RECENT ADVANCES IN SCIENCE 531 



parallax and apparent diameter of a cluster, so that a measure 

 of the latter enables an accurate determination of the parallax 

 to be deduced. The average probable error of a parallax is 

 only about 20 per cent. 



The distribution of the clusters in space exhibits several 

 important features. There is a strong tendency to concentrate 

 towards the galaxy and the distribution with respect to the 

 galaxy is remarkably symmetrical. The distribution in longi- 

 tude is surprising; the region from 41 ° to 195 is completely 

 devoid of clusters, whilst there is a remarkable concentration 

 about a longitude of 32 5 °. The most unexpected feature in 

 connection with the distribution is the existence of a galactic 

 belt within which no clusters are found : there is no cluster 

 within 1,300 parsecs (about 5,000 light years) of the galaxy. 

 Several possible explanations of this effect are considered, but all 

 are rejected. In the Observatory, 42, 82, 191 9, Shapley shows 

 that it is not an obscuration effect due to a cloud of absorbing 

 matter. Thus, whilst no explanation of the result is arrived 

 at, it is of importance as showing apparently that the clusters 

 are related to the galactic system. If this is so, we must con- 

 siderably enlarge our views as to the dimensions of the latter. 

 Some further evidence on this subject is to be given in a later 

 paper. 



The derivation of the parallaxes of the clusters permits their 

 actual dimensions to be calculated. The cluster Messier 3 

 may be taken as typical : it is 250,000 million million miles 

 from the earth. To cross the cluster, light must travel 470 

 years. Its total mass is from one-quarter to half a million 

 times the solar mass. A star of the brightness of the sun 

 would appear to be of magnitude 21*5, whilst the variable stars 

 in the cluster are nearly six magnitudes brighter. 



Einstein's Relativity Theory of Gravitation. — Reference has 

 already been made in these notes (Science Progress, 11, 623, 

 191 7) to Einstein's generalised relativity theory of gravitation, 

 and to the remarkable success which the theory has obtained 

 in providing a quantitative explanation of the motion of the 

 perihelion of the planet Mercury. This success at once brought 

 the theory into prominence and, in spite of certain difficulties 

 arising from the nature of the boundary conditions which 

 must be satisfied at infinity, it combined with the beauty of 



