This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1914 edition. Excerpt: ...by the second of (36), and this value of t0 becomes the date of the second observation when the successive observations are equally distant from one another. With this choice of t0 the errors in X' and X" are of the second order, while X is known up to the third order. 117. The Approximations when there are Four Observations. When there are four observations the equations which correspond to the last three of (28) are f co + C1T1 + c2Tl2 + C8Tl' = Xl--C4Ti4-I, C4T24-I, c4r34 H, C3r44 +. (37) The determinant of the coefficients of c0, Ci, c2, and c3 is which is not zero since the dates of the observations are distinct. The errors of lowest order in C0, Ci, c2 and C3 are determined from (37); when only the first terms in the right members are known they contain c4 as a factor. Let these errors be represented by Ac0, ACi, Ac2, and Ac3; their orders in the T, are required.