A It T I C L E XI V. 



On the Accuracy of the Tubular Longitude of the Moon, to be obtained by the construction of' 

 New Lunar Tables. By Micrs Fisher Longstrcth. Head January 3, 1851. 



The discovery of the inequalities of a long period, by Hansen, together with the reduc- 

 tion of the Greenwich Lunar Observations from 1750 to 1830, afford ample materials 

 lor the construction of new lunar tables, and lead to the inquiry, what additional 

 accuracy can be obtained. The co-efficients deduced from theory by Damoiseau, Plana, 

 Pontecoulant, and those deduced from observation by Burckbardt, (though differing con- 

 siderably,) give the moon's place with nearly the same accuracy. Where a difference 

 exists, 1 have carefully compared them with observation and deduced the most 

 probable value. To test the accuracy of the new co-efficients thus obtained, I have 

 selected from the " Reduction of Greenwich Lunar Observations" all the observations 

 made during the years 1820, '21, '2)5, "21, and '25, numbering 499, and have computed the 

 moon's place with the new co-efficients, by correcting Plana's, when necessary; they 

 having been used in the Reduction of Greenwich Lunar Observations to obtain the moon's 

 tabular place. In the following pages I have arranged for comparison the errors of 

 Plana's co-efficients and those of the new co-efficients, to which have been added the 

 corrections for Hansen's inequalities, and most of the corrections required by Plana's 

 theory deduced by G. B. Airy. Upon examination, it will be found that in many cases 

 where the errors of the new co-cflicicnts arc lanjc, that the observations have been made 

 while the sun was above the horizon, or during twilight. The errors here given arc 

 necessarily compounded of the errors of the tabular place and of those of observation. 

 It will be well to inquire what amount of error of observation is liable to be made, and 

 for this purpose I have selected from the Greenwich Lunar Reductions the following clock 

 error-, obtained by transits of stars differing little in right ascension, and observed by the 

 same person, therefore free from what is generally termed "personal error." 



