error for of Cos (h'sh) (84) 2 2 2 and secondly, that unity may be used, instead for Cos (84) in the expansion of Sin (A'-84). The sum of the errors arising from neglected quantities will amount at the maximum to rather more than o"3. But, that absolute accuracy may be arrived at, I have tabulated the effects. It will be found by expansion that the effect of the substitution of and the following Table gives the values of the correction to be applied to the computed value of dh : The effect of the omission of the second term in the expansion of Cos (d▲'), is + 1⁄2 dh (d▲)2 Sin '1′′, to be applied to the computed values of dh. It is tabulated as follows: I have, however, done away with the necessity of the use of the first of these Tables by computing, for small intervals of ' and ▲', (for the mean value of P,) very approximate values of dh, by which means the value of h’ can be obtained immediately with sufficient accuracy. & having been computed, h=h-dh is found, as also a, the R.A. of the geocentric position of the corresponding point by means of the right ascension of the zenith. Then Ad is computed by the formulæ : If then a and d be the difference of geocentric R. A. and N. P. D. of the moon's centre and the corresponding point, a A a and d = DA, from whence the geocentric distance of the point from the centre of the moon is easily found; and is equated to the moon's geocentric For the variation of the parallax in the time t, we have, for west hour angles, if the change of parallax be applied to the position of the corresponding point, The logarithms of the quantities A or Q' and Q" have been tabulated at intervals of 10" for all values of P from 53′ 30′′ to 61′ 40′′, to seven places of decimals, and the values of ' and B' to five places of decimals.. Log. C has also been tabulated to five places of decimals from A= 60° to ▲ = 110° at intervals of 1o. A general table has also been made, for mean value of P′ = 57', of the values of d (8 h) and d (ô ▲), at intervals of 5o, from ho to h = 100o, and from A = 65° to A = 115o, to be used as a check on the calculation by the preceding formulæ. The signs of d (8 A) must be changed for east hour angles. The other parts of the process of reduction need no explanation, as the co-efficients of the corrections to parallax, and to the assumed R. A. and N.P.D. of the star and the moon's centre, as well as those which depend on the error of time t, which enter into the expression for the distance of corresponding point from the centre of the moon, are computed by formulæ precisely the same as those used at Greenwich. The formulæ for the variation of this distance will be found at page 364 of my Astronomy before referred to, in which however it is to be observed that, by a misprint, the co-efficients of D and A have been effected with the same instead of different signs. For the sake of a more easy comparison of the results of occultations observed both at Greenwich and Oxford, the Greenwich notation has been retained, though it might have been desirable to substitute one more symmetrical. RADCLIFFE OBSERVATORY, OXFORD, ROBERT MAIN. |