N.^1 TURE 



[November 4, 1909 



its simplicity and convenience, were not nuicti in 

 error, in spite of the systematic character of the 

 motion of the stars in these two streams. For the 

 equations which result from Airy's method agree 

 closely with those of a valuable method of determining 

 the solar motion due to Bravais, which does not 

 assume the haphazard character of the peculiar 

 motions of the stars. But an entirely new fact m 

 stellar astronomy has been elicited in the discovery of 

 the systematic movements towards and away from 

 ^ Orionis. 



Mr. Eddington introduced a precise mathematical 

 definition in place of the somewhat nebulous phrase 

 star-stream. .\ "drift of stars " is defined as a group 

 of stars the velocities of which relative to some system 

 of axes are quite haphazard. The velocity of the 

 "drift" is the velocity of the system of axes, while 

 the " peculiar " velocity of a star is its haphazard 

 velocity relative to the system of axes. Haphazard is 

 defined as a distribution of velocities, according to 

 Maxwell's law for the molecules of a gas. Formula 

 are then developed to give the distribution of the 

 directions of proper motions in any small area of the 

 sky which would arise from the projection on the 

 face of the sky of a star drift with a given mean 

 peculiar velocity and a "drift" velocity given in 

 magnitude and direction. Mr. Eddington applied his 

 method to the consideration of the proper motions in 

 Groombridge's catalogue, recently determined at 



-Velocity diagram according 



hypothesis 



Greenwich by Messrs. Dyson and Thackeray. The 

 catalogue contains about 4500 stars within 52° of the 

 North Pole, a large proportion being between magni- 

 tudes 7 and 9. Comparing the actual distribution 

 with a theoretical one, based on the assumption that 

 the stars form two drifts, he found close accordance. 

 The stars were equally divided between two "drifts " 

 the apparent directions of which were in good agree- 

 ment with Kapteyn's results. The two streams did 

 not show any distinctive features, each contained 

 bright and faint stars, and stars of all types of spec- 

 trum, and, further, the mean distances from the sun 

 of the stars contained in the two "drifts" were the 

 same. Additional confirmation was obtained from 

 1200 stars within 10° of the North Pole, the proper 

 motions of which had been determined by comparison 

 of the Greenwich positions in 1900 with those found 

 by Carrington in 1855. In a later paper, and by a 

 somewhat different method, about 2000 fairly bright 

 zodiacal stars were also examined. 



According to Mr. Eddington 's determination, the 

 velocity of one stream relatively to the sun may be 

 represented by S.\, and that of the other by SB, while 

 the haphazard velocities of the stars composing the 

 streams are equally in all directions from the centres 

 A and B, and their mean values are represented by 

 the radii of the two spheres. The solar velocity rela- 

 tive to the centre of gravity of all the stars is repre- 

 NO. 2088, VOL. 82] 



sented by SG, and the rates at which the streams are 

 separating by AB. If SP denote the velocity of one 

 star relatively to the sun, this may be analysed into 

 SA, the "drift" velocity, and AP, the "peculiar" 

 velocity (which in this instance has its mean value); 

 the drift velocity S.A. may be analysed into SG, the 

 solar motion, and GA, the velocity of the stream. 

 Similarly, SQ, the velocity of another star, may be 

 resolved into a component of the second stream, the 

 peculiar velocity of which is BQ, or only half the 

 mean value. 



Prof. Schwarzschild assumes that the "peculiar" 

 motions of the stars do not obey Maxwell's law, but 

 a slightly modified law in which the resolved parts of 

 the velocities in one direction are all increased in a 

 definite proportion, thus giving a spheroidal instead of 

 a spherical distribution. When combined with the 

 solar motion, this distribution of "peculiar" velocities 

 gives two favoured directions for the proper motions 

 of the stars included in any small area of the sky, and 

 has the advantage of representing the stars as a 

 single instead of a dual system. Applied to the 

 Greenwich-Groombridge proper motions, the assump- 

 tion shows a very satisfactory accordance with facts. 

 .According to Prof. Schwarzschild, the observed proper 

 motions of these stars would be produced by a velocity 

 of the solar system SG and "peculiar" velocities of 



Fig. 2.— Velocity diagram according to Schwarzschild's hypothesis. 



the Stars the mean values of which in different direc- 

 tions are radii of the prolate spheroid ABA'B'. Thus 

 the velocity SQ of a star is resolvable into SG, the 

 solar motion, and GO, the "peculiar]' velocity. In 

 this instance the "peculiar" velocity is one-half the 

 mean "peculiar" velocity belonging to the direction 

 GO. In his second paper Prof. Schwarzschild de- 

 velops his theory with great mathematical elegance 

 so as to make it applicable to cases where the number 

 of stars per unit area is small. In this form it is 

 applied by Mr. Beljawsky to the stars of large proper 

 motion in Prof. Porter's catalogues, although its 

 application is not free from objection, as these stars 

 were selected on account of their large proper motion, 

 while the method is ' strictly only applicable to 

 unselected proper motions. 



Prof. Dyson collected all the proper motions greater 

 than 20" a century from various sources, and by a 

 simple graphical method determined the favoured 

 directions of motion. Partly owing to the small effect 

 of accidental error of observation on the direction of 

 the proper motion of these stars, and partly because 

 only large proper motions were considered, the two 

 apparent star streams were shown with great clear- 

 ness. In the large majority of cases it was possible to 

 assign individual stars to one or other of the two 



