(cos d−cos D)/(cos M cos S) = (cos d′−cos D′)/(cos M′ cos S′); whence
cos D′ = cos d′−((cos M′ cos S′)/(cos M cos S)) (cos d−cos D);
cos D′ = cos d′−((cos M′ cos S′)/(cos M cos S)) (vers D−vers d);
cos D′ = cos d′−((cos M′ cos S′)/(cos M cos S))· (2 sin^2 ((1/2)D) − 2 sin^2 ((1/2)d)); that is,
cos D′ = cos d′−((2 cos M′ cos S′)/(cos M cos S)) sin ((1/2)(D + d))· sin 1/2(D−d); whence
also vers D′ = vers d′ + ((2 cos M′ cos S′)/(cos M cos S)) · sin ((1/2)(D + d)) sin ((1/2)(D−d)).
It may be observed, that Requisite Tables 9–11, answer logarithmically to (cos M′ cos S′)/(cos M cos S); and the verse sines, and the cosines can be very readily taken out of the tables in the Appendix. Also no ambiguity can arise from the application of the rule before given: for all the arcs concerned in the operation will always be (each of them) less than a quadrant, except the resulting true distance, which cannot cause any ambiguity; and the verse sines are given in the Appendix, to 126°.
(_Example 2nd, p. 39, Requisite Tables_.)
Reserved log. from Tables 9 and 10 9.995307 Log. sin 62° 45′ 56″ = 1/2 sum app. dis. and diff. app. alts. 9.948971 Log. sin 40 43 31 = 1/2 diff. ditto ditto 9.814536 Log. 2 0.301030 -------- Nat. num. corres. 1.147741 0.059844 Nat. vers. 22° 48′ 16″ = diff. true alts. 0.078167 -------- -------- Nat. vers. 103 3 23 = true distance 1.225908 --------
_De l’Influence des Agens Physiques sur la Vie_. Par W. F. Edwards, D.M., Membre associé de l’Académie royale de Médicine de Paris, Membre de la Société Philomatique, de la Société de Médicine de Dublin, &c.
The researches of science among the phenomena of the physical world have long obtained a high degree of estimation and interest in general society; but it is of late years only that their application to living functions has attracted much of the attention of the literary world.
The laws which govern the action of animal organs (the proper department of Physiology) have usually been investigated by the medical profession, to which they especially [p138] refer. Now we find the public take some pains, and with reason, to inform themselves upon subjects connected with physiological knowledge. A well-educated person, disposed to philosophical inquiries, is not merely contented with the consciousness of living, and the common information he derives of its means by experience, but he seeks also to comprehend the relations subsisting between his own organisation and the matters with which he is surrounded, and which at once furnish him with nutrition, life, and support, and assail him with disease and annihilation. His own instincts and observation, joined to the more learned experience of his medical advisers, help him through the precarious stages of life, and these may perhaps be sufficient for all its purposes; and under this impression many will seek to know no more of the secrets of nature.