These tables are adapted to computation by the following modification of Bessel's formula, which was suggested by T. Henry Safford, Jr. 6=the latitude of the place. λ=its eastern longitude from Greenwich. log. e 8.9110835 log. (1-e2)=9.9971066 sin.ye sin. h= sec. cos. A k=(1-e2) sec. y sin. O' a=A―h sin. ( μ+2) b=B-Ek+Hh cos. (u+2) C=I C+Fk-Gh cos. (u+2) m=√(bc) If the instant for computation were correctly chosen at the time of beginning or end of the eclipse, m would be exactly equal to a. If m is not equal to a, the instant for a new computation, and which will be an approximation to the actual time of beginning, may be found by adding to the preceding time of computation an interval t, which may be obtained in seconds by the formulæ and if is taken of the same sign with a, it is a sufficiently near approximation to the angle of contact from the north towards the east. The magnitude of the eclipse is found by taking the difference (with regard to the signs) of at the beginning and end of the eclipse, and if this difference is denoted by 24, the magnitude of the eclipse is 24.5 sin. 2 or 24.5 cos. 2 accordingly as 4 is acute or obtuse. The value of o may also be obtained by the formulæ b' tan.x= a 4=4-x and the expression of t may be changed to t=1000000.m-a cos. x sin. sin. The elements of the sun for this table were derived from Bessel's tables, those of the moon from Damoiseau's tables corrected by Airy for Plana's theory, and with the additional corrections given by Hansen's new terms and by Airy's comparison with the Greenwich Observations. The following is an example under these tables for the computation of the beginning of the eclipse for the Washington Observatory. |