689 



upon larger or smaller trapezia in which the celestial sphere is divided. 

 Some investigators have made use of different methods and have 

 discussed and combined the respective i-esults ; Newcomb, in particular, 

 has done this in an admiral)le manner. It is therefore often diflicult, 

 even for the results of one investigator, to lix the exact value of. 

 the corrections to be applied to them, and whereas an accurate 

 knowledge of the foundation of our investigation, namely the exact 

 mean variation of the distances, is not yet attained, it would cer- 

 tainly not be worth while to make elaborate calculations concerning 

 the influence of this variation. We shall therefore only trace this 

 influence in a few simple suppositions concerning the method of 

 calculation followed. For this we use the formulae expressed in i?,„ , 

 as it can be seen at once that the values previously obtained for the 

 components of the parallactic motion will agree most nearly with 

 the corrected results for that distance. 



///, the first place toe loill consider the influence of the assumed 

 law of distances, upon the results for the precessional eonstant. 



a. Deterinination of the Precession frovi Right Ascensions. In 

 this deduction we may either determine the correction of the total 

 luni-solar precession Lp by expressing i\m and Ln in it, or, elimi- 

 nating A?z by attributing equal weights to the results from groups 

 formed according to the A. R., confine ourselves to the determination 

 of Lm\ the influence of Ln disappears of course, when the material 

 used is symmetrically distributed over north and south declinations. 

 If we allow for the influence of t\n, the correction terms which 

 contain sin ti must be taken into consideration, and we must 

 investigate how the influence of these terms will be divided between 



X 



the term in Ln which contains sin <i and that in —-, which is con- 



stant for all declinations. Now owing to the approximate equality 

 of two coefficients the whole coefficient of siji a is reduced to 



An sin d 4- 0.93 0.04 - cos" ö and, even without the rigorous 



Km R,n 



formation of the normal equations, it is clear that, for not too high 

 deelinations, the term with cos' é will principally infiuence the 

 parallactic motion. 



So it follows that, even if we take the infiuence of An into account, 

 provided our stars are distributed over all R.A. and we do not 

 attribute too great differences of weight to the different groups, we 

 may practically only pay attention to the correction terms which 

 do not depend upon u. Calling the value of Am (variation in 100 



