DEPARTMENT OE MERIDIAN ASTROMETRY. 12/ 



mass of the fainter star is very much greater than that of the brighter, we 

 shall find it very much more difficult to account for such a state of things. 

 Our present computations appear to remove the immediate necessity of 

 accepting or accounting for the existence of such an apparent anomaly, and 

 to that extent may be regarded as having performed a useful service. The 

 results will appear in the introduction and notes of the Catalog. 



As to proper-motion in general, the fundamental assumption is that the 

 individual star, or separate systems of stars, are in rectilinear motion with 

 uniform velocity. But if this is correct, then the motion of the stars as pro- 

 jected on the sky upon great circles are obviously not rigorously uniform in 

 those circles. Within periods sufficiently limited the angular proper-motion 

 of a star will be uniformly accelerated if the star is approaching the solar 

 system, and the contrary if receding. For any case in nature, however, this 

 foreshortening or perspective effect must be exceedingly minute. Hereto- 

 fore it has escaped identification. During the present year, however, we 

 have examined the meridian observations of 6i Cygni and Groombridge 1830 

 to find whether this effect of perspective is now to be recognized in the 

 meridian observations. In both instances the result has been affirmative, 

 though the probable errors of the respective results are nearly as large as 

 the effects determined. When the star's parallax and its motion in the line 

 of sight are known in combination with the proper-motion the variation of 

 the proper-motion on account of this foreshortening effect can be independ- 

 .ently computed as a predicted effect. This we have done for the two stars 

 in question, and the results obtained in this manner agree quite satisfactorily 

 with those obtained from the meridian observations. The uncertainties of 

 the computation, however, are necessarily very great in relation to the exces- 

 sively minute quantities under consideration; yet it may be regarded as an 

 auspicious beginning when it is found possible to bring to bear testimony 

 tending to show that our methods of determining stellar parallax and motion 

 in the line of sight lead to results that are in harmony with measurements of 

 stellar position. Furthermore, it is demonstrable that the precision with 

 which this test can be applied will rapidly increase with time — i. e., in a 

 geometrical ratio. 



Still more important is the fact that these computations shed some addi- 

 tional light, however feeble, upon a fundamental hypothesis. Are the mo- 

 tions of the stars sensibly rectilinear? Much evidence in the nature of infer- 

 ence already exists in favor of an affirmative answer to this question. The 

 present computations lead to results resembling evidence of a positive nature. 

 We can now foresee the time when it may be possible to say in reference to 

 several stars not only that their observed motions offer nothing to contradict 

 the hypothesis that the actual stellar paths may be rectilinear, but do afford 

 positive evidence that the curvature can not exceed a certain small and speci- 

 fied limit. The attainment of such evidence would obviously constitute a 

 distinct forward step of fundamental importance. 



9 — YB 



