till the true elevation of the axis be ob tained.
By making the like observations upon the same star on each side the pole in the six o'clock hour circle, the error of the axis, toward the east or west, may al so lie found and corrected, till the cross hairs follow the star quite round the pole ; for supposing aopbc, to be an arch of the meridian, make the angle a f p, equal to half the angle a f c, and the linef p, will point to the pole ; and if the angle o f p, which is the error of the axis, will be equal to half the angle, bf c, or min, found by the observation ; because the difference of the two angles, a f h, a f c, is double the difference of their halves, a f o, and a f p. Unless the star be very near the pole, allowance must be made for refractions. See QUAD