C *33 .]

in case the given obliquity of the ecliptic at the time be either greateror less than 23°. 28'. 15". And therefore in such case correctionsrauft be applied. Enter the table of the correction of right afcen-sion, p. xcii. with the right ascension (already found nearly) on theside, and the declination at the top or bottom of the table ; andtake out the correction with its proper sign. Likewise enter thetable of the correction of declination, with the right ascension alone,and take out the correction with its proper sign. And say, as 6 o'is to the difference between the given obliquity of the ecliptic and23 28k 15" :: so is the correction of right ascension or declinationjusi: found : to a fourth number; which applied to the right ascen-sion or declination already found nearly, with the sign of the tables,p. xcii, in case the given obliquity of the ecliptic be less than 23 0 .28'. 13", or with a contrary sign if the given obliquity be greaterthan 23°. 28'. 15", will give the true right ascension or declina-tion.

Exampie.

Let the longitude of the Moon be 2 S . 5 0 . 5'. 36", and latitude 4 0 .36'. y8"Touth, as found by Probi. XIV. and XV. her right ascen-sion and declination are required ?

The reduction by tab. p. xxviii, is — i°. yd'. 3i // ,9, thereforethe ecliptic right ascension is 2 S . 3°. g'. 4",! ; to which applying thecorrection + 51'. 55", p, found by tab. p. lxxxix (using treble pro-portion for greater certainty) the right ascension of the Moon will be2 S . 4 0 . i\ o ;/ ,o very nearly. The ecliptic declination by table, p. xxx,is"-}- 2 T. 10'. 34'',5 or north. The quantity to be substracted fromthe latitude by the table, p. xci, is 4/. 23",6, whence the latitudediminifhed is — 4 0 . 32'. 34^,4 or fouth j the sum of which, andthe ecliptic declination -f- 21°. io'. 34",5 or north, is + i6°. 38'. 0", 1

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