1 10 Astronomical and Nautical Collections. 



ascension of the moon,) is evidently the longitude of the first place 

 from Greenwich. 



In like manner let the longitude of the second place from Green- 

 wich be calculated, and the difference between the two longitudes 

 will be the difference of longitude required. 



Comparing the two calculations, and employing the same nota- 

 tion as before, the difference between the mean times at Greenwich 

 of the respective observations is := 

 a X 15° 

 k 



The difference between the sun's mean longitudes at these times 



Clin 



IS = 



h 



And hence the difference between the right ascensions of the 



meridian at Greenwich at the respective times is = 



And the difference of longitude between the two places is = 



An example will make this quite clear. 



Let the moon*s right ascension upon the meridian of the first 

 place be 0** 0' 0", and the sun's mean longitude the same. The 

 moon will pass the meridian of the first place at 0'' 0' 0" mean 

 time. 



Suppose that the daily increase of the moon's right ascension is 

 1^ 0' 0", and of the sun's mean longitude 0'^ 4' 0". Then the 

 second place being supposed to be in 12'' 0' 0" of the west longi- 

 tude from the first, the time of the moon passing the meridian of 

 the second is thus found, by the rule given in the explanation of 

 the Nautical Almanac. 



At mean noon, under the meridian of the second place, the moon's 

 right ascension is O** 30' 0", and the sun's mean longitude is 

 0'' 2' 0", the difference between which is O'^ 28' 0". Then as 

 24* + O** 4' 0'' '- P 0' 0" = 23'' 4' 0" : O** 28' 0" :: !»» 0' 0'^ 

 - 0* 4' 0" - 56' 0" : 0^ V 8". And O'^ 28' 0" + 0^ 1' 8" = 



