Transactions of the Royal Society of Edinburgh Volume 12 (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1834 Excerpt: ... p. 226. f Mem. de l'Acad. 1732, pp. 257-8. ready, in the case of a ratio of equality by MM. Parent and Godin f, as it has also been by most authors who have written on such subjects since. The following solution is different, I think, from any that have preceded it; and though it might, in some points of view, be deemed very elementary, yet as it is short, it might not be improperly introduced here, as another specimen of the method. It may be remarked that Godin professes to dispense with the differential calculus; but he does so only inform, as the elementary spherical triangle is in reality the one that is employed in his method "par les Infiniments Petits." The circles being represented as above, we have cosx =--cosp sin A + cos X sin (p cos 6 (1.) cot0 =--tan A cos 6 (2.) ndS = dx (3.) The first of these is the expression for the arc of the ecliptic intercepted between the first point of Capricorn and a point in the ecliptic, whose coordinates are f, 6. The second is the equation of the ecliptic, referred to the equator and winter colure; and the third is the given relation between the velocities of the sun in right ascension and longitude. From (1, 2) we get cosd), .. sin A andhencedv =-"n0dft (5.) -/sin A--cos' p Differentiating (2), we find fff- cosXdcp (6) sin d Vsin1 A--cos8 (p Inserting (5, 6) in (3), we get sin1 d s= n cos A (7.) which gives the north polar distance of the sun at the time in question, and agrees with the results obtained by other methods. Mem. 1704, p. 315. 1730, p. 27. VOL. XII. PART I. U U Combining (7) with (4) and (2), we get the sun's distance from the tropic of Capricorn, and hence from the beginning of Aries; and likewise his right ascension at the time. XXX. THE LOXODRQME, OR RHUMB-LINE. There is...