14 SEE— DETERMINATION OF THE [Januarys. 



§8. A Graphical Method for Determining the Depth of the 

 Galaxy, Based on the Study of Clusters. 



1. Make a diagram of lo or 20 concentric circles, separated by 

 equal intervals, each corresponding to 100 million light-years. In 

 this scheme no clusters will be included within the central circle, 

 because the actual measurements for parallax have excluded this 

 possiljility. P>ut the various clusters of the N.G.C. may be plotted 

 within the outer circles, or beyond them all, according to the results 

 given by Herschel's rule of brightness. 



2. It is required therefore to locate the clusters, and to indicate 

 their apparent angular diameters by dots of appropriate size. Some 

 allowance must of course be made for the varying stages of develop- 

 ment of the different clusters, but if there is a decreasing angular 

 diameter with distance it may be held that the method of estimating 

 distance devised by Herschel is essentially valid, and in fact our 

 only method of fathoming these immense distances, and thus deter- 

 mining the depth or profundity of the Milky Way. 



3. A careful attempt has been made to apply this method, using 

 the data of the N.G.C, and the results of the Crossley photographs 

 recently obtained at Lick Observatory. The results of this investi- 

 gation are shown to confirm the present theory. 



§9. Final Test of the Indefinite Extension of the 

 ]\IiLKY Way Desirable. 



This should be made by the graphical method just outlined, but 

 by means of more powerful instruments than any yet systematically 

 employed in this work. To feel satisfied that the universe extends 

 on indefinitely, we must have proof of additional clusters of stars 

 of smaller magnitude, and more compressed constitution, as from 

 the narrowing effect of perspective, at great distances. Probably we 

 shall not know what the sidereal heavens contain in the way of 

 vanishing clusters till the Milky Way is systematically photographed 

 for just such objects, and this very likely will require a long cam- 

 paign of photographic research with a large instrument. But as 

 many large reflectors are now coming into use, we may hope for it 



