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By David Milne

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Additional info for Essay on comets, which gained the first of Dr. Fellowes's prizes

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In the first place, let us assume S = 1. In this case, we find r* = 1-01553818 + 1-39488738 —-40500975 = 2-0054158 and log r = 0-1511022 r"2 = 1-01350140+ 1-29140059 —-53655312 = 1-7683488 ... logr"= 0-1237839 ft* = -00442821+ -02584555 —-00378598 = -02658777 ... + r" + &)» — (r + r" — fc) 5 = -81048, log = 9-9087423 9-0137302 r1 + /" = 2-02903958 + 2-68628797S2 — -9415628713 10-8950121 = 7-8526 days. ) The result ought to have been 3*8956 zzt + tf, rather less than half. Let us for a second hypotJtesis take S — -5.

From the diminution of the radius vector, it is evident that the comet was at this time approaching its perihelion. (L J T — 1)f» = 3sin(L — , formulae. . tan ft , andi sin . , —— . 895584 days I =-4803483 r = 1 -06904688 r" = 1-02652542, T = 3-895724 •00000714: -00000352, 3-895653 = T + -000071 Error. = -48037 It will be -000140 -00000714 •0000217 -00000949 Diff. Error. Diff. Error. •0001 40: -000069" '0000217: -0000107, hence 8 = -4808590 log 3 = 9-6815659 r= 1-0690406 logM= 0-0003235 •00000949 : -00000467, (r + r" + k)* — (r + i" — k)* = -4020855, log = 9'6043184 0-5905882 = 3-895724 days > *7 Fourth hypothesis, Fifth hypothesis, Let r3 = 1 -01553818 + -32187773 — -19455449 = 1-14286142, log r = 0-0289967 r"s = 1-01350140 + -29799761 — -25774400 = 1-05375501, log r" = 0-0113698 k2 = -00442821 +-00596400 —-00181867= -00857354, log k = 2-9665801 r = 1 -06904688, r" = 1-02652542, Tc = -09259342, vtV5I 77 PRIZE ESSAY ON COMETS.

APPIAN, between the years 1531 and 1539, had at tentively observed several comets ; and he was particularly struck with the discovery, that all of them, in "every part of their course, constantly kept their tails in a direction opposite to the sun. As the same fact was soon remarked, in many other comets, its general occurrence led astronomers to suspect some relation between them and the sun, on which the formation of the tail, as well as the motion of the comet itself, might probably de pend.

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Essay on comets, which gained the first of Dr. Fellowes's prizes by David Milne


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