150 SCIENCE PROGRESS 



integral of Cauchy is generalised for the regions C(p. 140), and thus the monogenic 

 function is proved to have derivatives of all orders, to be continuable along certain 

 lines, and to be representableby a series of Mittag-Leffler's polynomials (cf p. 141). 

 The "new monogenic functions possess the fundamental property of analytic 

 functions, uniqueness of continuation " (p. 144). This is a most important book : 

 we may remark that it contains a full exposition of the theories described in the 

 last number of Science Progress (1918, 12, 544), and referred to in a review of 

 The Book of the Opening of the Rice Institute in this number. 



Philip E. B. Jourdain. 



ASTRONOMY 



(1) The Dimensions of a Globular Cluster. 



(2) Globular Clusters and the Structure of the Galactic System. By Har 



low Shapley. (Reprints from the Publications of the Astronomical 

 Society of the Pacific, No. 172, December 1917, and No. 173, February 

 191 8, respectively.) 



(1) In the Astronomy section of "Recent Advances in Science" in the last number 

 of Science Progress mention was made (p. 552) of the methods by which 

 Mr. Harlow Shapley, of the Mount Wilson Observatory, has been able to make 

 reliable estimates of the distances of stellar clusters. These clusters are at such 

 great distances that direct measurements of their distances do not give reliable 

 results. The best determinations of stellar parallaxes have probable errors 

 which are many times larger than the parallaxes deduced by Shapley for various 

 clusters. The concordant values which he has obtained by different lines of 

 reasoning give confidence, however, that his values are at least of the correct 

 order of magnitude. 



In the first of the papers under review he has given detailed results for one 

 cluster, Messier 3, which gives one some idea of the enormous size of many of 

 these objects. This cluster is one of the brightest in the northern sky, being 

 visible under good conditions to the naked eye near the southern edge of the 

 constellation Canes Venatici. Its parallax is estimated to be o' /- oooo74. This 

 corresponds to a distance of nearly three thousand million times the distance of 

 the sun from the earth, so that the light now reaching us from the cluster left it 

 44,000 years ago. In a photograph taken with the Mount Wilson 60-inch reflector 

 more than 20,000 stars can be counted, excluding the central area where they 

 are clustered too thickly to be counted. With the new 100-inch telescope many 

 more stars would appear on a photograph. The diameter of the cluster as 

 ordinarily photographed is about thirty million times the distance of the earth 

 from the sun, and to cross the cluster light must travel 470 years. Many of the 

 stars are immensely superior in brightness to our sun, which, if situated in the 

 cluster, would not appear in the photograph, although the latter contains stars 

 as faint as the twentieth magnitude. Sirius would only appear as a very faint star 

 of the seventeenth magnitude. 



It would appear either that such clusters as Messier 3 are separate stellar 

 universes or that we must be prepared to revise the ideas we have hitherto held 

 as to the actual dimensions of our stellar universe. 



(2) The second paper gives a summary of numerous conclusions which 

 Shapley has drawn from his series of researches on Globular Clusters which have 

 previously been referred to in the Recent Advances section. Inasmuch as the 

 precise grounds upon which the conclusions are based are not detailed, but are 



