Then, by (1), (2), (3),
L = }} (d + d') + § (m' — m) M + {
— {(n' − n ) + (s' − s) } + \ (r− r') + \ (p′ − p) + ↓ (ƒ −ƒ' ́)............. (4)
This is the final expression for the latitude. As already mentioned, M=68′′698, and ʊ—1.”067. The correction to the meridian (p or p') may be computed by the equation,
p
2 sini
sin 1"
X
cos L cos d
sin Z
where i is the star's hour angle from the meridian, east or west; but it has not been necessary to use it in this case, all of the stars having been observed on the meridian, or so nearly so as not to necessitate any correction on that account. The correction for flexure, being only that which is due to the difference of the zenith distances of the two stars, is also inappreciably small, and has been neglected.
The correction for refraction, though small, is appreciable, and has been applied. It is found by the equation,
or, by (3),
↓ (r−r')=} {57′′7sin (≈-2′) sec z}
} (r-r') (57.7sin (mm) M sec z}
(5)
This correction bears the same sign as the quantity m'-m, as appears from this equation, as well as from the consideration that r-r' is positive only when z is greater than z', in which case, under the given conditions, m'—m is also positive.
Tabulation of results.-The observations, reductions and results will be found embodied in the following Table, wherein Column I gives the date of observation; Column II the star's name, as in Table I; Column III its B.A.C. number; Column IV its magnitude, from the Greenwich Nine-Year Catalogue for 1872; Column V its position, North or South of the zenith; Column VI the position of the instrument, Circle East or Circle West; Column VII the star's Apparent Right Ascension at transit over the meridian of the place; Columns VIII, IX the chronometer times of bisection and culmination, to the nearest second; Column X the interval, in chronometer time, between bisection and culmination; Column XI the approximate error of the chronometer for each date; Column XII the micrometer readings, m,m', for the two stars of each pair, in revolutions and parts; Column XIII the quantity (mm); Column XIV, XV the readings of the north and south ends of the level, for both stars of each pair; Column XVI half the difference of the level indications for the two stars, or the quantity {(n^—n) + (s'—s)}; Column XVII the star's Apparent Declination at transit over the meridian; Column XVIII half the sum of the declinations for each pair; Columns XIX, XX, XXI the corrections for micrometer, level and refraction, computed as already explained [see equations (4) and (5)]; and Column XXII the resulting value of the latitude from each pair.