QUADRANT. 



tlrawii from A to the degree and minute of right afc-iifion, 

 counted from B towards C, and the point in this line, 

 where an occult arc, drawn tlirough the declinahon from 

 the centre A, interfefts it, will he the place of the heavenly- 

 body in quefUon. 



Tlie two parallel arcs contained between the tropic TD 

 and the quadrantal arc B C, arc the fcales of days and 

 months, which are divided by the aid of a table of meridian 

 altitudes of the fun for each day, calculated for the parti- 

 cular latitude, for which the quadrant is conftruited. It 

 is hardly neced'ary to obferve, on the conilruftion of fuah 

 table, that if the latitude and declination be both north, or 

 both fouth, the declination mud be added to the co-latitude 

 far the greateft altitude ; but if of contrary denominations, 

 fubtrafted. The degrees and minutes contained in fuch 

 table are transferred into the Icale of months by a line ex- 

 tending acrofs it from the centre A to the quadrantal arc, 

 as before. 



The centre of the horizon will be in the meridional line 

 AC, and if a point H be taken fuch, for the co-latitude 

 38° 28' for inftance, that AH may be the correiponding 

 tangent to radius A F, then ^v,,'V of that radius will be its 

 diftance from A, and the occult arc defcribed from H, with 

 the extent HE, beginning at E in the equinodfial, and end- 

 ing at the tropic TD, will be the required horizon. This 

 horizontal arc may be divided thus ; as radius is to the fine 

 of tlie latitude, fo is the tangent of any number of degrees 

 in the horizon, to the tangent of a correfponding aix in 

 the quadrant ; and from a table thus conftrufted any point 

 in the horizon may be put in by interfeClion of a line drawn 

 from A to the tabular number as read on the quadrantal 

 arc, as in the former cafes. 



A third table of the fun's altitude for inferting the hour 

 lines maybe calculated thus; when the fun is in the equator, 

 as radius is to the co-fine of the latitude, fo is the co-fine 

 of any hour from the meridian, to the fine of the fun's 

 altitude at that hour ; but when the fun has declination, 

 fay, as the co-fine of the hour from the meridian is to 

 radius, fo is the tangent of the latitude, to the tan- 

 gent of a fourth arc ; then if the latitude and decli- 

 nation have like denominations, and the hour fall between 

 noon and fix o'clock, fubtraft the declination from 

 the faid fourth arc, and the remainder will be a fifth 

 arc ; but if the_^latitude and declination have unlike deno- 

 minations, or the hour be between fix and midnight, add 

 the declination to the fourth arc, and the fum will be a 

 fifth arc, which muft be thus ufed ; as the fine of the fourth 

 arc, is to the fine of the latitude, fo is the co-fine of the 

 fifth arc, to the fine of the altitude fought. The determi- 

 nation of fuch table by this fundamental method is however 

 operofe, and Margett's horary tables, which give the fuc- 

 ceflive altitudes in any given latitude, would greatly fliorten 

 t'he labour, by giving the refults by infpeftion, which may 

 at the fame time be inferted by transfers from the quad- 

 rantal arc, fimilar to thofe we have already defcribed. 

 When the horary points are put in for each fucceflive hour, 

 when the fun is in the equator, at each tropic, and at a few 

 intermediate places, the horary lines may be drawn through 

 the faid points, which will give the liour for any given day, 

 when the inllrument is ufed as hereafter defcribed. 



A fourth table, for putting in the azimuth lines, will re- 

 quire the fun's altitude to be calculated for each degree of 

 azimuth, when the fun is at the equator, at each tropic, 

 and at other intermediate places, which may be done thus: 

 when the fun is in the equator, as radius is to the 

 co-fine of the azimuth from the meridian, fo is the tange.it 

 of the latitude, to the tangent of the fun's altitude at the 



azimuth in the equator : but out of the equator the rule ia, 

 as the fine of the latitude, is to the fine of the declination, 

 fo is the co-fine of the fun's altitude at the equator at a 

 given <\zimuth, to the fine of a fourth arc. When the 

 latitude and declination have the fame name, in all azimuths 

 from the piime vertical to the meridian, add tliis fourth arc 

 to the arc of altitude at the equator ; but when the azimuth 

 is above (j3°, fubt'^aft the altitude at the equator from this 

 fourth arc ; alfo when tlie latitude and declination have un- 

 like names, fubtraft the faid fourth arc from the arc of alti- 

 tude at the equator, for the altitude at the propoled azimuth. 

 The points correfponding to the tabular numbers, thus 

 afcertained, mufl be inferted by interfeftion of lines drawn 

 from A, as before, to the quadrantal arc BC, and lines 

 uniting thofe points will be the lines of azimuth for each 

 hour in every day of the year. But to complete the in- 

 (Iruments, two fights or vanes muft be fixed on the meri- 

 dional line AC, and a fmall plumb-line, with an adjultable 

 bead, muft be lufpended from the point A of the quadrant. 



In addition to the lines already defcribed, Gunter's quad- 

 rant has iometimes a fquare under the angular point A, 

 called a quadrat, as fccn in the figure, two fides of which 

 are divided into ten equal parts each, and thefe again fubdi- 

 vidcd into others, the ule of which is to meafure angular 

 diftances ; and fometimes the large fquare is fubdivided into 

 a number of fmaller ones, for the purpofe of performing 

 arithmetical proportions by infpeftion. See Bion on the 

 Conftruftion and principal Ufes of Mathematical Inftru- 

 ments. 



It would be tedious to enumerate all the ufes of this quad- 

 rant, and to exemplify all the problems that it is capable 

 of performing, or rather of illuftrating (for great accuracy 

 cannot b;e expected in the indication of fo fmall an inftru- 

 ment) ; but we will fpecify a few of the moft ufeful, which 

 may be varied by reverfing the procefles, and by altering the 

 data, to a great extent. 



Problem I. — Tojind the Sun's Right Afcenfion. 



Stretch the thread from the point A over the fun's 

 place, as- marked in the graduated ecliptic, and the degree 

 cut by it in the quadrantal arc will give the, correfponding 

 right afcenfion. 



Peob. II. — Tojind the Sun's DecUnal'ion. 



Stretch the thread as before, and Aide the bead till it 

 refts on the fun's place for the given day, and then turn it 

 to the fcale of declination, where the correfponding degree 

 will be feen under- the bead. 



Pkob. III. — Tojind the Sun's Meridian ylUUude on any Day. 



Extend the thread over the day of the month given, in 

 its proper fcale, till it reaches the quadrantal arc, and the 

 fun's greateft altitude for that day will be indicated thereby. 



Prob. IV. — Tojind the Hour oj the Day. 



Extend the thread over the day of the month, and, hold- 

 ing it there, Aide the bead till it lies on the line of twelve 

 o'clock ; then elevate the quadrant fo that the folar ray may 

 pafs through the upper fight-hole exaiSly upon the fecond, 

 and allow the plummet to reft, and then the bead will indi- 

 cate the hour, before or after noon, as the cafe may be. In 

 a fimilar manner the fun's altitude may be meafured by the 

 thread fallirig on the quadrantal arc, when tlie folar ray 

 paffes as above defcribed. 



Pkob. V. — Tojind the Sun's Atnpiilude. 



Let the bead be reftified for the given time, and be 



brought 



