DESCRIPTION OF SEXTANTS.
The history of the sextant having been already de tailed in our article on NAVIGATION, we shall add no thing farther on this subject, but proceed to the de scription of Hadley's instrument.
This valuable instrument is shown in Fig. 5 of Plate CCCCLXXXVII. The contrivance of it is founded on this obvious principle in Catoptrics: that if the rays of light diverging from, or converging to, any point, be reflected by a plane polished surface, they will, after the reflection, diverge from or con verge to another point on the opposite side of that surface, at the same distance from it as the first; and that a line perpendicular to the surface passing through one of these points, will pass through both. Hence it follows, that if the rays of light emitted from anv point of an object be successively reflected from two such polished surfaces, then a third plane, per pendicular to them both, passing through the emit ting point, will also pass through each of its two suc cessive images made by the reflections; and that these three points will be at equal distances from the com mon intersection of the three planes: and if two lines be drawn through that common intersection, one from the original point in the object, the other from that image of it which is made by the second reflection, they will comprehend an angle double that of the in clination of the two polished surfaces.
Let RFH and RGI, Plate CCCCLXXXVII. Fig. 3. represent the sections of the plane of the figure by the polished surfaces of the two specula BC and DE, erected perpendicularly thereon, meeting at R; which will be the point where their common sections, per pendicular likewise to the same plane, passes it; and IIRI is the angle of their inclination. Let AF be a ray of light from any point of an object A falling on the point F of the first speculum BC, and thence re flected into the line FG, and at the point G of the second speculum DE. reflected again into the line UK, produce GF and KG backwards to AI and N, the two successive representations of the point A; and draw RA, RM. and RN.
Since the point A is in the plane of the figure, the point AI will be so also, by the known laws of Catop trics. The line FM is equal to FA, and the angle MFA double the angle HFA, or MFI-I; consequently RM is equal to RA, and the angle LIRA double the angle HRA, or MRII. In the same manner the point N is also in the plane of the figure, the line RN equal to RM, and the angle 1\IRN double the angle MRI, or IRN; subtract the angle MRA from the angle MRN, and the angle ARN remains equal to double the difference of the angles MRI and MRH, or double the angle IIRI, by which the surface of the speculum DE is reclined from that of BC; and the lines RA, RM, and RN are equal.
Coro]. 1. The image N will continue in the same point, although the two specula he turned together circularly on the axis R, so long as the point A re mains elevated on the surface of BC: provided they retain the same inclination.
Coro]. 2. If the eye be placed at L, (the point where the line AF continued cuts the line GK;) the points A and N will appear to it at the angular distance ALN, which will be equal to ARN. For the angle ALN is the difference of the angles FGN and GFL; and FGN is double FGI, and GFL double GFR, and consequent ly their difference double FRG or therefore L is in the circumference of a circle passing through A, N, and R.
Corol. 3. If the distance AR be infinite, those points A and N will appear at the same angular distance, in whatever points of the figure the eye and specula are placed, provided the inclination of their surfaces re mains unaltered, and their common section parallel to itself.
Corol. 4. All the parts of any object will appear to an eye viewing them by the two successive reflexions as before described, in the same situation as if they had been turned together circularly round the axis at R, (keeping their respective distances from one another, and from the axis.) with the direction HI, i. c. the same way the second speculum DE reclines from the first BC.