Brightness of the Corona of January 22, 1898. 



43 



17. The discrepancies are again not large, and some of them may be 

 due to the extrapolation which was necessary for the brighter parts of 

 the corona, the standard squares not having been given a long-enough 

 exposure (as • stated in the former paper) to compare with the long 

 exposure of 50 sees, to the corona. Measures on plates with a shorter 

 exposure to the corona will perhaps allow of more accurate results near 

 the sun's limb. Unfortunately no plate is available with an exposure 

 shorter than 5 sees., but measures on this plate, so far as they have 

 gone, indicate a closer accordance with the theoretical formula near the 

 limb. Further measures are, however, required. 



18. With the assumed law 



where r represents distance from the sun's limb in solar radii, the total 

 brightness of the corona is 



Thus the ratio of the total brightness to that of the moon is -|- A. 

 In 1898 the value of A was approximately 2 1 ' 15 = 2 "2, and thus the 

 whole corona was about equal to the full moon. In 1893 the value of 

 A was 2 ' 23 = 1*2 j and the whole corona was thus about 0'6 of the 

 full moon. 



19. But we have omitted the constant illumination of the sky in this 

 integral. If we include a portion of sky extending to distance E from 

 the limb, and B be the value of the constant for "glare," which in 

 1893 was taken as 2- 7 s = 0-0046, and in 1898 was 2~ 6 ' 4 = 0*012, then 

 we must add to the above quantities 



It is not, however, easy to assign a definite value to R. 

 20. The integral brightness of the corona was measured in 1893 by 

 the late Mr. James Forbes, jun.,* and found to be 1*1 full moon. We 



brightness = Ar 6 , 



the total brightness of the full moon being represented by 



find [0-6 + B (R 2 - 1)] full moon. 



If the two quantities be equated, we get 



B(R 2 - 1) = 0-5 

 or R 2 = 0-5/0-0046 



= 110 



or • R = 10-5. 



* ' Phil. Trans.,' A, 1896, p. 433. 



