A general theory for the mensuration of the angle subtended by two objects, of which one is observed by rays after two reflections from plane surfaces, and the other by rays coming directly to the spectator's eye / [G. Atwood].

  • Atwood, G. (George), 1745-1807
Date:
[1781]
Catalogue details

Licence: Public Domain Mark

Credit: A general theory for the mensuration of the angle subtended by two objects, of which one is observed by rays after two reflections from plane surfaces, and the other by rays coming directly to the spectator's eye / [G. Atwood]. Source: Wellcome Collection.

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    is proportional to the fine of FI and the cofine of DL jointly; confequently the fine of FI being the fame, fin. i ED is propor- tional to the coline of DL; this will lead to the realon why in enumerating (art. 4.) the * conditions which limit the magnitude of the obferved arcED,the pofitionof the fecondaryKP,in refpedt of the point of interfe&ion Q^and of the fixed fecondary KO, was annexed : for it will appear, that every thing elfe being the fame, the magnitude of the arc ED will depend on the polition of the fecondary KP, whether it be on one fide of the fixed fe- condary KO, or on the other, the angles PKO,/KO, being equal. Having fet off Op = OP draw, the fecondary Kp interfering the parallel FIMU in the point U; and through B and U draw the arc of a great circle BUW *, take UVV = BU ; and through D and W draw the arc of a great circle DW : then by the conftrudtion and demonstration in art. 6. the angle fubtended by the obferved objeCts will be meafured by the arc DW, and it will be eafy to fhew, that DW is not equal to DE, except in two extreme cafes; that is, when the fixed plane of reflection DFB is either coincident with the primitive fecondary KO or perpendicular to it. Through the points F and U draw the arc of a great circle VFU, and from D draw the arc DV perpendicular to VFU: fince + the fines of half the arcs DE, DW, are in a proportion compounded of the proportions of the fine of IF to the fine of FU, and of the cofine of DL to the cofine of DV, the fines of IF, FU, being equal by the conftrudhon, the fines of half the arcs ED, DW, will be in the fame proportion with the cofines of DL and DV, which are evidently unequal; confequently, the fines of half the arcs DE, DW, and therefore the arcs themfelves, muft be unequal. 11. The angles PKO, OK/, remaining equal, when the fixed plane of reflection BFD (fig. 4.) is coincident with the * Compare fig. 2.. t Supra. Secondary