ton 



ASTRONOMY. 



HIDES. 



J ' loiiiiJ. 

 Computing the moon's geocentric radius, by the formula j^ ' wo have for tho four observations : 



The longitudes of the first three observatories are con- 

 sidered well known, and, by taking their moans, we 

 obtain + OB. -067. The correction from the assumed lon- 

 gitude of Georgetown is + 0. -121 ; therefore the dif- 

 ference, + Os. '64, is to be converted into an error of lon- 

 gitude. 



Tho motion of the moon in R. A. at the time of George- 



town transit, by the formula d L 



d A' d A' 



where d is + 115s. -08 in 1m., or + Os.-03197 in 1 second 

 of sidereal time hence the correction of the assumed 



longitude is ^ r^ Is. -69, or the true longitudefrom 



this observation is 5h. 8m. 21s.-C9 west. 



The following additional example of the determination 

 of longitude, by observation of the moon and moon-cul- 

 minating stars, is from Struve's Geographical Investiga- 

 tion in Turkey. 



1S31, May 22, the following transits of the moon and 

 moon-culminating stars were observed : 



APPARENT RIGHT ASCENSIONS. 



Taking the mean of the apparent right ascension at 

 Dorpat and Cracow, we obtain 



h. m. a. 



Virginia 



174 '. '. 



13 



1 13 

 20 45 

 35 874 



86} 



77 



-74) 



The following table of reductions is formed : 



By applying which to the observed right ascension of 

 the moon's 1 L., the right ascensions of the moon's 1 L. 

 are obtained, viz. 



At Schurscha ... 13 I' 46-49 



Dorpat ... 13 13 40-97 



Cracow . . . 13 14 34 00 



Greenwich ... 13 17 10 34 



Proceeding, then, with an assumption of longitude of 

 Si'hurscha=4, we obtain a correction of the ephemeris 

 d A', which includes both the error of tho opln-iiH'ris, 

 and also the motion of the moon in R. A. producod by 

 an error in the assumed longitude. The error of the 

 ephemeris having been determined by the comparison of 

 the observations at Dorpat, Cracow, and Greenwich, the 

 residual error at Schurscha will be entirely due to tho 

 erroneous assumption of the longitu lo of the latter place. 

 Thus, if d A bo the correction of tho ephemeris deter- 

 mined at the three standard observatories ; and, if the 

 observed right ascension of tho moon at Schurscha be a', 

 and that from the ephemeris A', so that a' A' = dA', 

 then the correction of the assumed west longitude 



dA' dA 



dLi = 



/ 



The longitude of the place deduced from the lunar 

 culmination will be then L= L + d L. 



H is the increase in R. A. (in arc) for the time of obser- 

 vation at the required place. 



Assuming L'= Ih. 34m. Os. -0 from Paris, and com- 



E uting the value of the geocentric radius of the moon, 

 y the preceding method the following table is formed : 



The three obervatorio give an error of the ephemeris 

 nlant ; the mean U d A 0*-88, with p = 

 0-4744. 



2173 + 088 20"-85 



dL -~ 04744 -04744- 



h. m. a. 



or the loncituiU- uf .Schurscha - I 34 41-0 from Paris. 

 The comparison with tho individual observatories 



-21*32 h - m - 



With Dorpat dL=. - -44-91on. = l 34 1 1 ;i. 



-21-72 

 Cracow --^^---45-9..= 459. 



10 '40 

 Greenwich -- -*M - 41 ]. 



The Mean h . . =-1 34 440. 



