ASTRONOMY: SEARES, VAN MA AN EN AND ELLERMAN 
5 
tance of the observer from the plane of the sun's equator. If the field be 
that of a uniformly magnetized sphere, 2 
kA = { 3 sin (20 - D) + sin D) cos i 
+ { 3 cos (20 - £>) + cos D) sin * cos X (1) 
in which 
A = displacement of spectral line; 
0 = heliographic latitude of point observed; 
D = angular deviation of observer from plane of sun's equator; 
1 = inclination of sun's magnetic axis to axis of rotation; 
X = heliographic longitude of north magnetic pole referred to central 
meridian; 
k = constant depending on the units and the behavior of the line in a 
field of known intensity. 
For i = 0, equation (1) reduces to 
kA = 3 sin (20 - D) + sin D, (2) 
and, if D also is zero, to 
kA = 3 sin 2 0. (3) 
Since the maximum value of D is about 7°, equation (2) differs but little 
from (3). The displacement curves derived by Mr. Hale from preliminary 
observations agreed substantially with these equations, whence it follows 
that i must also be small and that the difference between equations (1) and 
(2), which represents the influence of i, is a quantity of the second order. 
When A is expressed in thousandths of a millimeter, k, for the lines observed, 
is of the order of unity. The maximum displacement, by equation (3), is 
therefore 3 or 4 ix (about 0.001 A). To determine the position of the magnetic 
axis, quantities of the order of 0.5 \x must accordingly be evaluated. This in- 
dicates sufficiently the nature of the problem and the degree of precision that 
had to be attained. It was evident from the beginning that a long and care- 
fully executed series of observations would be required for a successful attack 
on the problem. 
The original investigation by Mr. Hale was based on only four lines. Later 
observations have increased the number known to be affected by the sun's 
field to 30, for 18 of which results were communicated at the Atlanta meeting 
of the American Astronomical Society in December, 1913. For the investiga- 
tion here described three chromium lines, XX 5247, 5300, 5329 were selected, 
which are of special suitability for measurement because of intensity (2 and 
3), location in the spectrum, and magnitude of displacement. . 
From June 8 to September 23, 1914, these lines were photographed daily 
under the direction of Ellerman, with almost no break in the series. The cir- 
cumstances were most favorable owing to the small number of sun-spots, whose 
magnetic fields, many times the intensity of the underlying field of the sun, 
seriously complicate the investigation. Because of advantages connected 
