I9I2.] DEPTH OF THE MILKY WAY. 11 



or apparent angular width of 21,600 light-years by the number of 

 degrees in the radius, 57.3. This gives for the depth 1,237,680 light- 

 years, and this value might be considerably increased by adjustments 

 in the data which are not improbable. 



(c) In addition to these general arguments, founded on the prin- 

 ciples of geometry, we might introduce another based on actual 

 measurement. The Lick helium stars, of average brightness 4.14 

 mag., were found to have an average distance of 540 light-years. If 

 they were brought near enough to us to appear of ist magnitude, 

 this distance would have to be divided by 4= V (2.512)^, and thus 

 we find for the first magnitude helium stars a distance of 135 

 light-years. 



Now in calculating the plan of the construction of the heavens, 

 from the apparent breadth of the Milky Way, Herschel arrived at 

 the conclusion that the thickness of the stratum is about 80 times 

 greater than the diameter of the sphere including the first magnitude 

 stars represented by Sirius (Phil. Trans., 1785, p. 254). And if the 

 average distance of these stars be taken as 135 light-years, the mean 

 diameter of the shell in which they are included will be 270 light- 

 years. This would give exactly 21,600 light-years for the thickness 

 of the stratum of the Milky Way, as before. 



It is true that Herschel classed all first magnitude stars in one 

 group, and took no account of the fact that the helium stars are the 

 more remote and the more brilliant ; yet regarding the Galaxy as a 

 stratum of stars chiefly of the helium type, which certainly is true 

 of all the more distant portions of that magnificent collection of 

 stars, we may consider the reasoning of this great astronomer as 

 still valid. And the argument in regard to the depth of the IMilky 

 Way is thus the same as that given above under (a) and (b). 



m 



§ 7. The Effects of the Extinction of Light in Space. 



This problem has been treated with some detail in the 23d chap- 

 ter of my "Researches," Vol. II., 1910, but we shall here examine 

 the subject with greater care, especially as to the most probable 

 average value of the coefficient of extinction. The light was shown 



