153 Wisconsin Academy of Sciences, Arts and Letters. 



most half of it, there are vaUiable discoveries by the Mel- 

 bourne observers and by Mr. Stone; and in the northern 

 hemisphere, and part of the southern, we have Auwers' 

 Bradley and the other compilations which have been just 

 mentioned. I estimate that probably two thousand stars in 

 the whole heavens have proper motions exceeding 0".l (a 

 tenth of a second) annually, which have already been cal- 

 culated by least squares, or some similar process, and only 

 need revision. 



The field of investigation in this direction now open is, of 

 course, boundless; what needs to be done for the next twenty 

 years is mainly a critical study of the materials, their re- 

 duction to a fixed epoch and least square calculation there- 

 from, and adding (probably) a smaller amount of new ob- 

 servations than has been accumulating in a routine way, 

 without much plan, for the last half century; to say nothing 

 of the great catalogues which have been better planned . I 

 have not mentioned these newer catalogues in detail as they 

 are well known. 



For the epoch 1900 it ought to be possible to construct a 

 catalogue like that of the British Association for 1850 in 

 general plan, but complete to the seventh magnitude, and of 

 great accuracy both in its positions and proper motions, 

 and before that time we ought to have a definitive settle- 

 ment of the problem of the solar motion, which will go far 

 to give us definite notions of the general structure of the 

 universe. For I have long ago shown that, in this way only 

 can we find much more about the average stellar distances. 



