( 375 ) 



between the age of 5 and J 5 days and for the second limb between 

 tliose of :14 and 25 days and I simply rejected the observations at 

 the age of 4 and '2() days which are few in number. Perhaps il 

 would have been better to ai)i)ly a special correction at least to the 

 I'esults at the age of 5 days. 



As stated above, the values in the 2"'^ and 3"^ cohimns of the first 

 table are those found after the rejection of the two exii'cme groups, 

 and from them I derived further the differences II — I and the values 

 of V2 (I ■+ II)- ^^^^ II — I I'epresent the differences between the personal 

 errors for the two limbs. In the tirst three years these differences show 

 considerable variations, but for the last five years there is a good 

 agreement. However, as at first I only discussed the period 1895 — 1899 

 I adopted a mean value of II^I for these years and anothei- for the 

 following three, and for the corrections to be applied to the obser- 

 vations of the first and the second limbs to reduce them to the mean 

 of the two I assumed for 1895—1899 ± 0^02, for J 900— 1903 

 ± 0^.03. 



For a closer investigation of the personal errors it would be 

 necessary to discuss separately the results of the different observers. 



6. After having applied the corrections for personal error we 

 must now compute for the separate observations the corrections to be 

 applied to the mean longitude: in the first place those resulting from 

 the corrections of the parallactic inequality of the annual equation, 

 of the variation and of the evection — the last three as derived 

 by Newcomb — and secondly the long period corrections. From the 

 corrections of the mean longitude we must then derive those of 

 the right ascensions. 



The corrections of the first kind (comp. Newcomb Invest, p. 10 and 

 37 and Battermann N". 5 p. 21) are, using Hansen's notations: 

 7iöz = -\- l."69 mi D 4- 0."16 sin (D — (f) — 0."24 sin {D -|- cj) 

 + O."09 sin g' — 0."38 sin 2D — 0."21 sin (2 X> — g). 



For the application of these corrections I have calculated 2 tables, 

 parti}' ai-ranged as Newcomb's Table VII and VIII. 



For the long period corrections I first tried to derive accurate 

 values from the whole ax'ailable material. 



For although the empirical correction derived by Newcomb in his 

 Researches, has i-educed the differences from the observations to a 

 much smaller amount, there still remain unaccounted for discre- 

 pancies. This has been shown by Tisserand in his very lucid 

 account of the (juestions involved here "Sur l'état actuel de la theorie 

 de la lunc" in the 3'^^ volume of his Mécanique Celeste. He also 

 showed there that we caimot improve the agreement by altering the 



