The solar parallax and its related constants; including the figure and density of the earth - Softcover

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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. 1891 Excerpt: ... distances from the center, La Place showed that 2C-A-B =--?r(£-Jff0)a2 f przdr 3 J f F" whence, as I prdr zz-J. and A and B are assumed to be equal 4 C-A=20-ir0)EV (306) o By eliminating C--A between (305) and (306), the following expressions result for finding the flattening of the Earth from the observed values of Ss and Sv: sin2Psin2GJ,,. Ss Sv---(e--i(70)--zz 'A G H With the numerical values from Table VI, (57) (78), (292), (302) and (303), (305) and (307) give C--A----0-000 1 34 44 E' arSs,--+ 0 000 1 5 2 93 E' (rSv ez= + 0-coi 73392--0-000 201 67 5s =. + 0-00i 733 92 + 0-000 229 40 Sv On account of accidental errors in the observed values of Ss and Sv, the two formulae in each of these pairs will seldom yield identical results. To obtain the most 7, T.3,liv. 7, chap. 2,? 20, probable values of C--A and e we must therefore resort to the method of least squares, and when the probable errors of Ss and Sv are equal, that gives C--A zz(--o-000 075 836 Ss + 0-000 066 668 Sv)E'az. e = + 0-00i 733 92--0-000 1 13 75 5s-f0-000 The formulae (309) are independent of all theories respecting the distribution of matter within the Earth, Sir Geo. G. Stokes having shown that equation (306) remains valid, whatever that distribution may be; and, as Dr. Hill has carried the expressions (302) and (303) to terms of the eighth order in the lunar theory, the uncertainty in the coefficients of Ss and Sv is not likely to exceed four or five units in the last place of decimals. For comparison with (309), it will suffice to quote the formulae found respectively by Pont£coulant and Hansen. Those of Pontecoulant are algebraically identical with (307), but his series for G and H are not pushed so far as in (302) and (303), the expressions employed beingf Tt f-i-l9il...

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