STELLAR ASTRONOMY 423 



If we do this the time will probably come when we shall again be 

 led to evident discord with observation. The discordance will point 

 the way to a modified theory, which will be accepted as a third ap- 

 proximation. We must thus come nearer and nearer to the truth. 



The theory thus may undergo a series of changes but the principle 

 must remain unaltered: our distances shall be measured by the 

 parallactic motion. 



Meanwhile, in order to give a solid basis to such theories, we want 

 new data. 



In my opinion the most decisive advantage of such theories as the 

 above, defective though they may still be, lies for the present moment 

 in this, that they point out which are the data most wanted for the 

 further development of our knowledge of the structure of the universe. 

 They put definite problems for the solution of which definite data of 

 observation are wanted. The practical astronomer may thus find 

 reliable guidance in the preparation of his working programme. 



This is not the place to inquire into what these desiderata may 

 be. Still even this lecture has brought us more than once face to face 

 with difficulties which for their satisfactory solution demand obser- 

 vational data for very faint stars. 



Their number is so enormous that their complete observation is 

 out of the question. Happily the purposes of statistical investigation 

 are nearly as well served by specimens so chosen that we may safely 

 admit that they are representative of the whole. 



Photography will help enormously in obtaining such specimens. 



Specimens giving the number of stars of the several photometrically 

 defined magnitudes. 



Specimens giving proper motions. 



Specimens giving the class of the spectrum and the radial velocity 

 of stars of as many different magnitudes as are accessible to our ob- 

 servations. Last, not least: 



Specimens giving parallaxes. 



About these last I may perhaps be permitted to add a few words, 

 bearing on the importance of statistical investigations such as were 

 treated in this lecture. 



There is, I think, a very general and very natural feeling that the 

 science of the stars will lack a truly solid basis as long as it is not 

 founded on direct determination of distance. 



Mathematically speaking, this may be so. 



Practically I think we may be slightly less exacting without serious 

 risk. At all events, we must be less exacting if we wish to advance 

 at all. 



For the great majority of the stars must certainly have parallaxes 

 far below 0"01. Granting for the moment that we need not despair 

 of measuring such small quantities, even for individual stars, it will 



