DIAMETERS OF THE STARS DAN JON. 179 



darker from the center outwards just as is the solar disk. Admitting 

 that Betelgeuse has the same distribution of brightness as the sun, 

 the value obtained from the formula must be increased by an amount 

 which can not be exactly computed but which is about 15 per cent. 



Michelson even proposes to determine the law of distribution of 

 brightness upon the disk of Betelgeuse by a thorough study of the 

 change in the sharpness of the fringes in approaching the minimum. 



Admitting for the present the value 0".047, let us get the linear 

 diameter of the star. The best parallax from measures by several 

 observers is 0".0l7. The diameter of Betelgeuse is therefore 



0.047/0.017=2.7 astronomical units 

 =300 solar diameters. 



The equator of this giant star would thus contain the earth's 

 orbit (two astronomical units in diameter) and nearly that of Mars 

 (3.4 astronomical units.) That is in full accord with the earlier 

 estimates. 



The measurement of Arcturus made by Pease February 12, 1921, 

 has also checked with the theoretical value. For this star it Avas 

 necessary to use the total available length of the interferometer, 6 

 meters. This gives for Arcturus a diameter of 0".024. The diam- 

 eter predicted by Russell was 0".019. The parallax of the star is 

 0".095, according to van Maanen and Russell. Its diameter in 

 linear measure is, therefore, 28 times that of the sun. 



Finally, more recent observations have led to the value 0".040 for 

 the angular diameter of Antares. The most probable parallax is 

 0".023. Whence we deduce a diameter for Antares 200 times lar<rer 

 than the sun's. Again the order of magnitude predicted is con- 

 firmed. 



