2 PROCEEDINGS OF THE AMERICAN ACADEMY 



Let S, s = the light of the Sun and of the star expressed in stel- 

 lar magnitudes by means of the scale of Pogson, in which a difference 

 of one magnitude corresponds to the logarithmic ratio, 0.4. This 

 ratio, expressed in numbers, is approximately 2.512. 



Let p = the parallax of the star in seconds of arc. 



The observed light of the star will be to that of the Sun as / b^ is to 

 £- ; the difference in their stellar magnitudes, or 



s — S=2.5 log f^., =2 5log B—o\ogb— 2.5 log I. 



Hence, log b = \og B + 0.2 S— 0.2 s — 0.5 log /. 



The radius of the Sun equals 16' 2", and accordingly B= 1924". 

 The value of S is more uncertain. Various determinations of the ratio 

 of the light of the Sun to that of Sirius have been made by different 

 observers. In 1698, Huyghens found the value 756,000,000 by re- 

 ducing the light of the Sun by a minute hole.* Wollaston, in 1829, 

 compared the image of the Sun and of a lamp reflected in a silvered 

 bulb of glass, and deduced the ratio 20,000,000,000.t Steinheil, iu 

 1836, using the Moon as an intermediate standard of comparison, 

 gave the value 3,840,000,000.t In 1861, Bond determined the rela- 

 tive light of the Sun and Moon by comparing their reflections iu a 

 glass globe with that of a Bengola light. Combining his measures 

 with the comparisons of the Moon and Sirius by Herschel and Seidel, 

 he deduced the value 5,970,500,000.§ In 1863, Clark found that, 

 if the Sun was removed to 1,200,000 times its present distance and 

 Sirius to 20 times its distance, they would appear equally bright, and 

 equal to a sixth-magnitude star. Their ratio, consequently, equals 

 3,600,000,000.|| Reducing these measures to magnitudes, we obtain 

 the values, Huyghens, 22.20 ; Wollaston, 25.75 ; Steinheil, 23.96 ; 

 Bond, 24.44 ; and Clark, 23.89. The mean of all of these is 24.05, 

 with an average deviation of 0.84. The last three agree well, and 

 give 24.10, with an average deviation of 0.23. Probably 24.0 is 

 not far from the truth, and may be assumed to represent this ratio as 

 closely as it is at present known. If we adopt — 1.5 for the magni- 

 tude of Sirius, from the measures of Herschel and Seidel, we obtain 

 for the stellar magnitude of the Sun — 25.5. 



* Cosmotheoros, La Ilaye, 1698. 



t Phil. Trans., cxix. 1^8. 



J Elemente der Ilelligkeits-Messungen, Munich, p. 24. 



§ Mem. Amer. Acad., viii. n. s., p. 2i)8. 



II Amer. Jour. Sci., xxxvi. 7G. 



