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viz. by means of ^he fixed fights and plummet, and by the 

 label. 



Quadrant, U/e of the Surveying. To tale the height or 

 depth of an objell "with the fxeil fighls, and phmmet. — Place 

 the quadraiil vertically, and the eye under the figlit next 

 the arc of the quadrant : thus diredl I he inllrumcnt to the 

 object, e. gr. the top of a towf r, till the vifual rays of it 

 ftrike through the fights upon the eye. 



This done, the portion of the arc intercepted between 

 the thread and the femidiameter, on which the fights are 

 faftened, flievvs th? complement of the objed^'s height above 

 the horizon, or its dillance from the zenith ; and the other 

 portion of the arc intercepted between the ' hread and the 

 other femidiameter, fliews the height itfelf of the objetl 

 above the horizon. 



The fame arc likewife gives the quantity (if the anijle 

 made by the vifual ray, and a horizontal line, parallel to 

 the bafe of the tower. 



Note, to obferve depths, the eye mull be placed over 

 that fight next the centreof the quadrant. 



From the height or depth of the oLjetl in degrees thus 

 found, which fuppofe 35*^ 35' ; and the dillance of the foot 

 of the objeft from the place of obfervation carefully mea- 

 fured, which fuppofe 47 feet ; its height or depth in feet, 

 yards, &c. is eafily determined by the moft common cafe in 

 trigonometry. 



For we have here, in a triangle, one fide given, vi%. the 

 line meafured, and we have all the angles ; for that of the 

 tower is always fuppofed a right angle : the other two, 

 therefore, are equal to another right angle ; but the angle 

 obferved is 35° 35', therefore the other is 54° 25'. 



The cafe, then, will be reduced to this : as the fine of 

 54° 25' is to 47 feet, fo is the fine of 35° 35' to a fourth 

 term, wz. 33i feet ; to which add the height of the ob- 

 ferver's eye, fuppofe 5 feet ; and the funi, 38^ feet, is the 

 height of the tower required. 



Quadrant, the farther ufe of the, in taking of altitudes 

 of objects, both accejfdile and inaceejpble, fee under the article 

 Altitude. 



Quadrant, Ufe of the, in taking heights and difianees by 

 the index and fights — To take, e. gr. a height, as that of 

 a tower whofe bafe is acceffible ; place the plane of the in- 

 llrumcnt at right angles to the plane of the horizon, and one 

 of its edges par.illel to it, by means of the plummet, 

 which, in that cafe, will hang down along the other. In 

 this fituation turn the index, till, through the fight, you 

 fee the top of the tower ; and the arc of the limb of the 

 quadrant between that fide thereof parallel to the horizon 

 and the index will be the height of the tower in degrees ; 

 whence, and from the dillance meafured as before, its height 

 in feet, &c. may be found by calculation, as in the former 

 cafe : or, without calculation, by drawing from the data, 

 on paper, a triangle fimilar to the great one, whofe bafe is 

 the diftawee ; and its perpendicular, meafured on the fcale, 

 is the height of the tower. 



Quadrant, Ufe of the, in meafuring horizontal dijlances, — 

 Though the quadrant be a lefs proper iiiftrumeiit for this 

 purpole than a theodolite, femicircle, or the like, becaufe 

 angles greater than quadrants cannot be taken by it, yet 

 neceffity fometimes obliges perfons to have recourfe to it. 



The manner of its application is the fame with that 

 of the femicircle ; all the difference between the two inftru- 

 ments confiding in this, that the one is an arc of 180°, and 

 can therefore take an angle of any quantity ; and the other 

 is only an arc of 90'^, and is therefore confined to angles 

 of that quantity. See, therefore. Semicircle. 



Quadrant, in /JJironomy, is an inllrument by which 



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the altitude of a heavenly body is meafured, and is compefej 

 of one-quarter, or one-eighth of a circle, accordingly as the 

 meafurenient is made by means of diredt vifioii, or by the 

 refledted image of the object to be viewed. When a fuf- 

 pended circle was made ufe of with revolving fights, called 

 an adrolabe, the accuracy of an obfervation could never be 

 depended on, partly becaufe the radius was fmall, and 

 partly becaufe tiic inllrument vibrated when fufpended by 

 the hand, and was otherwifc inconvenient to ufe, as well as 

 liable to have its equipoife didurbed by the various pofitions 

 of the index and fights : therefore, fuch a portion of the 

 circle was ado])ted as was competent to ineafure the greateil 

 poiT.He altitude, and an increafe of radius was thereby ob- 

 tained, which promifed to contribute to accuracy, without 

 affefting the portability ot the inllrument. But though 

 the conilruflion was varied by difierent ingenious men, the 

 quadrant was but little, if at all, conducive to the improve- 

 ment of nautical or of aftronomical fcience, till the appli- 

 cation of telefcopic fights, and an improved mode of gra- 

 duating the limb, togetlier with the addition of a vernier 

 fcale, gave it powers on which the mariner and aftronomer 

 could confide. Quadrants have been conltrufted of different 

 materials, fuch as wood, ivory, brafs, &c. and of various 

 dimenfions, agreeably to the ufes for which they were in- 

 tended, in order to accommodate purchafers of every de- 

 nomination ; but as it is not our province to notice every 

 plaything that has ufurped the appellation of quadrant, we 

 will confine our account to fuch inilruments chiefly as have 

 been of aftual fervice in navigation and aftronomy. We 

 have, however, already anticipated the hiflory, we might 

 here have introduced, of the various improvements fuccef- 

 fively made in quadrants, at the beginning of our article 

 Circle; and under the article Graduation we have 

 given, at confiderable length, the different methods of di- 

 viding and fubdividing allronomical inftruments in general ; 

 to vvhicli articles we beg to refer our readers, who wifh for 

 information on thofe points, and which may be read in con- 

 junftion with our prefent article. 



Our arrangement of quadrants will be moft fyftematic, if 

 we divide them into two clalfes, -oix. thofe which meafure 

 altitudes by direct vifion, and thofe which determine mea- 

 furements in all dircClions, vertically, horizontally, and 

 obliquely, by means of refleftion. The former clafs have 

 been found ufeful in aftronomy chiefly, and the latter in 

 navigation, where the motion of a fhip interferes with the 

 fteadinefs of any fixed pofition of an inilrunient. 



The firft quadrant, in its rude Hate, was probably a 

 quarter of the allrolabe enlarged, with fixed fights placed 

 in, or parallel to, the vertical line pafiing through zero ; 

 and a fine thread, or wire, ftretched by a plummet, indi- 

 cated the altitude on the divided limb, according to the re- 

 prefentation in Jig. 4. of Plate I. of AJlronomical Injiruments. 

 This conftruftion might be uled iii obfervations of the fun, 

 without injuring the eye of the obferver, by allowing the 

 folar ray to pafs through the tiril fight-vane, or hole, lo as 

 to fall on the fecond, at fome dillance from the former, 

 while the thread relied nearly in contact with the elevated 

 limb ; but the want of minute, and at the fame time accu- 

 rate fubdivifions, and the fenfible thicknefs of the thread, 

 were impediments to accuracy that did not admit of remedy, 

 until another mode of reading the altitudes was devifed, and 

 until a method was contrived of rendering the light of the 

 fun tolerable lo the eye of an obferver. The former of 

 thefe defiderata was accoraplilhed firil by diagonal fcales, 

 with a fiducial edge of an index, and afterwards by that 

 admirable contrivance, fometimes called a Nonius, but more 

 properly denominated a Veruier, from the name of its in- 

 ventor ; 



