8 
ASTRONOMY: SEARES, VAN MAANEN AND ELLERMAN 
were calculated by a least-squares solution giving differential corrections to 
the approximate values read from the curve. 
The theoretical curve for tan i cos X corresponding to these elements is also 
shown in Fig. 2. So far as accidental errors are concerned, the representa- 
tion is very satisfactory, for the amplitude of the curve corresponds to an 
extreme difference of only 1 ^ in the position of the individual displacement 
curves. There is some evidence of a gradual increase in tan i; but no empha- 
sis is placed on the phenomenon. Whether it is real or whether it is due to 
errors of measurement and the influence of spots and the 'dark markings' of 
the Greenwich observers cannot now be determined. Days on which spots 
were near the central meridian were generally avoided. The magnetic fields 
surrounding some of the 'dark markings' noted at a later time (our attention 
was first directed to them in 1915) were measured and found to be two or 
three times as intense as the sun's general field; but their existence and influ- 
ence upon the measures here discussed cannot now be traced. 
JUNE1914 JULY AUG SEPT 
7 17 21 7 17 27 6 16 26 5 15 25 
FIG. 2. THE CURVE Y = tan i cos X 
Each plotted point is derived from data for a single day similar to that illustrated in Fig. 
1. Approximate values of i, P, and t Q were read from a provisional curve. Differential 
corrections derived by a least-squares solution gave the final values, which correspond to the 
curve shown in the figure. 
The result for P is of much interest in relation to the rotation period of the 
sun. For the reversing layer this ranges from 26.4 days (synodic period) at 
the equator to about 30.5 days at 45°, the value for P not being equalled until 
approximately 55° is reached. Hence for latitudes lower than this limit, the 
magnetic axis in its motion about the axis of rotation appears to lag behind 
the reversing layer. The bearing of this circumstance upon the physical con- 
stitution of the sun must await further elucidation. In the meantime, how- 
ever, it should be noted that P may not be constant. The present series of 
measures, at any rate, is insufficient to establish its freedom from fluctuations; 
and none of the earlier observations, which were made with other purposes in 
view, are adapted to the invest r gation. 
The fact that the observed values of Y agree satisfactorily with the periodic 
function tan i cos X does more than show that i is not zero; it affords a most con- 
vincing demonstration of the existence of the magnetic field itself. The meas- 
ures of each of the three lines, on each of the sixty odd days, define a displace- 
ment-curve which is an independent confirmation of the existence and general 
character of the field; but the fact that the curves for the separate days are 
