October 12, 191 1] 



NATURE 



499 



having become intermixed. We have also to take noie of 

 " moving clusters," that is, groups of stars widely 

 separated in space, which have almost identical motions, 

 and are thus clearly connected in their origin. A whole 

 class of stars, those of the helium type of spectrum, are 

 exceptional, as they do not show the phenomenon of the 

 two star-streams, and have very little motion of any sort, 

 individual or systematic. This is perhaps due to the fact 

 that they are extremely remote, and lie beyond the region 

 through which the star-streams prevail. Finally, there is 

 the recently discovered connection between spectral type 

 and linear motion ; the later the type of spectrum (as 

 regards evolutionary development) the greater the average 

 speed of the stars. 



By considering the stars known to have a parallax greater 

 than 0-2" (seventeen in number), some important results 

 are illustrated, notably the sparsity with which stars are 

 distributed in space, the very heavy proportion of binary 

 systems, the very different degrees of intrinsic brightness 

 of stars, and the fact that the relative frequency of the 

 different spectral types as seen in the sky is utterly mis- 

 leading as an indication of their abundance in space. The 

 publication by Prof. Boss last year of more than 6000 well- 

 determined proper motions of stars distributed over the 

 whole sky has greatly assisted investigations of the two 

 star-streams. The bipolarity of the stellar motions is very 

 clearly shown in the new data. Besides the theory of two 

 star-drifts, an ellipsoidal theory, and more recently a three- 

 drift theory, have been employed to represent the distribu- 

 tion of velocities. The theories have much in common, 

 and it will be very difficult to distinguish between them. 

 An attempt has been made to arrive at the law of veloci- 

 ties directly from the observations, without recourse to a 

 particular theory; but the work, which involves an integral 

 equation, has presented some difficulties, and is not yet 

 completed. 



The remarkable result that a star's motion appears to 

 increase with its age, apparently implying that a star is 

 born with practically no motion, leads us to inquire into 

 the causes which produce stellar motions. From the con- 

 sideration of the moving clusters it appears that the chance 

 approaches of neighbouring stars have no appreciable 

 effect, and the cause must be the resultant attraction of 

 Hie whole mass of stars — a solution which, however, is 

 not without its difficulties. Dr. Halm has suggested a 

 Vaw of equipartition of energy among the stars implying 

 .hat the dependence of velocity is not really on the spectral 

 type, but on the mass of the star ; it seems that the stars 

 of later types are progressively less heavy than those of 

 early type. A third possibility is that distance from the 

 centre of the stellar system is the determining cause. The 

 hypothesis has recently been revived that the stellar system 

 forms a spiral nebula similar to the thousands of spiral 

 nebulae in the sky. This theory, though highly speculative, 

 appears to represent fairly well the observed distribution of 

 the stars and the Milky Way. and the double-branched 

 spiral form presumably involves motion in two opposite 

 directions in the centre of the system similar to that pre- 

 sented by the two star-streams. 



During the subsequent discussion Prof. Turner exhibited 

 a model of the Ursa Major " moving cluster," specially 

 showing that the component stars were nearly in one plane. 

 Mr. A. R. Hinks emphasised that at present we are only 

 getting at the central parts, and we do not know what 

 fraction this part bears to the whole. In reference to the 

 bun-shaped system, he considered that absorption of light 

 had not been taken account of as it should be. He thought 

 the spiral nebula conception was unnecessarily grandiose ; 

 he did not think that the star clouds of the Milky Wax- 

 were well represented by the arms of a spiral nebula, as the 

 latter seemed generally to be gaseous. He questioned 

 whether anyone had yet explained the dynamics of the 

 spiral motion in a nebula. He considered it premature to 

 assume that there were not more than seventeen stars 

 with parallax greater than 0-2". He also criticised various 

 points in nomenclature : in particular, the term star-cluster 

 wis lieinff used in two senses. 



