( 371 ) 



111 1876 Newco:\[i? published a coiiiparisoii of (lie observations of 

 the moon from 1862 — 1874 with the tables of Hansen ^) and showed 

 the existence of slowly increasing errors in the tabular mean longitude. 

 On the other hand, after having applied theoretical corrections to 

 ihe coefficients of some of Hansen's inequalities of short period, ho 

 found a hitherto unsuspected inequality in the true longitude of the 

 form a sin((/ -\- N), where (/ represents (he mean anomaly and N 

 an angle increasing by about 20^ per annum. The long period errors 

 were further investigated by Newcomb in his Resedrches ^), which 

 appeared in 1878. After an elaborate investigation of all the obser- 

 vations before 1750, he embodied the errors found in an empirical 

 formula, which apparently satisfied all the available observations. 



In the same year he published his "Corrections to Hansen's tablc\^ 

 of' the moon'', where tallies were given for the application of the 

 long i^eriod corrections according to the empirical formula alluded to 

 above and for the correction of a term of the true longitude accidentally 

 introduced into the tables with a wrouü' si"n. For the time being he 

 (Hd not consider it advisable to apply other corrections. These 

 "Correction.^" have since been introduced into all the lunar ephenierides. 



For the enqnrical term of long period no theoretical basis has 

 been found until now. As for the term depending on </ -j- JV^, 

 Neison's and Hill's investigations have shown that it may be the 

 "Jorian Erection". 



f I. Inve.^t.i<icition of the errors of lonxjitude. 



3. In my investigation I followed the same method as Newcomb 

 in his paper of 1876, that is to say, instead of the errors of longitude 

 and latitude 1 used those of right ascension and declination. Although 

 in this way the calculations become somewhat more intricate, it offers 

 tlio great advantage that the errors of observation, tlie systematic 

 and Ihe chance errors, in the two coordinates do not become intermixed. 



Thus in in\estigating the errors of longitude, I started from the 

 dilferences A «, which, in accordance with Newcomb I take in the 

 sense : Computation — Observation. 



4. In the lirst place I had to investigate the systematic errors 

 in tlie observed transits of the two limbs, but, as it is welMviiown, 

 tiie values found for them depend to a high degree on the value 

 adopted for the parallactic inequality. This renders an independent 

 determination of the two very difficult, as, for instance, it may be 



^) S. Newcomb, Invedtigation of corrections to Hansen's tables of the moon with 

 tables for tlieir application. Washington 187ü. 



-j S. Newcomb, Researches on the motion of the mopu. Washington 1878. 



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