36o SCIENCE PROGRESS 



To discriminate between the two possibilities, he considers 

 the distributions in distance of stars of given apparent magni- 

 tude obtained from the two sets of assumptions, and compares 

 these with the results of the investigations of Dyson and 

 Eddington concerning the distribution in distance of the stars 

 contained in Carrington's and Boss's catalogues respectively. 

 The representation appears to be much better on the assump- 

 tion of a constant star density than on that of a luminosity law 

 independent of distance. 



The counts made by Shapley of the stars in the cluster 

 Messier 13 are utilised to support this conclusion. The stars 

 in a stellar cluster can all be assumed to be at the same distance 

 from the sun, and therefore the absolute magnitudes differ from 

 the apparent magnitudes only by a constant, and the counts 

 can be taken to refer to absolute magnitudes. It is shown to 

 be impossible for the assumption of a uniform luminosity law 

 to represent the counts ; but if the star density is assumed to 

 be the same at all points of the cluster, a luminosity law can be 

 found which will enable the observational data to be satisfied. 

 It is, however, doubtful to what extent results obtained in the 

 case of a star cluster can be regarded as valid for our own 

 stellar system. Halm appears to consider the fact that in 

 certain clusters a galactic condensation has been found as 

 affording some justification for the assumption. But it is 

 impossible to suppose that the density in a cluster can be 

 constant at all distances from its centre ; there must be a 

 limit beyond which any increase in exposure would only reveal 

 the fainter field stars which do not belong to our system. It is, 

 moreover, doubtful to what extent the law obtained by Dyson 

 and Eddington is valid, as the distances are measured from the 

 sun, which is not at the centre of the galactic system : it is 

 therefore improbable that the distribution is dependent only 

 upon the distance, and not also upon the direction. The 

 assumption of uniform density may, however, be a first 

 approximation in the neighbourhood of the sun, and the most 

 important result brought out by Halm in his discussion is that 

 the available statistical evidence does not seem to support 

 the generally accepted statement that the luminosity law is 

 the same at all points in space. 



In another paper, entitled " On the Systematic Motions of 

 Stars derived from Radial Velocities " {M.N., R.A.S., 80, 682, 

 1920), Halm analyses the available radial velocity determina- 

 tions on the assumptions (i) that, apart from their random 

 velocities, the stars move in two interpenetrating drifts ; 

 (2) that, in addition to these two drifts, there is a third drift which 

 is at rest in space. Hahn had previously brought forward 

 evidence in favour of such a third drift, derived from an 



