DIAMETERS OF THE STAES — DAN JON. 167 



The apparent intensity of a luminous source depends upon two 

 factors; its intrinsic brilliance and its surface. If two stars have 

 the same intrinsic brilliance, their apparent brightnesses will be pro- 

 portional to their surfaces. 



Let us take as an example Sirius and our sun, of which the " mag- 

 nitudes " are —1.6 and —26.7. The difference is approximately 25 

 magnitudes, corresponding to a ratio of apparent brightness 



( Sun ) / ( Sirius ) = 10,000,000,000. 



If we admit for the moment that the two stars have the same 

 brightness per unit surface, we must then also admit that their ap- 

 parent surfaces are in the same ratio, 10,000,000,000. The apparent 

 diameters are in the ratio of the square root of this, or 100,000. 

 Since the diameter of the sun is 1,800", that of Sirius is 0".018. 



Let us consider another example: Betelgeuse is 2.5 magnitudes 

 fainter than Sirius. Its brightness is therefore 10 times smaller ana 

 its diameter the square root of 10 times smaller or 0".006. 



These diameters correspond to their true diameters only provided 

 that the intrinsic brightnesses of these stars and of the sun are all 

 the same. A priori, nothing could be less certain. However, these 

 values, taken in their proper significance, are precise. They are the 

 diameters which we must assume for fictitious stars of the same sur- 

 face brightness as the sun, in order that if substituted for the real 

 ones, their brightnesses would be of the same magnitude as the real 

 ones. E. C. Pickering has designated such values as equivalent 

 diameters. 



Having reached this far, to go farther we need to know more of 

 the surface brightnesses of the stars. This becomes possible through 

 the advance of spectroscopy and the physics of radiation. From the 

 laws of radiation we glean two essential properties of radiating 

 bodies : 



First, the energy of radiation per unit surface increases with the 

 temperature; it is proportional to the fourth power of the absolute 

 temperature when the body is a " black body." (Law of Stefan.) 



Second, the spectrum composition of the emitted light also varies 

 with the temperature; in the spectrum of a black body, the wave- 

 length corresponding to the maximum intensity of energy is in- 

 versely proportional to the absolute temperature. (Law of Wien.) 

 In simpler words, as a body becomes hotter, its emitted light changes 

 from red to white to blue. 



We therefore have reason to think the yellow and red stars are 

 colder than the white or blue ones. Consequently the former radiate 

 much less light than the latter for equal surfaces. The equivalent 

 diameters cannot in general be equal to the true diameters. The 

 stars of superior intrinsic brightness to the sun are smaller than our 



