20 KNUT LUNDMARK, GLOBULÅR CLUSTERS AND SPIRAL NÉBULiE. 



in 



m 2h — m H = + 1 ) io. (9) 



With the use of this law the values for in 25 , put in parentheses, have been cal- 

 culated, and out of these values the parallaxes "k h have been obtained according to 

 Shapley's method. 



Of the 15 parallaxes obtained in this way, 8 agree well with Shapley's values, 

 and iti regard to N. G. C. 2099 and 6705 the concordance with parallax-values cal- 

 culated after Shapley"^ principles would certainly also be a very good one. The 

 remaining 5 values are of the same order of magnitude as tt sä , and the difference 

 between tc 8ä and % H is considerable only as regards N. G. C. 5897. Kritzinger 108 gives 

 a lower value for the total magnitude, from which would follow tz h = 0", 000020. How 

 to account for the remaining difference, I will for the present leave out of consi- 

 deration. 



The great value of observations of the total magnitudes is shown by the cal- 

 culated n H . It is very desirable that the determination photographically of the total 

 magnitudes of clusters, for instance by means of extra-focal photometry, would be 

 undertaken. A step in that direction has been made by Hertzsprung 88 , and it is 

 to be hoped that his works on this subject will be continued. 



Otherwise there would present themselves several ways of determining relative 

 parallaxes for globulars. The strong correlation shown by Charlier 39 between the 

 number of stars and the diameter in globnlar clusters, indicates a way of obtaining 

 relative parallaxes, and determinations of the apparent average distance between the 

 stars for instance by counting the number of stars in a certain area on a cluster 

 plate, another. In wiew of the scantiness of the material at hand in these cases 

 we shall nevertheless not at present occupy us with the determinations of relative 

 parallaxes by means of these methods. 



II. Determinations of the Solar Apex from the Velocities of Clusters 



and Nebulae. 



Slipher's 10 radial velocities in Table III for globnlar clusters give us a pos- 

 sibility of determining the Apex of the solar motions in its relation to the former. 

 Thereby one may be able to test whether these objects are far away or in our 

 .immediate neighbourhood. For in the latter case the value for the Apex ought not to 

 differ very much from the one adopted earlier, nor should the speed of the sun's motion 

 turn out to be of another order. The small number of velocities measured, naturally 

 causes that the Apex that is being determined by their aid, caimot possess any high 

 degree of accuracy. Yet we will here put in mind the fact that Herschel in 1783 

 with only 13 stars obtained an Apex-value that differs only very little from the one 

 now commonly adopted. 