The Astronomer Royal (Prof. F. W. Dyson) emphasised 

 the value of the information given by measured parallaxes 

 and the importance of making more determinations. The real 

 dtfficultv is a lack of a knowledge of the actual distances 



NO. 2l8q. VOL. 87] 



of stars. He thought that the best way was to try to 

 explain the velocities of stars gravitationally, and alluded 

 to Lord Kelvin's satisfactory attempt in this direction to 

 connect the total mass of the stars with the observed 

 velocities. Prof. Turner and Mr. F. Bellamy explained 

 the work done at Oxford in determining large proper 

 motions ; these were (unlike the stars as a whole) dis- 

 tributed nearly uniformly round the sky, the slight excess 

 being in directions at right angles to the Milky Way. 

 Father Cortie asked if there was not a contradiction in the 

 fact tht.t whereas the later-type stars had the larger veloci- 

 ties, yet they were relatively more abundant in the slow- 

 moving drift than in the fast one. Mr. S. Stratton pointed 

 out the anomalous position of the planetary nebula? ; their 

 large velocities would place them at the end as the last 

 stage of evolution. Mr. H. Hilton asked whether the 

 velocity would not be least at the centre of a system of 

 stars and increase outwards. 



Mr. Eddington, replying to Prof. Turner, explained that 

 the excess with large proper motions at right angles to the 

 Milky Way was due to the solar motion coming in with 

 greatest effect there in the Oxford zone. Replying to Mr. 

 Hilton, he explained that he had regarded the stars not 

 as moving in orbits, but as moving from outside to inside, 

 and vice versa. Replying to Father Cortie, he explained 

 that it is the individual motions of later-type stars that 

 are greatest, as distinct from the drift motions. 



Father Cortie and Mr. J. H. Worthington gave some 

 particulars in regard to endeavours to view the recent 

 eclipse. 



The programme for Wednesday, September 6, contained 

 two papers by Mr. S. Stratton, which in his enforced 

 absence had to be taken as read. One of these, on an 

 unusual meteor observed at Portsmouth on August 31, 

 described a meteor with an apparent path in the form of a 

 letter J, which probably arose from foreshortening accom- 

 panied by swerve. The swerve might be traced to spin and 

 resistance or to unequal heating effects. The second paper, 

 on the possible relations between sun-spots and the planets, 

 contained a discussion of sun-spot material tabulated to 

 show phase effects due to Venus and Jupiter. The con- 

 clusion is against the validity of conclusions come to 

 recently by Prof. Schuster in connection with the influence 

 of Venus and Mercury. A longer period of observation is 

 apparently necessary before trustworthy results can be 

 obtained. 



Mathematics. 



In the department of mathematics Lieut. -Colonel Allan 

 Cunningham, R.E., read a paper on Mersenne's numbers. 

 These numbers are of the form M, = 2' - I , where q is a 

 prime number. Since the appearance of Mr. W. W. Rouse 

 Ball's paper in 1S92 Prof. F. N. Cole has factorised M 67 , 

 Lieut. -Colonel Allan Cunningham has factorised M n , 

 M l63 , and M,, 7 , while H. J. Woodall has recently factorised 

 M,„. This leaves still unverified (as composite) only 

 fifteen out of the forty-four numbers (with q<257) origin- 

 allv affirmed by Mersenne to be composite, viz. when 



9=101, 103, 107, 109, 137, 139, 149, 157, 167, 173, 193, 

 199, 227, 229, 241. 



A complete list of all the possible divisors <i million of 

 these fifteen numbers has been prepared by Mr. A. GeVardin 

 (of Nancy, France) and Lieut. -Colonel Allan Cunningham, 

 working independently. These trial divisors have been 

 tested by the latter up to ^00.000 without success (every 

 " trial divisor " was tried twice). 



Prof. J. C. Fields read a paper on relations between 

 the double points and branch points of a plane algebraic 

 curve F(xj) = y" + F„_,j'" -1 + , &c, which presents no 

 singularities at infinity and the finite point singularities of 

 which consist of nodes and ordinary cusps. On represent- 

 ing an arbitrary polynomial in (*,y) of degree « — 2 by the 

 notation G{x . y) = '5, r ^l rr x r }>' a simple proof was given of the 



formula 2 x c x *' ' -</„, „_., where the summation is ex- 



F^laA) 

 tended to all points (a x ./> x ) which are ordinary branch 

 points, nodes, or cusps of the curve, the coefficient c k 

 having as value either 1, 2, or 3, according as the corre- 

 sponding point is an ordinary branch point, a node, or a 

 cusp. 



