174 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1921. 



What has been stated shows how, without direct measures, the astro- 

 physicists have succeeded in obtaining the dimensions of stars, and 

 also that they have brought to light a number of quite unexpected 

 facts. Despite the likelihood of the hypotheses developed on the 

 way, a direct verification becomes increasingly desirable. Back in 

 1868 Fizeau proposed a method for the direct measurement of stellar 

 diameters. Stephan approached the problem at Marseilles with a 

 telescope of 0.80 meters, but only showed the extreme minuteness of 

 the stellar disks. He proved that in order to measure them a much 

 larger instrument would be necessary. The task came to Prof. A. A. 

 Michelson of developing the exact theory and of making its first 

 successful application to the stars. We will in the succeeding sec- 

 tions outline his methods saying here only that his measurements con- 

 firm in a remarkable manner the most hazardous deductions of the 



astrophysicist. 



THE INTERFERENTIAL METHOD. 



We have said that in 1868 Fizeau proposed the application of the 

 interference of light to the measurement of star diameters. The 

 method rests upon the following principle. When we try to pro- 

 duce interference by Young's apertures, Fresnel's mirrors, or a 

 biprism, we find that the apparent diameter of the luminous source 

 must be very small if the fringes are to be pure. 7 If we employ as the 

 source of light a hole of variable diameter, lit from behind, we find 

 in fact that the sharpness of the fringes decreases as the diameter 

 of the hole increases. For a certain value of the diameter the 

 fringes become completely invisible. The finer and more marked 

 the fringes, the smaller must be the source. There is a proportion- 

 ality between the separation of the fringes and the limiting diameter 

 of the source. Michelson, to whom we owe the complete theory of 

 the phenomenon, showed in 1891 that the fringes of Young and of 

 Fresnel become invisible wdien the angular diameter of the source is 

 a little greater than the interval 8 which separates one fringe from 

 the next. He found indeed that 



w=1.22 8 



Why do the fringes disappear in the case of an extended source? 

 It is easy to see why. Each separate point of the source will give, 

 if it alone exists, a system of pure fringes. But the s} 7 stems 

 corresponding to the different points of the source will trespass 

 upon each other's ground and mutually blend together. The com- 

 plete disappearance comes when the superposition of the various 



7 The reader may observe an example of the " interference fringes " of which we are 

 about to speak, if he will admit sunlight through an almost vanishingly narrow slit 

 upon white paper within a darkened room. 



