252 REPORTS ON THE STATE OP SCIENCE. 



catalogues of proper motions — namely Auwer's Bradley and Dyson 

 and Thackeray's Groombridge catalogue. A great opportunity for 

 advance has recently been afforded by the publication last year of a 

 series of over six thousand very accurately determined proper motions 

 distributed all over the sky — Professor Boss's Preliminary General 

 Catalogue. This new and specially favourable material for analysis 

 confirms in the main the results previously reached. Analysing the data 

 on the two-drift theory, 8 it is found that approximately three-fifths of 

 the stars belong to Drift I. and two-fifths to Drift II. Drift I. is 

 moving with a velocity of 1'52 towards E.A. 90°'8, Dec.-14°'6; and 

 Drift II. with a velocity of 0-86 towards E.A. 287°-8, Deo.-64°-l, the 

 velocities being measured in terms of the theoretical unit 1/h usually 

 employed in this work. These are the motions relative to the sun. 

 The vertex or direction of the line of relative motion of the two drifts 

 is E.A. 94°'2, Dec. + ll°'9, very near to the position which Kapteyn 

 originally announced. The bipolarity of the motions is shown most 

 plainly in the data, and the results from the different parts of the sky 

 are in excellent accordance with one another. 



It is convenient for the purposes of explanation and for mathe- 

 matical analysis to represent this bipolarity in the stars' motions as 

 being the result of two systems of stars having become intermingled. 

 I think there is much to be said in favour of this view ; but, as Professor 

 Schwarzschild has well shown, it goes beyond what the observations 

 strictly entitle us to assert. By putting together two systems moving 

 in different directions a good representation of the phenomena is ob- 

 tained, but a good representation can also be obtained in which the 

 duality is not evident. The ellipsoidal hypothesis of Schwarzschild 

 regards the stars as forming a single system, although it represents 

 the streaming in two favoured directions. More recently Dr. Halm 10 

 has introduced the idea of a third drift in order to obtain a closer 

 approximation to the observations. Our theoretical ideas as to the 

 mode of origin of this curious bipolarity of the stellar motions — whether 

 we must divide the stars into one or two or three systems — will 

 probably depend on which of these representations gives the closest 

 account of the observed motions ; but, neglecting these ulterior con- 

 siderations, the distinction between these theories is surprisingly 

 small. 



Let us examine a little more closely what it is that we wish to find 

 out. Our immediate goal is, I think, to be able to state a frequency law 

 of star motions. Just as Maxwell's law states how many molecules 

 of a gas have a given velocity (u, v, w), we require a law stating how 

 many stars have any specified linear velocity. Such a law need not in 

 the first place be a mathematical expression ; it may be embodied in a 

 numerical table or a diagram ; but if we could obtain this information in 

 some form we could afterwards decide whether it corresponded most 

 nearly with the formulae of the two-drift, ellipsoidal, or some other 

 theory. The materials of observation ai*e the proper or angular motions 



8 Eddington, Monthly Notices, lxxi., p. 4. 



9 Gbttingen Nachrichten, 1907, p. 614. 

 10 Monthly Notices, lxxi., p. 610. 



9 



