Practical And Spherical Astronomy for the Use Chiefly of Students in the Univer
Practical And Spherical Astronomy for the Use Chiefly of Students in the Univer
Robert Main
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= - 36309 8 '! Note. As the method of interpolation by second differences, which is applied without explanation in the text, may not be familiar to the student, I subjoin the following explanation of it. Let a; be a function capable of being expressed in the form x = a + It + cf. 'LONGITUDE OF WASHINGTON. 315 And let x_ v X Q and a? +1 be its values corresponding to values of t, -1, 0, and+1. Then we have 2nd diff. 2c sum of 1st differences of x for values x_ l9 x and and, differencing, we get,... 1st diff. B-c b + c . '. 2b and 2c = second difference of x. Hence the method in the text is obvious. As a second example we will deduce the longitude of the Observatory at Washington, U. S. , by comparison of the observed R. A. Of moon's first limb, and ty* Cancri, on Feb. 14, 1859, with the corresponding Greenwich observations. The Washington observations are given in the Monthly Notices, Vol. XX. P. 287. Greenwich. E. A. Of D 1 L 7 . 28 . 55-67 i|r 2 Cancri 8. 1 . 59'83 Sl = + 76 8 '79 7 = 168 9 -02 Washington.
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