328 PROFESSOR L. BECKER ON THE DISTRIBUTION OF 



exposures. The outstanding errors thus contain, apart from the errors of h, all the 

 systematic errors arising from erroneous records of times of exposure. The points 

 belonging to Photographs I., Vb., ~VIb. which ai-e placed on the curve are shown by 

 dots, while the observed correlative points are marked by circles. The systematic 

 errors are clearly reflected in these points. 



8. Question ivhether or not the Formula (D), 7, hold* good at any 



Position-angle ? 



Table I. gives at intervals of 15 of position-angle the amount 8/1 by which the 

 distance from the sun's limb of an equal-intensity curve exceeds the mean distance of 

 that curve. Since these quantities were obtained from measurements on Photographs 

 I., VIII., and IX., which have a uniform background all round, systematic errors of 

 measurement will be eliminated in the differences, and their errors are more com- 

 parable to the errors given in Table III. than to those derived in last section. At a 

 certain point of an equal- intensity curve, which is h + oh from the sun's limb, the 

 intensity is expressed by formula (D), in which h designates the mean distance of 

 the intensity-curve. The intensity at the point may also be expressed by 

 (c+Sc)(A + 8/i + 140)~ 4 , and if c + Sc be a constant, i.e. SA/A + 140 = 8c/4c = constant 

 at a series of points, the formula will hold good for these points. The values 

 a = 1008/J/A + 140 are entered in Table II. The value of the constant c + Sc, which 

 gives at /i + S/t a value of the intensity equal to that given by formula (D) involving 

 c and the mean distance h, is given by 8 log c = 0'017a, (0'017 = 4 mod/100). Accord- 

 ing to Table II. the quantities a differ for the same position-angle, and they vary 

 systematically with the distance. I adopt for the same position-angle the same 

 constant at all distances, and determine it by 8 log c = 0'017a , and hence the 

 logarithm of the calculated intensity at h + 8h will differ by (a a) 0'017 from that 

 calculated by formula (D). I choose for a the mean of the values a belonging to 

 the same position-angle, and find that a u a lies between and 4 for 90 per cent, of 

 the number of points and, therefore, the difference of the intensities is from to 17 

 (log T17 = 0'068) per cent, of the intensity. An error of 17 per cent, in the intensity 

 is equivalent to an error in distance h of 9 at h = 100, 21 at h = 400, 44 at h = 1000. 

 The errors of h belonging to formula i = (c + Sc) (/i + 8A+140)~ 4 are those thus 

 derived combined with the errors given at the end of 7. The residuals in h left 

 by such an intensity curve would, therefore, be in excess of the errors of the observed 

 values of h. 



. At some position-angles 8c/c changes little with the distance from the sun and 

 therefore the formula represents the observations satisfactorily, and in some regions 

 the representation would be improved if points lying on a curve be considered 

 together. Whether these curves agree with the coursa of the streamers or not I 

 have not investigated. 



