963 



]/X' + T' = 2"83 X (0.846)"'-5" 



to which the values correspond verj accurately. For the magnitude- 

 factor Kapteyn (Gron. Publ. 8) found the value 0.78 and Unthank 

 (Mon. Not. R.A.S., April 1916) 0.847 ; from my two determinations of 

 ^Y' + Y' followed 0.79 and 0.90 respectively. 



For Z a constant value of -|- 1"88 can best be taken ; according 

 to my determinations Z would increase rather than decrease in tlie 

 direction of the smaller magnitudes. 



From the ratio between Z and I^X' -f- ^^ it immediately 

 follows that the apex-declination D must also become abnormal. It 

 increases greatly with decreasing magnitude. 



Weersma, also (A determination of the Apex of the solar motion 

 etc. Groningen 1908), found a high value for D, from Taylor's 

 stars, viz. S'^O . . . D = -\- 51°8, while Comstock (Astr. Journ. 655) 

 found for very faint stars: 



11"^.! ^ — + 71°. 



Although we should not perhaps attach too much weight to the 

 latter results, they all point to deviations in the same direction, so 

 that one feels inclined to seek other than accidental causes for them. 



The Z component, upon which the apex-declination depends, 

 reveals itself as a constant term in the star declinations, that is one 

 not dependent upon the K. A. We should, therefore, in the tirst 

 place look for the cause of an abnormal behaviour of Z and D in 

 constant errors of the declinations, and it would even be natural 

 to account for them by these, as long as we confine ourselves to a 

 determination of the apex coordinates. If such errors exist and work 

 in the satne direction as the ^-component of the solar motion, when 

 we proceed to fainter stars the equatorial component will decrease 

 in a greater degree than the one at right angles to it, and we shall 

 thus find a higher apex-declination. 



If, on the other hand, we consider the Z-component itself, we 

 shall continue to find that it decreases and even always by the same 

 absolute amount, unless, when bright and faint stars are taken from 

 different catalogues, the (f-errors are larger in the second case, and 

 when the same catalogue is used for both, a magnitude-error in 

 declination enters into it. As in my two investigations the value of 

 Z certainly did not decrease towards the faint side, and as 

 this does not seem to be the case either in the mean of the other 

 material examined, so that in the various cases declination-errors 

 would have to be assumed largely varying in a direction favourable 



