ASTRONOMY: SEARES, VAN MAANEN AND ELLERMAN 243 
We have therefore rediscussed the data from this standpoint, with results 
which seem to be conclusive. The investigation has had to meet the difficulty 
that the percentage errors in the data, in the nature of the case, are large; but 
there seems no doubt that there are irregularities in the field-strength at least, 
which cannot be accounted for on the basis of systematic or accidental error. 
In order that the numerical quantities involved in the above solution — which 
we may refer to as the uniform-field solution — might be utilized as completely 
as possible, we have based the discussion upon the formulae there used, namely, 
Ax-i- By ^ ^ } 
X = cos ij y — sin i cos \ \ (1) 
Y = y/x — tan i cos X J 
A and B are known quantities, functions of the heliographic latitudes of the 
sun's center and the points observed; A is the observed displacement of the 
spectral line; and i and X are the inclination of the magnetic axis and the lon- 
gitude of the magnetic pole. F is a function of i and X, whose value is calcu- 
lated for each day from all the measured A's for that day. The discussion of 
the resulting series of F's then leads to the required values of i, to, P, and 
finally to k, which is connected with Hp, the field-strength at the pie, by the 
relation 
in which C is a constant depending on the spectral fine employed. 
For the uniform-field solution, the values of F were calculated separately 
for three different lines. For the investigation of the deviations from the uni- 
form field, the measures of the three lines were combined (this is possible since 
the values of x for the three lines are sensibly equal) and the entire collection 
of data then subdivided according to zones of heliographic latitude as follows: 
I > +10° 
II -M0° ^ <p^ -10° 
III cp < -10° 
The outer limites for forces I and III vary somewhat, but are approxi- 
mately 45? 
To the data within these limits we have applied equations (1), much as 
described above. In other words, we have derived separate uniform-field 
solutions for each of the zones. Had the three series of results agreed within 
the uncertainties affecting their determination, we could only have concluded 
that there is no evidence for the existence of appreciable deviations from the 
uniform field originally presupposed. As a matter of fact, we have found a 
large difference for k, which leads to the conclusion expressed above. 
Certain details require comment. The fundamental equation — the first of 
(1) — cannot be applied directly to either zones I or III, because of the numeri- 
