LONGITUDE FROM MERIDIONAL TRANSITS OF THE MOON. 23 



geocentric zenith distance ; z 1 the apparent zenith distance ; and d the 

 geocentric N.P.D. 



59. The arrangement of the observations in Table X., and the values of 

 the longitude derived from them, require but little explanation. The 

 observed R.A. of the Moon's bright limb has been corrected for diurnal 

 aberration, and the Tabular R.A. has been interpolated with fourth differences 

 from the section Moon-culminating Stars in the Nautical Almanac, on the two 

 assumptions that the longitude was 10 h . 31 m . s . and 10 h . 32 m . O. west of 

 Greenwich. The adopted correction to the Tabular R.A. is taken from 

 the Appendix, and depends upon all the observations made at Greenwich, 

 Washington, Paris, Konigsberg, Strasburg, Oxford, and the Cape of Good 

 Hope. These corrections are generally reliable to the extent of 9< 05, but 

 occasionally, as at the end of the 1874 October lunation, and at the end of 

 the 1875 January lunation, they are doubtful to the extent of s * 1 or even 

 more. 



60. The clock-correction, proper to apply to the transit of the Moon to 

 obtain the apparent Right Ascension of the limb, has been given with the 

 observed transit, Table IV. When a sensible difference occurs between the 

 clock- correction obtained from stars near the Moon in declination and that 

 obtained from the other stars of the same group, the former has been 

 adopted, if the Right Ascensions are sufficiently well determined. 



61. The weights assigned are proportional to the square of the change 

 of Right Ascension in 1 s . Half weight has been given to the observations 

 on October 20, October 24, October 27, January 17, for reasons contained in 

 the Notes. 



62. The longitude of the transit pier is obtained as follows : 



Observer. J> I. Number of Obs. ? II. Number of Obs. Mean. 



Mean 10. 3i. 26-0 



These results are, however, not entirely free from systematic error, proceeding 

 from the circumstance that the observations at Honolulu were made by 

 eye-and-ear, whereas the observations at the fixed observatories, from which 

 the errors of the tables are deduced, were made generally by the chrono- 

 graphic method. 



