THE LIGHT OF THE STARS 297 



the upper limit of £' as representing the class of very small nebulae. 

 For the intermediate class which includes those objects called " small " 

 by Herschel and " large " in the Lick catalogue, and which may be 

 designated as medium, I take a diameter five times as great, or 2^'; 

 and for Herschel's " large " nebula?, I take a diameter of 5'. The 

 reason for these selections shall now be given. 



I take for the diameter of the Andromeda nebula, 110'. This sub- 

 tends the longer axis of the oval figure of the more condensed spiral 

 arms. The fainter extensions are omitted because these are seldom 

 included in the more distant nebula?. Taking a suitable value for the 

 coefficient of transmission, the curves giving the relation between 

 brightness and distance become congruous for the two catalogues, if we 

 take x, the unknown ratio of distance for large and small nebula?, equal 

 to 2 for Herschel's catalogue, and x = 5 for the Lick catalogue. This 

 gives the following sequence: 



Nebular Class Diameter Distance Transmission 



Andromeda IIO'.O, fl 1 = 1.0 andromede, t = 0.996 



Large nebulas 5'.0, a 2 = 62.5 andromede, t a = 0.778 



Medium nebulae 2'.5, a 3 = 125.0 andromede, t a = 0.606 



Very small nebulas 0'.5, c 4 = 625.0 andromede, t a = 0.082 



The statement which was made for the ratio of brightness among 

 the groups in the Lick catalogue (vf and / -J- b for large and small 

 nebula?) can be repeated in identical language for Herschel's catalogue 

 by merely substituting the fraction f instead of f ; that is to say, 

 Herschel's nebula? are not only nearer than the Lick nebula?, but are 

 more nearly at a common distance; and the fraction expressing the 

 ratio of brightness for the two groups of near and distant objects 

 among the Herschelian nebula? approaches nearer to the value of 

 equality which it would have if all of the nebulae were at the same 

 distance, for then there would be equal absorption, and large and small 

 objects should be equally grouped about a mean value. 



Eatio of brightness 

 for large and for 

 small nebulas 



If equidistant, 1 : 1 

 Herschel, 2 : 1 



Lick Obs'y, 3:1" 



The absorption exerted by the medium between us and the nebula? 

 is in the main a non-selective one. If it were not so, but resembled the 

 ordinary selective absorption of the planetary atmospheres, the most 

 distant nebula? should be deep red instead of white. Some selective 

 absorption may, however, be exercised by the misty quasi-atmospheric 

 envelopes which we have reason to believe are associated with some or 



11 For the details of this investigation reference may be made to my paper, 

 "Are the White Nebulas Galaxies?" Astronomische Nachrichten, No. 4536, Bd. 

 189, 441-454, November, 1911. 



