( 377 ) 



Obviously tlic last values cannot be vcrv cei-tain. 



After (lins having formed (he total corrections to be ap|)lie(l to 

 the mean lonu'iliide, Ihey have been I'ednced (o corrections of tlu^ 

 I'iglil ascensions. Kor this I'cdiiction I could use ihe \alues F and 

 (r. «) giv(>n b_v Nkwco.mi; in his Table IX and XI. 'I'he vei'v small 

 reduction from orbit longitude to ecliptic longitude could be neglected. 

 (Comp. also /nre.^ti(/((tioii p. 12 and 14). 



7. The A (I corrected in this way were now used to derive from 

 them the corrections of the true longitude, which depend on the 

 sine and cosine of the, mean anomaly. In his JuvesfU/ation p. 16 

 Newcomb has showen that for this purj)ose we may use instead of 

 the residuals of true longitude those of right ascension and although 

 the error of the longitude of the iiode which is assumed to be 

 small lias increased since 18G8, his conclusion still holds. 



For each year the A a were arranged in 18 groups according to 

 the values of the mean anomaly, the first group containing those 

 between ƒ/ = 0^ and 2(V, the second those between </ = 20" and 

 4(r etc. Then the sums and the means for each grouj) were formed 

 and Avere regarded as corresponding to 7 =: 10'^, 7 = 3Cr etc. just 

 as had been done by Newcomb. 



If we represent the corrections wiiich are to be applied to the 

 true longitude of Hansen by 



d7 = — Ii sin (J — k cos g 

 we obtain for each year 18 equations of the form 



c -|- h sin g -\- k cos ^ = ?' 

 where c is the outstanding mean error of longitude, whilst for h 

 and l the signs are in accordance Avitli Newcomb. 



The equations were solved for each year by least squares with 

 due regard to the weights of r, which were assumed to be pro- 

 portional to the number of observations used. 



So I obtained the following values of h and k -. 



h k 



1895.5 + 0"29 + 0"44 



1896.5 +O.GG +1.16 



1897.5 -fO.57 +1.77 



1898.5 +0.51 +2.10 



1899.5 —0.98 +2.83 



1900.5 —1.66 +1.12 



1901.5 —1.46 +0.52 



1902.5 —1.18 +0.01 



It is obvious that these coefficients cannot result from errors in the 



