326 PROFESSOR L. BECKER ON THE DISTRIBUTION OF 



The mean error of an equation of unit weight is found = 0'017 as compared with 

 the adopted value of O'OIO. Any possible error A 7 cannot alter the value of the 

 variables by more than a small fraction of their errors, and a was deduced from 

 experiments with an error of 0'01. So far the time records have not been used; 

 I determine A< 5 as under (a) from the recorded times t l to t & , neglecting A? 7 and A. 

 The result is A/ r , = 0'140'06. I substitute this value and calculate the errors on 

 the supposition that Af 7 = l*'0, Aa = 0'02, which certainly exceed the true 

 errors. The result is 



re=13919, y = 4'000-17, 



t t becomes 1T40 0'50, which lies between the limits derived for t e in 6 (a). In 

 this solution no use has been made of the time of exposure assigned to the sixth 

 photograph. 



The error of y may be combined with that of x (see above). 



(C) o:=13923, y = 4 '00. 



The results (A), (B), (C) agree very well ; the good agreement of (A) and (B), 

 which rest on different material, is remarkable. Considering that all the material 

 contributed to (C), I might adopt it as final. I change x by a unit to round off the 

 figure. Hence 



(D) / = <?(/; + 140 23)-*. 



h is counted from the sun's limb in unit of 10~ 3 solar diameter and log c = 12'228 

 expresses the intensity in unit of the intensity of the corona at h = 1000. The 

 residuals left by (D) and calculated with the corrected values of F appear in 

 Table IV. under heading (v). I employ them to derive the errors of the distances. 

 I divide the residuals in each column in three groups and regard the mean of the 

 residuals in each group as the error of log(/i B +140)-log(/ m +140), where h n and h m 

 are the mean distances in each group. The errors of measurement will be about the 

 same on the first two photographs and they can therefore be calculated. The 

 calculations of the errors of h n is sufficiently evident. The result is : 



h. 100. 200. 400. 600. 800. 1000. 1200. 1400. 



Errors. .1-4 5 15 27 47 70 100 130 



These errors are almost twice as great as those in Table III. The excess must, 

 I think, be mainly set down to systematic errors of measurement which are different 

 for the several positives. 



Fig. 7 shows a comparison of the intensity curve with the observations. 

 As the observations do not give absolute intensities, but the ratio of the 

 intensities at two correlative distances, I adopt at distances h lt A M , and /<, the 

 intensities as calculated from the formula (D) and calculate the intensities at the 

 correlative distances h a , /i 3 , A 4 , /j ta , h^, h lt from the latter and the known ratios F. 



