July i i, 1907] 



NA TURE 



249 



deduced by Prof. Dyson and Mr. Thackeray from 

 their re-reduction of Groombridge's Catalogue. The 

 number of stars included is 4200, all confined to a 

 region within 52° of the North Pole. About 1100 

 Carrington proper motions were also examined ; these 

 were all within 9° of the Pole. These two catalogues 

 contain a large proportion of stars much fainter than 

 those of Bradley, and enable the inquiry to be ex- 

 tended as far as magnitude 9-5. The same two 

 streams are found to prevail among these faint stars, 

 and it seems a fair conclusion that all the stars down 

 to at least magnitude 9.5 — more than half-a-million 

 in number — are within the scope of the theory. It 

 should, however, be remembered that only samples 

 have been taken, in limited regions of the sky, for 

 these fainter stars, so that there is a possibility of 

 unexpected deviations from theory in the at present 

 unexplored regions. 



To indicate how it is possible to distinguish whether 

 the stars in a given region of the sky belong to a 

 single system or to a double system, or to something 

 still more complex, it will be well to take an actual 

 instance. In Fig. i the curve P has been drawn to 



summarise the proper motions of the stars in a region 

 of the skv comprising parts of the constellations Draco, 

 Bootes and Hercules. The radius drawn from the dot 

 to the curve in any direction represents (by its length) 

 the number of stars moving in that direction, or 

 rather within 5° on either side of that direction. 

 Now the distribution of proper motions indicated by 

 this figure cannot possibly be due to a system of stars 

 forming a single "drift," that is, a system in which 

 the motions of the stars inter se are haphazard, 

 though the system as a whole may be in motion 

 relative to the sun (or, as it is more usually expressed, 

 the sun may be in motion relative to the system). 

 The tvpe of curve resulting from such a drift can be 

 calculated mathematically ; R and S are such curves. 

 It is not difficult to see that, having regard to the 

 position of the origin, no curve of this symmetrical 

 t3'pe could be chosen which would at all approximately 

 coincide with the observed curve P. The hypothesis 

 of one drift, therefore, does not give even an ap- 

 proximation to the observed distribution of proper 

 motions. But by combining the two drifts R and S, 

 we obtain the curve O, which agrees very closely with 



NO. 1967, vol.. 76] 



the observed curve. The differences between P and Q 

 are, in fact, insignificant, and of a purely accidental 

 character. 



For each of seven regions into which the Groom- 

 bridge stars were divided, as well as for the Carring- 

 ton stars, the obser\-ed distribution of proper motions 

 allowed itself to be dissected in this way, and 

 exhibited as the result of two simple drifts inter- 

 mingled. The agreement between the observed dis- 

 tribution and the theoretical distribution was not 

 always quite so perfect as in the case illustrated. For 

 instance, in one region the observed curve showed 

 twenty-four stars moving where they ought not to 

 have been ; presumably they formed a local system ; 

 but such an irregularity is small compared with the 

 two main drifts, which in that region each included 

 more than 400 stars. Most of the regions, however, 

 did not show even such a small irregularity as this. 



The shape of the simple drift curve depends on the 

 velocitv of the drift (relative to the sun) as compared 

 with the mean velocity of the stars of the drift relative 

 to one another. Naturally, for high drift-velocities 

 the curve becomes more elongated, for the tendency 

 then is for all the stars to move nearly in the direction 

 of the drift, the individual motions being relatively 



^ 



Q., 



r^' 



Fjg. 2.— The region within 52° of the North Pole. The arrows shew the 

 magnitudes and directions of the drift velocities. — — ^_ 



small; for low drift-velocity the curve is rounder, 

 approaching the form of a circle about the origin for 

 the limiting case of zero drift-velocity. The curves 

 R and S correspond to drift velocities 1-20 and 

 045 respectively (the unit is o-886 of the mean peculiar 

 speed of the stars). The analysis, therefore, not only 

 shows the directions in which the two systems of stars 

 are moving, but also their velocities. 



Fig. 2 is a diagram of the part of the sky covered 

 by the Groombridge catalogue. At seven points (the 

 centres of seven regions into which the area was 

 divided) are drawn pairs of arrows representing^ the 

 velocities of the two drifts in magnitude and direc- 

 tion, determined for each region independently, as 

 explained above; but in each case the shorter arrow 

 of the pair has been drawn on twice the scale of the 

 longer one, so that the difference in velocity of the 

 two drifts is even greater than appears from th'-- 

 figure. This attempt to represent a considerable por- 

 tion of the sphere on a plane surface is necessarily 

 imperfect, but it is sufficient to show that each set of 

 arrows is directed approximately from a point, viz., 

 the longer arrows from the point Q, (R..'^. iSh.. 

 Decl.-t-i8°) on the left of the figure, and the shorter 



