QUA 



the horizon : if the fun or moon be obferved, either tlic 

 upper or lower limb mull be fubftitiited for the centre, and 

 the obfervatidii muil be afterwards reduced to the centre, by 

 applying the femi-diameter, -|- or — , from the proper column 

 for the given day, as given in the Nautical Almanac, or Ephe- 

 meris ; in doing this, the face of the obferver mull be turned 

 towards the objeft whofe altitude is to be meafured, and 

 while the index is gradually moved forward along tlie limb, 

 the image will defcend till it approaches the horizon : in 

 this fituation, care muft be taken that the contact of the 

 image be made with the vifible horizon at the line of fepa- 

 ration, between the filvercd and unfilvered parts of the fore 

 horizon-glals, that both objefts may be vilible together ; 

 ■•and alfo tliat the index may not be pufhed too far, fo as to 

 require a retrograde motion in finifliing the contadl : there- 

 fore fix the clamping piece, if there is a tangent fcrew, and 

 complete the contadl by a flow motion, and the altitude will 

 remain unaltered till the vernier has been examined by a 

 magnifying glafs, which ought always to be at hand, to alTift 

 the eye in examining the coincidence of fome one line of the 

 vernier with fome line of the limb ; or, when there is not an 

 exaft coincidence, in cftimating the quantity that is beyond 

 coincidence, as compared with the contiguous quantity that 

 is fliort of it. To fucceed well in perfedling a fore obferva- 

 tion taken at the horizon, the obierver mull learn to give a 

 vibratory flow motion of his body to the right and left, his 

 heel being the centre of motion, that the image obferved may 

 be made to move backwards and forwards ni the arc of a 

 circle, of which the horizon is a tangent, in order that the 

 altitude may not be taken at one fide of the tangental point, 

 and confequently be too great. Care inuft alfo be taken 

 that the faint fecondary image refieiled from the pofterior 

 face be not miftaken for the primary image, reflected from 

 the proper, or anterior face of the mirror. When the alti- 

 tude is marked down, as read on the limb and vernier, the 

 corredlions mull be applied, for either the fun or moon, for 

 parallax, refraftion, dip of the horizon, and femi-diameter, 

 before the true altitude of the centre is obtained : but for a 

 ftar no parallax is wanted, nor yet allowance for femi- 

 diameter ; thcfe apparently diminutive bodies being fituated 

 at fucli an immenfe diftance from the earth, as to fubtend no 

 fenfibW angle, nor to have any perceptible parallax in 

 altitude. 



It 13 from meridian altitudes thus taken, that, by the ap- 

 plication of a heavenly body's declination, + or — , as the 

 body may be below or above the equator, the co-latitude, 

 and confequently the latitude, is readily determined ; and alfo, 

 the latitude being known, from an altitude taken towards 

 the eall or well, that the time is determined at one obfer- 

 vation, but more accurately by a feries of equal altitudes 

 taken at oppofite fides of the meridian ; the reduftion, how- 

 ever, for the fun's change of declination during the interval, 

 muil, in this cafe, be taken from tables of correftion for 

 equal altitudes, fuch as are contained in the pamphlet of the 

 late Mr. Wales. 



In making the bacL obfervation, the coloured glafs, or 

 glafles, mull be feledled, as before, to fuit the eye, and the . 

 plane of the inftrument held vertically, as in the fore obfer- 

 vation, but the face of the obferver muft view the point of 

 the horizon oppofite the fun, or that pointed to by his own 

 Ihadow ; firll, let the eye be directed through the vane of 

 the back horizon-glafs to the tranfparent (lit that divides the 

 mirror, and let it view the horizon, then move the index till 

 the image of the fun is jull feen on the filvered part of the 

 glafs ; a vibratory motion now given to the oftant from the 

 eve, as the centre of motion, will make the fun's image move 

 ;it a curve of which the convex part appears uppermoil ; in 



Vol. XXIX. 



