412 ASTROMETRY 



Total velocity Frequency 



to 10 kil. pro sec. 0.025 



10 to 20 .145 



20 to 30 .252 



30 to 40 .259 Sun's velocity 20 Kil. 



40 to 50 .178 pro sec. 



50 to 60 .093 



60 to 70 .035 



70 to 80 .011 



80 .002 

 1.000 



In the same hypothesis we may also derive the law from the 

 astronomical proper motions. Time does not allow, however, to enter 

 into this matter, which I have tried to explain elsewhere. 1 



The time that remains I would rather devote to some considerations 

 about the fundamental hypothesis itself. In what precedes I have 

 sketched what, in my opinion, is a good plan of attack of the sidereal 

 problem. The ease with which such problems as, for instance, the 

 much-debated question about the most general structure of the Milky 

 Way, may be settled makes such a plan very attractive. 



The fundamental hypothesis on which the whole investigation 

 rests has already done good service and has led to results which are 

 pretty generally accepted. But still everybody must feel that here 

 lies the weak point of the method. As far as I know, no proof of its 

 general correctness has as yet been attempted, not even within the 

 limits in which such proof seems feasible without serious difficulty. 



That there must be divergences in detail seems extremely prob- 

 able. That there is a certain a priori probability that these divergences 

 may be considerable cannot be denied. 



What is more important still : 



Every astronomer who has devoted much thought and time to the 

 study of the proper motions must be aware of the fact that there 

 remain not inconsiderable anomalies. They prevent him from ac- 

 cepting our fundamental hypothesis on other terms than as a pro- 

 visional one, to be used for want of a better. 



If we base our study of the structure of the universe on this 

 hypothesis, we must do it on the principle that out of several evils 

 we should choose the least. Conceding all this, does it follow that we 

 have to accept the conclusion of a critic who denied any astronomical 

 interest to any research based on this one hypothesis? 



1 believe not. 



Are the objections sufficient to make us neglect the whole of the 

 data furnished by the proper motions? 



1 Publications of the Astronomical Laboratory at Groningen, no. 5. 



