QUA 



1. If the object be south when ob. 

 served, call the xen th-distance, south ; 

 and vice verva. Then, if the zenith-dis- 

 tance, and the declination, be of contrary 

 names, (that is, if the sun, or star, comes 

 to the meridian in the north, and has south 

 declination, or per contra), the zenith-dis- 

 tance, added to the declination, gives the 

 latitude of the place of observation ; the 

 designation will be north, or south, ac- 

 cording as the declination may be. 



2 When the zenith-distance, and the 

 declination, are of the same name, that 

 is, when the sun, or star comes to the 

 meridian in the north, and has north de- 

 clination ; or per contra , then subtract 

 the lesser from the greater ; and the re- 

 mainder is the latitude. 



This general rule decides whether it be 

 north or south. When the declination is 

 greater than the zenith distance, the la- 

 titude is of the same name with the decli- 

 nation ; but if less, the latitude is on the 

 opposite side of the equator. For fur- 

 ther particulars, see LATITUDE. 



QUADRANT of altitude, is a thin piece 

 f metal, n general applied to the globe, 

 and marked with the degrees, from to 

 90 : when laid upon the meridian of any 

 place, it shows its latitude or distance 

 from the equator. 



QUADRANT of a circle, or the fourth 

 part of its circumference, is contained 

 under two radii standing at right angles. 

 The quadrant contains ninety degrees, 

 and is the parent ot various lines of the 

 greatest utility in many branches of the 

 mathematics, such as the lines of chords, 

 of sines, of latitude, &c. See MATHE- 

 MATICAL instmments, and DIALLING. 



QuADHANTS,#zwer's, are made in va- 

 rious manners, some ot them having levels; 

 but the most simple construction, with 

 which we are acquainted, is that made 

 with a staff about a foot in length, having 

 on one side a quadrant, which, by means 

 f a pendulum of metal, shous the ex- 

 act angle made by the chase, or bore. 

 The staff being put into the muzzle of a 

 mortar, or howitzer, so as to lay, in con- 

 tact, evenly with its lower side, and the 

 quadrant part being turned down, imme- 

 diately beyond the muzzle, the pendulum- 

 wire, which is fixed to a small pivot in 

 the right angle, exactly at the centre, 

 whence the quadrant was described, will 

 be kept perpendicular by the weight at- 

 tached thereto ; and will thus indicate the 

 exact elevation of the piece. The point 

 of oscillation, i. e. the pivot, must, how- 

 ever, be always kept very smooth ; that 

 there may not be the least roughness ; 



else the action would be affected, and the 

 index prove erroneous. 



QUADRAT, a mathematical instru^ 

 ment, called also a geometrical square, 

 and line of shadows ; it is frequently an 

 additional member on the face of the 

 common quadrant, as also on those of 

 Gunler's and Button's quadrants ; but we 

 shall describe it by itself, as being a dis- 

 tinct instrument. 



It is made of any solid matter, as brass, 

 wood, &c. or of any four plain rules joined 

 together at right angles, as represented in 

 Plate XIII. Miscell. fig. 2, where A is the 

 centre, from which hangs a thread with a 

 small weight at the end, serving as a 

 plummet. Each of the sides, E E and 

 D E, is divided into an hundred equal 

 parts ; or, if the sides be long enough to 

 admit of it, into a thousand parts ; C and 

 F are two sights, fixed on the side AD. 

 There is, moreover, an index, G H, which, 

 when there is occasion, is joined to the 

 centre, A, in such a manner as that it can 

 move freely round, and remain in any 

 given situation ; on this instrument are 

 two sights, KL, perpendicular to the 

 right line going from the centre of the in- 

 strument. The side D E is called the up- 

 right side, or the line of the direct or 

 upright shadows ; and the inside E E is 

 termed the reclining side, or the line of 

 the versed or back shadows. 



To measure an accessible height, A E t 

 (fig. 3) by the quadrat, let the distance, 

 E D, be measured, which suppose = 96 

 feet, and let the height of the observer's 

 eye he 6 feet ; then holding the instrument 

 with a steady hand, or rather resting it 

 on a support, let it be directed towards 

 the summit A, so that it may be seen 

 clearly through both sights ; the perpen- 

 dicular, or plumb-line, meanwhile hang- 

 ing free, and touching the surface of the 

 instrument : let now the perpendicular be 

 supposed to cut off on the upper side, 

 K N, 80 equal parts ; it is evident, that 

 L K N, A C K, are similar triangles, and 

 (by prop. 4. lib. 6. of Euclid) N K : K L 

 : : K C (i. e. ED) : C A ; that is, 80 : 100 

 : : 96 CA : therefore, by the rule of three, 



C A= 



^20 feet, and C E 



6 feet being added, the whole height E A 

 is 126 feet. 



If the observer's distance, as D E, be 

 such, that, when the instrument is direct- 

 ed as formerly towards the summit A, the 

 perpendicular fall on the angle P, and the 

 distance, E E or C G, be 120 feet, C A will 

 also be 120 feet: forPG:GH:: GC: 



