1904.] on Sjyectrosco^ic Studies of Astropliifsical Problems. 447 



balanced in a large number of measures on different civil dates, 

 unless we suppose a periodic widening of tbe bright line, which 

 could only be explaineel by greater pressure at a pericentre ; and the 

 admission of a pericentre is the acceptance of an elliptic orbit. The 

 only systematic error remaining is the fraction of a measurement 

 due to a small shift of the apparent centre of the dark line. The 

 dark line is measurably thinner when the bright line is seen on both 

 sides of it than when seen on one side only, and half the difference 

 appears, in my trial of the method, to be a satisfactory correction. 



It is obvious, from this description of the suggested method of 

 dealing with the velocity problem, that many photographs are wanted 

 on different civil dates for the elimination of errors ; and at least 

 four times the number would be necessary for a determination of the 

 four epochs of maximum and mean displacements. But the need of 

 a great multitude of observations has n«ver yet blocked the way of a 

 zealous astronomer, nor is he now deterred by the weight of photo- 

 graphic plates to be packed in his store room. You could hardly 

 expect me to place before you any result obtained from the small 

 number of plates in my present collection. But the trial was made, 

 and I will venture to show you the figures, confident that you will 

 not condemn my method of studying the problem on account of its 

 present shortcomings. The tabulations on the screen give the mean 

 greatest length-interval from the centre of the dark line to the edge 

 of the bright line at 16-3 divisions of the micrometer head, from 

 18 dates, between extreme readings of 18*5 and 14-0 divisions; and 

 the mean least length at 7*5 divisions, without variations on four 

 successive dates. The difference, 8 • 8, is a little too great, owing to 

 the encroachment of the bright line already mentioned, and the 

 correction is shown in the lower half of the table. The resulting 

 maximum relative velocity of the stars is 120 km. /sees. ; and this is 

 encouraging when taken in conjunction with Belopolsky's direct 

 measures at the Pulkowa Observatory: for, on the supposition of 

 equal velocities, the maximum sight-line-velocity of either star with 

 reference to the sun would be 60 km. /sees., to compare with the 

 67 kms. given by the light power of the great Russian telescope. 



In the next table (projection on screen) we have the analysis of 

 the measures which would point out the four epochs wanted, if 

 the number of dates were great enough. At present the table offers 

 no certainties. Of the four epochs indicated in it two are in favour 

 of elliptical motion and two are against it, while all four are im- 

 possible in a circular orbit. The two epochs which favour the 

 ellipse are well marked in the tabulations, one within 15 hours, 

 the other within 24 hours intervals ; but the number of dates within 

 each interval is too small. And for the unfavourable epochs, the 

 number of dates might be enough, but they spread over long intervals 

 of the cycle, one over two and a half days, the other quite four days. 

 Seen in this light, the necessity of long and patient work is more 

 clear. "We are fortunate in having so many as four plates within 



