A manual of spherical and practical astronomy, embracing the general problems of spherical astronomy, the special applications to nautical astronomy, and the theory and use of fixed and portable astronomical instruments, with an appendix on the method of least squares . f and m being the intersections of this plane with thesurfaces of the mirrors. Let AMbe the direct ray falling upon themirror Jf, which we shall first sup-pose to lie in the direction MC;let Mm be the direction of the rayafter the first reflection, and mEits direction after the second re-flection. Draw 31B parallel toEm, MP per
A manual of spherical and practical astronomy, embracing the general problems of spherical astronomy, the special applications to nautical astronomy, and the theory and use of fixed and portable astronomical instruments, with an appendix on the method of least squares . f and m being the intersections of this plane with thesurfaces of the mirrors. Let AMbe the direct ray falling upon themirror Jf, which we shall first sup-pose to lie in the direction MC;let Mm be the direction of the rayafter the first reflection, and mEits direction after the second re-flection. Draw 31B parallel toEm, MP perpendicular to MC\and Mp perpendicular to the mir-ror m. The angle AMB is thedifference of the first and last di-rections of the ray. The anglePMp is the same as the angle contained by the mirrors, being obviously equal to 31 , therefore, to prove that AMB = 2P3Ip. If we conceive a perpendicular drawn at m, parallel to 3Ip, weeasily see that j^Mm is equal to the angle of incidence of the rayMm falling upon m, and p3IB is equal to the angle of reflectionof the same ray; and since these angles, by a principle of Optics,are equal, we have pMm = pMB = PMp + P3IBBut, on the same principle, we have PMm = PMA = AMB + PMBThe difterence of these two equations gives. We whence PMp = AMB — PMpAMB = 2PMp 80, In order to apply this principle, let the mirror Mhe at-tached to an index arm 3ICI, which revolves upon a pivot atiHf in the centre of a graduated arc OIN, and let vi be perma-nently secured in a fixed position at right angles to the plane ofthis arc. Let 310 be the direction of the central mirror and ofthe index arm when it is parallel to the fixed mirror m, and iCtthe graduation of the arc commence at 0. In this position, anincident ray ^If from a distant object 5 will be reflected first tom and tlien in the direction 77}E. which will be parallel to the M SEXTANT. first direction BM. If then the ohject is so distant that two raysfrom it, BM and byn, falling upon the two mirr
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Keywords: ., bookcentury1800, bookdecade1, booksubjectastronomicalinstruments