Q IJ A 



tills fituation, let the flow motion by the tangent fcrew, if 

 any, bring this image till one of its limbs coincides with the 

 horizon feen tlirougii the tranfparent flit, and the obferved 

 altitude will be determined as beiore. Whenever the horizon 

 is clear both before and behind the obferver, he may reverfe 

 his inllrumcnt and alfo his body hailily, when the fun is on 

 the meridian, and make the fore and back oblcrvations check 

 each other, which will alfo, from time to time, prove the 

 refpe(ftive politions of the two mirrors, and lead to a deteftion 

 of the error of the back liorizon-glafs, when that of the 

 former is known, which it may always be from a double 

 mcafure, one back and one forwards, of the fun's diameter. 

 If the difference of the altitudes of the fame body taken 

 both ways be equal to the known index-error of the fore 

 horixon-glafs, it will be known that the back horizon-glafs 

 has no error ; but if the faid quantities are not the fame, their 

 difference, -(- or — , will be the index -ei;ror of the back 

 horizon-glafs ; hence the back horizon-glafs may be adjufted 

 from a knowledge of the error of adjullment of the fore 

 horizon-glafs, which method, we believe, was never before 

 fuggeftcd. 



yuABRANT, Hadley's, Theory of. It is a firft principle 

 in optics, that the angle of incidence, whatever be the in- 

 clination of the incident ray, is equal to the angle of reflec- 

 tion, /. e. if the angle of incidence D B A be 30', the angle 

 of refleftion D BC will be alfo 30^. It is alfo plain, that 

 if while the radiant A {Plate II. Navigation, Jigs. I and 2.) 

 remains in the fame place, the mirror E F, by revolving 

 round B, moves into the pofition fe, then the alteration in 

 the angle between the incident and refledled ray will be 

 double to the angle fliewing the change of pofition in the 

 mirror. Suppofe the mirror changes 10° from the radiant, 

 then the perpendicular BD goes 10° farther from the 

 radiant A into the pofition B(/; and the incident angle 

 ^BA is 40°, and the rcflefted angle </Bc is 40^; fo the 

 angle A B C is altered from 60° to 80^ ; a difference of 20° 

 for 10° change of pofition in the mirror. Suppofe again 

 the mirror to change, in pofition, 10" towards the radiant 

 A, then the perpendicular is changed into B </, 10° nearer 

 to the radiant ; and the angle D B A of 30'"' becomes rfB A 

 of 20'' = dUc; fo that the angle A B i: is 40°, whereas 

 ABC was 60° ; that is, by altering the pofition of the 

 mirror 10", the angle ABC was altered 20"^. It may be 

 otherwife demonllratcd, that with a Hadley's quadrant, the 

 angle of elevation under which an object is feen, is equal to 

 twice the arc which the index has paffed over. The in- 

 ftrument or angle A C B (fig. 3.) is 45° ; ab'iiz reflefting 

 glafs fixed parallel to C B ; CD is the index with a re- 

 fledling glafs at G, fo fixed as to be parajlel to a b, when 

 C D coincides with C B ; S the fun ; S G a folar ray re- 

 flefted from G to F, and from F to E, the place of the 

 eye ; and H F E the horizontal line at the time of the ob- 

 fervation. Then will the angle of elevation I G S be equal 

 to twice the angle BCD; for the angle of refleftion D G F 

 = the angle of incidence S G C = C G L. And the angle 

 of refleftion i F E = the angle of incideuce a F G = F L E 

 iab being parallel to LE) = F E L. But TGC = 

 HPC = PCE-fPEC (the external angle being equal 

 to the two internal and oppofite) = PCE + FLE = 

 PCE fGCL + CGL. Or, I G C = I G-S + S G C 

 = PCE (or GCL) GCL + CGL =. 2BCD + 

 CGL. Confequently I G S = 2 B C D. See Robert- 

 fon's Navigation, book ix. p. 295, &c. p. 390, &c. 



Mr. Mitchell has recommended Hadley's quadrant for 

 furveying, and efpecially the furveying of harbours, and alfo 

 for piloting fliips into harbours. Phil. Tranf. vol. Iv. 

 art. 10. p. 70. 



U Mr. 



