HI. UK-VIOLET LIGHT IN Till sni.AR CORONA ON AUGUST SO, 1905. 321 



this curve there is equal blackness on the photograph and the same blackness occurs 

 on Photograph VI. at a point at distance h, which was illuminated by ' during t 6 . 



Hence 



//i = constant = (, + f,) 1 '/ v '. 



The mean distance of the equal-blackness curve is the average value of p which 

 is r. But r is, by assumption, the distance of the point on the corona at which the 

 intensity is i. Hence the menu distance of the equtil-hliickness curve and h t are 

 correlative distances on the corona. The same result holds good for the three 

 eccentrically superposed pictures ftbc of the VII th photograph, and the constant F,, 7 is 

 equal to (ti + fa + fx) l "/ta". Photograph VII. may therefore be measured and reduced 

 in the same way as the other photographs, provided that always two opposite points 

 of an equal-blackness curve be measured. Terms of the second order have been 

 neglected in this derivation ; they amount to only a fraction of the distance AC 

 (O'll diameter) and are small quantities compared with the errors of measurement. 



7. The Formula, which gives the Intensity of the Corona as a Function of the 



Distance h. 



I first tried whether the observed distances satisfied Professor TURNER'S formula 

 (intensity inversely proportional to the sixth power of the distances from the sun's 

 centre), but find inadmissible residuals. Another formula has therefore to be derived. 

 If the distances given in columns I. to Vre., Table III., be plotted as ordiuates, and 

 the corresponding distances standing in the first column as abfccissae, the points 

 belonging to the same column lie as nearly in a straight line as can be expected from 

 the accuracy of the observations, and all these five lines can be made to intersect in a 

 point x, x. 



Hence 



= y n (h f + x), n 1 to 5, x a constant. 



The intensity * being a function of the distances h, which are counted from the 

 sun's limb, I write i = cf(h+x). Hence ', = cf(hi + x) = </[y. (A.+x)] and 

 * = </(/ +x), 



'i = constant F. 



as /, and h n are correlative distances on the corona. This relation is satisfied by 

 j(z) = z~*. Hence i ' = c(li + jc)~* and F t , = y~ y - The formula is the same as 

 Professor TV UN KK'S, with this difference, however, that x need not be the radius of 

 the sun. 



Approximate values of x and y are found in this way. I assume x = 0, 40, &c., to 

 320 (solar diameter = 1000) and calculate y from hi, h m , and x. The residuals are 



VOL. ccvii. A. 2 T 



