. Asiatic Researches. 100 ON THE FORMULA FOR CALCULATING circumstances—similarly |3 Ursae Minoris and 3 Cephei, the two stars in former editions of the Nautical Almanack nearest the Pole, have 1' 23* and 1' 12^'' for their stationary periods. It must, however, be remarked, that the hypothesis, on which that enquiry is conducted, is not rigorous ; for it is therein taken for granted that the same vertical circle will pass through the upper and lower positions of the star at equal lapses of time before and after the Maxi- mum, an assumption which, though perfectly admissible for the end therein
. Asiatic Researches. 100 ON THE FORMULA FOR CALCULATING circumstances—similarly |3 Ursae Minoris and 3 Cephei, the two stars in former editions of the Nautical Almanack nearest the Pole, have 1' 23* and 1' 12^'' for their stationary periods. It must, however, be remarked, that the hypothesis, on which that enquiry is conducted, is not rigorous ; for it is therein taken for granted that the same vertical circle will pass through the upper and lower positions of the star at equal lapses of time before and after the Maxi- mum, an assumption which, though perfectly admissible for the end therein proposed, will not bear to be much extended : as for instance, suppose it were required to determine what would be the effect on the Azimuth, if instead of the precise instant of the Maximum, the observa- tion were made at any time before or after that phenomenon. To this end let PSZ be the polar triangle right angled at S, and let be the place of a star before or after arriving at >S'—Draw the Arcs of great Circles PS', SS', ZS', and then since PSS' is Isosceles, if a perpendicular were drawn from P on SS' it would divide that side, and also the angle at P into two equal and similar parts, so that if h P, h Z denote the variations of the hour angle and Azimuth, we have 1st. Tan P>S'*S'= Cot 1 5 P Sec 2d. Sin h SS' - Sin ^ h P Sin PS Hence, because of the right angle at S, we have sin ZSS' = cos PSS' and cos ZSS' — i sin PSS' and therefore the general equation becomes (vide Woodhouse's Trigon. page 157—3d edition).. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Calcutta
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Keywords: ., bookcentury1800, bookdecade1830, bookpublishercalcu, bookyear1833
