166 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1921. 



relationships. In a few generations doubtless the time will come to 

 nse the rich harvest of observations now patiently being accumulated. 

 Then in its turn sidereal astronomy will become clear, logical, deduc- 

 tive. At least it is a patriotic wish that it may be so, for it is a task 

 especially suited to the French genius. 



EQUIVALENT DIAMETERS. 



The direct measurement of star diameters fills a whole chapter in 

 astronomy till now rather hypothetical. A long time ago all hope 

 had been lost of detecting the disks of the stars with the ordinary 

 instruments of our observatories. At the focus of our telescopes, 

 diffraction spreads the light received from a luminous point into a 

 circular diffuse spot surrounded by rings. Since such a spot is much 

 larger than the true geometrical image of a star, it is impossible to 

 distinguish between the image of a star and that of a point. If we 

 try to measure with a micrometer the angular diameter of a star, 

 the value obtained will have no relationship with the true dimen- 

 sions. The measurements will give merely the diameter of the 

 diffraction spot which depends solely on the aperture of the objec- 

 tive of the telescope. 2 



It is true, we can measure extraordinarily small relative displace- 

 ments of stars, of the order of a few hundredths of a second of arc. 

 For instance, the annual parallax 3 has long since been determined. 

 The two problems are really very different in nature and difficulty. 

 We can determine with great precision the center of the diffraction 

 spot and its displacements, although some special device is necessary 

 to force it to deliver up its secret of the true nature of the luminous 

 source. 



The measurement of stellar diameters is therefore a difficult task 

 to approach since we are unable to produce true images of stars by 

 any direct means. Consequently, for some time we have exercised 

 our ingenuity in avoiding this difficulty by evaluations more or less 

 hypothetical. Sometimes the evaluations have rested on solid foun- 

 dations. We know, for example, the fruitful researches relative to 

 eclipsing variables, but the information thus gathered does not 

 suffice for an exhaustive study. Let us leave aside this aspect of our 

 subject, very interesting though it be in itself, in order to consider 

 a general method based upon the comparison of the relative bright- 

 ness of stars and the sun. 



- The diameter of the diffraction spot is inversely proportional to that of the objective. 

 An aperture of 12 centimeters (5 inches) gives a spot about two seconds of arc (2") in 

 diameter. An aperture of at least 5 meters (16 feet) would be necessary before the disk 

 of the greatest star (0."05) would begin to be appreciable. 



' The annual parallax of a star is the angle which the radius of the earth's orbit about 

 the sun occupies as seen from the star. 



