Quadrant. 



288 



a point on the left edge of the quadrant are drawn the 

 two ecliptics, having the signs of the zodiac, and from 

 the same point are drawn the two horizons. The limb 

 is graduated both into degrees and hours, and, from the 

 sun's altitude, the hour of the day may be found to a 

 minute. The divided quadrants nearest the centre 

 contain the kalendar of months, and beneath them is 

 the sun's declination. Several of the most remarkable 

 stars between the tropics are laid down on the projec- 

 tion, and immediately below the projection is the qua- 

 drant and line of shadows. The method of using this 

 quadrant is nearly the same as that of Gunter's. 



6. Description of the Horodictical Quadrant. 



This little instrument derives its name from its pro- 

 perty of telling the hour of the day, and is made as fol- 

 lows : The quadrant CAB, Fig. 12. has its limb AB di- 

 vided into 90, and round its centre C are described se- 

 ven concentric circles, having the signs of the zodiac add- 

 CCCCLXXVI. ed to them. A ruler is now applied to the centre C and 

 Fig. 12. the limb AB, and on the several parallels are marked the 

 degrees corresponding to the altitudes of the sun when 

 in those degrees, for the given hours. The points be- 

 longing to the same hour are then connected by a 

 curve line, and the number of the hour added. A 

 pair of sights are now fitted to the radius CA, and a 

 thread furnished with a plummet, and a sliding bead, 

 is attached to the centre C. By bringing the bead to 

 the parallel on which the sun is, and directing the qua- 

 drant to the sun till a solar ray passes through the 

 sights, the bead will point at the hour of the day, as 

 the plummet-line cuts all the parallels in the degrees 

 corresponding to the sun's altitude. As the bead is in 

 the parallel which the sun then describes, the bead 

 must show the present hour, even though hour-lines 

 pass through the degrees of altitude to which the sun 

 rises every hour. 



7. Description of the Sinical Quadrant. 



Descrip- 

 tion of the 

 horodicti- 

 cal qua- 

 drant. 

 PLATE 



drant. 

 Fig. 13. 



Descrip- This instrument, Fig. 13, which is chiefly of use in 



tion of the navigation, consists of several concentric quadrantal 

 sinical qua- arches, divided into eight equal parts by radii, with 

 straight lines crossing one another at right angles, and 

 parallel to the rectangular radii. 



Any one of the arches, as BC, is used to represent 

 the horizon, or meridian, though it may represent a 

 quadrant of any great circle of a sphere. If BC is taken 

 as a quadrant of the horizon, either of the sides, as AB, 

 may represent the meridian ; and the other sides as AC 

 will represent a parallel, or line of east and west; while 

 all the other lines parallel to AB will be also meridians, 

 and all those parallel to AC east and west lines, or pa- 

 rallels. 



The eight equal parts into which the limb is divided 

 by the radii contain 11 15', and represent the eight 

 parts of the compass on the quarter of the horizon. 

 The arch BC is divided into 90; and by means of dia- 

 gonal lines each degree is subdivided into twelve parts, 

 or five minutes each. A thread is fixed to the centre, 

 and divides the horizon, by being laid over any degree 

 of the quadrant. 



If this quadrant is taken to represent a quarter of 

 the meridian, one of its sides AB may be taken for the 

 common radius of the meridian and the equator, and 

 then the other AC will be half the axis of the world. 

 The degrees of the circumference BC will represent 

 degree* of latitude, and the lines parallel to the side 



QUADRANT. 



AB assumed from every point of latitnJe to the axis 

 AC, will be the radii of the parallels of latitude, and 

 likewise the cosines of these latitudes. 



If it is now required to find the degrees of longitude 

 contained in 83 of the lesser leagues in the parallel of 

 48. Lay the thread over 48 of latitude, ou the cir- 

 cumference, and count the 83 leagues from A upon AB. 

 These will terminate at H, allowing for every small in- 

 terval four leagues, and the interval between the broad 

 lines twenty leagues. By then tracing out the parallel 

 HG from the part H to the thread, the part AG of 

 the thread will show, that 125 greater, or equinoctial 

 leagues, make 6 15'; allowing 20 leagues to a degree, 

 and 3' for one league; and, consequently, that 83 lesser 

 leagues AH, which make the difference of longitude 

 of the course, and are equal to the radius of the paral- 

 lel GI, make 6 15' of the above-mentioned parallel. 



When the ship sails on an oblique course, this course, 

 besides the north and south greater leagues, gives lesser 

 leagues easterly and westerly, to be converted into de- 

 grees of longitude of the equator. But as these leagues 

 are made neither on the parallel of departure, nor on 

 that of arrival, but in all the intermediate ones, a mean 

 proportional parallel between them must be found. 

 For this purpose, the quadrant has a scale of cross la- 

 titudes, so that we have only to take with the compasses 

 the middle point between the parallels of which we 

 want the mean, and the middle point will be the mean 

 parallel required. 



The chief use of the sinical quadrant, is to form tri- 

 angles upon it similar to those made by a ship's course 

 with the meridians and parallels ; the sides of these tri- 

 angles being measured by the equal intervals between 

 the concentric quadrants, and the lines of N. and S. E. 

 and W. Every fifth of the lines and arcs is distin- 

 guished by a broader line, so that if each interval is 

 made to stand for a league, there will be five between 

 two adjacent broad lines ; or if each interval represent 

 four leagues, there will be twenty leagues, or a sea 

 degree, between two adjacent broad lines. 



If we. suppose a ship to have sailed 150 leagues 

 north-east, one-fourth north, which is the third point, 

 and makes an angle of S3* 45' with the north part of the 

 meridian, then making A the place of departure, reckon 

 by means of the concentric arch along the point the ship 

 sailed on, as AD, 150 leagues from A to D, then is the 

 point D the point of the plane to which the ship has ar- 

 rived. Let DE be the parallel to the side AC, and we 

 shall then have a right angled triangle AED, similar to 

 that of the ship's course, difference of longitude and lati- 

 tude. The side AE gives 125 leagues for the difference 

 of latitude northwards, which makes 6 15', reckoning 

 twenty leagues to a degree; and the side DE gives 

 eighty-three lesser leagues, answering to the parallels 

 which, when reduced as above shown, will give the 

 difference of longitude. 



8. Description tfthe Common Gunners' Quadrant. 



This instrument, represented in Fig. 14, consists of 

 two branches, made of wood or brass, one of which is 

 about twelve inches long, eight lines broad, and one 

 line thick ; and the other four inches long. Between 

 these branches is placed a quadrant, divided into 90, 

 the divisions, commencing at the shorter branch, which 

 is furnished with a thread and plummet. 



The use of the quadrant is to point cannons, mortars, 

 &c. which is done by placing the longest branch in the 

 mouth of the piece of ordnance, and by elevating the 



Deserip- 

 tion of the 

 lunar or 

 conimon 





