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nearly. Then, taking T to represent the approximate time of end, find t' and t", omitting the computation of t, and T' + tt" will be the time ť of the end.
To find an arc v, expressing the angular distance, from the sun's vertex, of the point at which the eclipse begins or ends.
12. With the values of u and v, at the time T, for beginning, and their hourly changes of value u and v, at that time, find the value of u and v, at the true time of beginning. Then using these values, to log. of u add Ar. Co. log. of v, and the sum will be the log. tangent of an arc Q, less than 180°, which must have the same sign as u, and which will be numerically less or greater than 90°, according as v is affirmative or negative. Then V 270° + Q − (N + F) will be the distance of the point of beginning from the sun's vertex, reckoned to the right or west if V is affirmative, but in a contrary direction if V is negative. Finding, in like manner, u and v, and then Q, for the true time of end, we have V — 270° + Q (N
If u, v, and Q be found for the true time of greatest obscuration, and we take V 270° + Q — N, when (d+v q) at the approximate time of greatest obscuration is affirmative, but V90+QN, when (d+vq) is negative, then will V express, for the time of greatest obscuration, the angular distance of the moon's centre from the sun's vertex reckoned as before to the right or west.
ANNULAR OR TOTAL ECLIPSE.
13. If the value of (d+vg), at the approximate time of greatest obscuration, is numerically less than (h- 5464) or if it is so little greater, that the sum of log. cos N and log. of (dv-q) is numerically less than log. of (h-5464), the eclipse will be total or annular; total when (h5464) is negative, but annular, when it is affirmative.
14. When it is ascertained that the eclipse will be total or annular, take N, F, (pu), and t'as found for the approximate time of greatest obscuration (art. 9), and find t and ť, using (h 5464) instead of h. Then will T + t and Tt be the times at which the
eclipse begins and ceases to be total or annular.
Note. The times obtained by the above rules are expressed in mean time at Greenwich. They may be changed to mean time at the given place by Prob. V.
2. The above rule follows from the formulæ for eclipses investigated in the Appendix to Part I.
It is required to calculate for Philadelphia, the eclipse of the sun of May 15th, 1836.
The approx. time of new moon is 15d. 2h. 8m., Greenwich mean time.
log. 2.1790 p'
c = +98
· v′ = + 2180
p' — u'—+3359
log. 3.3385 N
A. C." 6.4738 N
log. cot. 9.8123 p¬u+c=+3720 log. 3.5705
1.9913 ť + 0.78
log. sin 9.9237
log. sin 9.9237
A. C. " 6.4738
approx. time of gr. obscur.
For true time of greatest obscuration and approximate times of beginning and end.