144 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 3 5 



and from these distances the luminosities can be calculated readily 

 by the aid of the relationship which we have already considered 

 connecting apparent brightness, distance, and luminosity. 



There are, however, other methods that reverse the process, and, 

 instead of deriving the distances directly and then the luminosities, 

 we derive the luminosities directly and then the distances. A simple 

 example will illustrate how such a method operates. Suppose we 

 observe an incandescent lamp some distance away and can measure 

 accurately the amount of light we receive from it, or its apparent 

 brightness. If we know its distance we can determine its candle- 

 powder by the aid of the inverse square law as we have already seen. 

 If, however, we do not know its distance but do know its candle- 

 power, we can use the same law to determine the distance. So in 

 the case of the stars the question at once arises whether there is 

 any means for determining their candlepowers or luminosities 

 directly. 



There is a class of stars in the sky that vary in light in a peculiar 

 way throughout a definite period. A careful study of stars of this 

 class in star clouds where they are known to be at closely the same 

 distance, and of others at known distances, has led to the estab- 

 lishment of a law connecting the luminosities of such stars with the 

 length of period of their light-variations. This law is quantitative, 

 so that the luminosity can be determined when the period of varia- 

 tion is known. Stars of this character have been recognized in the 

 stellar systems of outer space, their periods of light-variation have 

 been observed, and from these periods the luminosities of these 

 stars have been derived. These in turn give us at once the distances 

 of the nebulae of which they form a part — the only accurate means 

 as yet devised for determining the distances of these enormously 

 remote objects. 



This method illustrates one of the direct ways in which stellar 

 luminosities can be determined for stars of a certain class. Another 

 method which has very wide applications depends upon the physical 

 properties of stars, and a somewhat more detailed analysis will per- 

 haps be of interest, not only because the method has been fruitful 

 in its results, but also because it illustrates many of the principles 

 used in modern astrophysical study. 



The temperatures of the surfaces of stars have been measured by 

 several different methods and are known with considerable accuracy. 

 As we might expect they differ widely: some of the dull red stars 

 have temperatures as low as 2,000° on the Centigrade scale, while 

 many of the blue stars reach temperatures of 20,000° or more. The 

 temperature of the surface of our sun is about 6,000° C. or nearly 

 11,000° on the Fahrenheit scale. One of the ways in which the 



