F. H. Bigelow — Further Study of the Solar Corona. 351 



disk will exhibit a progression of values as we pass along the 

 ray. As each quadrant has been considered independently, no 

 effort was made to generalize the angle a, but it is counted 

 from the plane of the disk to the plane passing through the 

 point on the ray, at the axis of intersection of the planes 

 through the center of the sun. 



_ 87T sin'tf 



"~ ~3~ ' r 



Let x x = i\ sin d, and y t = ?\ cos 1} the accents indicating the 



first point that is measured on a ray. 



x * 



r = 's/x' + f sin 9 6 = -^ = 



3 (x'+y*)* 



As a first approximation, assume that the axis of the planes 

 of rotation lies in the plane of the apparent disk ; hence^ by 

 rotating a ray from the edge of the disk to its actual position, 

 the values of y are unchanged, while those of x are reduced. 

 The radius of revolution is x 1 = r x sin 0„ therefore x = x 1 sec a. 



_, , . „ 87r r^ s\n i O l sec 2 « 



Substituting, JS = — - . 1. 



3 (ri 2 sin 2 ^ setfa + r* cos 2 ^)* 



Since the points are on the same ray, we take 



rf sin'fl, r, 2 sin 2 2 





X' 



X' 











r l 



x 1 + y' 





x- 





•(rf sm% setfa + r^cos^d)* (r/ sin 2 2 sec 2 « + r s s cos 2 2 ) 

 (a; 2 2 sec 2 « + ?//) 2 _ £ 2 2 

 (aj^sec'a+y!*)' ^ 



x$y?—yfx$ 



sec'« = — j j — . 



The application of this formula gives the values of a corres- 

 ponding properly to the mid-point between the two points 

 from which it was derived. They also have a progressive 

 value, indicating that the pole of the corona is not on the 

 plane of the disk. It will not be far wrong to assume that 

 value of a which is nearer the first a than the second, as would 

 be seen by inspection from the points on a sphere. 



Now substituting these values of a in 

 8n cc 2 sec 2 or 



n = t ; v 



6 (x^sec-a + y*)* 



we find that the ranging nature of the JSTS has ceased, and 

 that there remain only such irregularities as are occasioned 

 by the inaccuracy of the measurements themselves. 



