688 



M-; = 



— 0.82 —0.21 —0.03 — 0.2J —0.11 



-f [+0.82 +0.04 +0.11 +0.11 +0.08 J .vm « 



+ [+1.00 +0.82 +0.31 +0.11 +0.04 + 0.43] ra.- « 



— [+ 0.03 + 0.21 + 0.08 ] sin 2« 



— [+ 0.21 — 0.03 + 0.20 ] cos 2a 

 + [+0.04 +0.10 ] sin Sa 

 + [+ 0.10 — 0.04 ] cos 3« 



Using these formulae we can now ti-ace the influence which the 

 sj'stematic difference in the distance of tiie stars of the same mag- 

 nitude will have upon the derivation of tiie precessional constant 

 and of the elements of the parallactic movement, and thus "deduce 

 the corrections, which must be applied to results in the derivation 

 of which the differences of distance were not taken into account. 

 When we consider this question more closely, however, we soon 

 see that a sharp determination of the corrections, which would hold 

 for all the determinations of these constants hitherto made, is hardly 

 possible. 



Even if we assume that the same law of mean variation of 

 distance with the gal. latitude holds for all individual magnitudes, which 

 is perhaps still doubtful for the brightest classes '), it does not follow 

 that it will also hold for the mean magnitude oi" a material which 

 extends over several classes, as the distribution of the separate 

 magnitudes may be different for the different regions of the heavens. 

 The working of the simple law may also be disturbed, when, as 

 is often done, and fi'equently quite rightly, proper motions above 

 certain limits are excluded from the discussion. 



Further, it is evident that the correct value of the necessary 

 corrections will be influenced by the manner, followed in each par- 

 ticular ca.se, of establishing and solving the equations. Where the 

 separate determination of the various unknown quantities is just 

 possible, we may try to do so, or by preference take those which 

 would be determined with the least weight from other investigations. 

 There is, moreover, ample room for differences of opinion as to the 

 attribution of the weights, and often in different instances diflerent 

 distributions of weights will recommend themselves. If there is reason 

 to believe that a group of stars belong together physically, this may 

 determine us to attribute to it the weight of only one star, and in 

 general, the discussion may be based upon tlie individual stars, or 



1) Newcomb in his Precessional constant Section XIV p. 43 — 46, points out 

 the difficulties which the answering of this question presents. 



