BLUE- VIOLET LIGHT IN THE SOLAR CORONA ON AUGUST 30, 1905. 317 



where t' can be determined from the equation. The formula expresses that (I + S) 

 acting on the film during t gives the same blackness as S acting during t and if, 

 t' being, of course, after (or before) t. Hence the positive sign stands for " the one 

 exposure after the other." Each of the terms may be replaced by a term of the form 

 a m b, which equals it in value [see (2)], and a expresses the intensity, 6 the time. The 

 terms may be written in any order [see (1)]. 



(/) Elimination of the Diffuted Light oj the Sky. Let t and I belong to the 

 corona, * and S to the sky. On the second half of the m th photograph I-fS m 

 illuminates the film during t m , and thereafter S m+l during t m ^ ; on the first half of the 

 (m-f l) th photograph S M illuminates the film during /, and thereafter !. 

 during +,. Let both produce equal blackness. By (e) 



+S-,*,^, = constant = S\A.+(I.+i+S. + ,)'<. + , 



The last two terms disappear, and therein lies the advantage introduced for Photo- 

 graphs V. to VIII. by the failure of the mechanism during the eclipse ; 



1'V., = I\ + ,. +l , where J ' - I [(j+ 1 )"- (?)"] 



Substitute i and * [see (a)] and introduce F by (c) ; therefore 



A = F. where .' = i m [7?=+ lY- feYT". 



'.+i LW / WJ 



Equal blackness was observed at the distances A m and A m+ i, hence h m and A M+ , are 

 corresponding distances ; they are, however, not correlative distances on the corona, 

 because the ratio of i m and i m +i, the intensities of the corona at /< and A w+l , does not 

 equal F' w m+i- On the other hand, the distances h m + &h m , A W+1 + AA 1I1+ ,, at which the 

 intensities of the corona equal i' M and i' m +i, are, by definition (</), correlative distances 

 on the corona. Hence we have 



I calculate log i and the differential quotient by the formula derived in this paper, 

 which gives i as a function of h ; further, i' for = O'fi, and thence A/i. The values 

 are: AA = for h = 200, AA = -3 for h = 600, AA = -15 for h = 1000, and AA = -35 

 for h = 1400. The measured corresponding distances are correlative distances on the 

 corona with an error AA. These systematic errors are insignificant compared with 

 the accidental errors of measurement (see Table III.) up to A = 800, and even for the 

 most distant parts of the corona they do not reach these accidental errors. The 

 correlative distances determine the intensity formula (see 7), and in the equations 

 the residuals appear under the form r = &h m F 1 ' 4 .-,, AA W _!. I observed on 



