FINDING LONGITUDES.] 



ASTRONOMY. 



1021 



12h. 50m. l-ls.-33 ; therefore, by a proportion, the longi- 

 tude from this observation is 8h. 48m. 59s. -67 east. 



Proceeding in a similar manner, we find for the obser- 

 vation in 1839, June 25, for assumptions of longitude 

 8h. 49in. east and 8h. 48m. east, the right ascensions of 

 the moon's 1 L. IGh. 59m. 9s.-95 and l(5h. 59m. 12s.-36 

 respectively (a correction of + Os. '09 being applied from 

 the Hamburg meridian observation). 



The result of the meridian observation at Port Essing- 

 ton is 16h. 59m. lls.-ll ; therefore the resulting longi- 

 tude is 8h. 48m. 31s. -12 east. 



The second method will include the use of moon-cul- 

 minating stars observed at other stations. The simplest 

 way is to form differences at each observatory between 

 the transits of the moon's limb and each moon-culmi- 

 nating star (properly corrected for the rate of the clock in 

 the interval). Comparing these differences with the 

 respective differences at other stations, the increase of 

 the right ascension of the moon's limb will be obtained, 

 which will, however, differ from the increase in the right 

 ascension of the moon's centre, in consequence of the 

 change of the moon's geocentric semi-diameter in the in- 

 terval of the two passages. This correction may be com- 

 puted as follows : If the geocentric radius of the moon 

 culminating in A be called r, and the true declination d ; 



and for a culmination at another station, B, these quan- 

 tities are called p and S respectively, the correction 

 will be 



I f r p 



-r- 7= 3 



~~ 15 ^cos. a cos. 



the true difference of the right ascension of the centre 

 for both times of observation. The sign applies to 

 the western limb, and the sign + to the eastern limb. 



But, if the apparent right ascensions of all the objects 

 observed are given at the stations, the more direct way 

 will be as follows (Struve's method) : 



Example. 1840, March 10. The following correspond- 

 ing observations of the moon 1 L. and moon culminators 

 were observed at Greenwich, Oxford, Hamburg, and 

 Georgetown (U.S.) Observatories. The differences of 

 longitude of Greenwich, Oxford, and Hamburg are sup- 

 posed to be accurately known ; and it is proposed to 

 determine the longitude of the Georgetown Observatory. 



The longitude of Oxford is . 

 Hamburg . 

 Georgetown . 



. 5m. 2s.-6W. 

 . 39in. 54s.-l E. 

 5h. 8111. 20s. + West. 



1846, March 10. Apparent Eight Ascensions Observed : 



Then, comparing each star with the Greenwich Observation, we have the following corrections :- 



When the above corrections are applied to the right ascension of the moon's limb, we shall be enabled to give 

 its place independent of any errors, either in the assumed equinox, or of any small residual instrumental correction. 

 Thus, the following sidereal times of observation are formed : 



Interpolating for these times, from the Nautical Almanac, we find the following right ascensions, decimations, 

 and seuii-tiiarnoturs of tho moon : 



