OF ARTS AND SCIENCES. 351 



pivots, produce a supposititious personal equation of this sort in a series 

 of observations so entirely differential in character as the present; and 

 the second complete year will not be finished till July, 1884. 



In the attempt to compare the present observations with similar 

 ones of earlier dates I was at once met with the difficulty arising from 

 the lack of exact proper motions. The two early catalogues which 

 are most available for their computation are Aiiwers's Bradley and 

 Struve's Dorpat Observations of 1814-15. But I have not yet had 

 time to complete the long calculations necessary for this purpose. 

 The plan which I have formed is, first, to reduce to a fixed epoch all 

 observations of these close polars which are free from dependence 

 upon a meridian mark of the old fashion; omitting especially Fedorenko, 

 Piazzi, Groombridge, and Pond, all of which require either large sys- 

 tematic corrections or frequent allowance for abnormal discrepancy. 

 The better catalogues, without especial systematic correction, will give 

 by least squares values of the proper motions, which will contain the 

 personal equations, it is true, but the residual errors will afford some 

 guide to their signs and amounts. The process would be analogous 

 to that which Professor Newcomb has employed for standard right 

 ascensions and Professor Boss for standard declinations ; that is, in 

 the least-square solution, one part of the chance errors for any given 

 star is owing to the systematic error of the catalogues employed. It 

 is of course impossible in this way to obtain the absolute values of the 

 systematic corrections, and quite likely that the final results will not 

 agree any better than if two catalogues, an old and a new one, were 

 arbitrarily adopted as the basis for these corrections ; but the method 

 has at least the merit of exhibiting such discrepancies as really exist, 

 and of showing what parts of the problem are for the time being abso- 

 lutely insoluble. The observations of the next half-century are in 

 fact necessary for its complete solution. It is my intention to con- 

 tinue these calculations, which have been long begun, and in which I 

 have been assisted by one or two of my former pupils. 



A rather serious stumbling-block in this matter, which will for a 

 long time to come make it difficult to obtain exact reductions from 

 one stiuidard to another, and still more difficult to find a standard 

 which is not in some degree arbitrary, lies in the relation between 

 Bradley and Struve. For stars so near the pole as these, Bradley's 

 observations give larger right ascensions than Struve's of 1814-15, 

 so that, as ^lUdler has long ago pointed out, considerable positive 

 reductions are needed to reduce the latter to the standard which he 

 adopted, — the Posiliones Medics. Whether this standard was held to 



