SPECTROSCOPIC OBSERVATIONS OF THE ROTATION OF THE SUN. 99 
With the exception of latitude 75°, the differences between the two groups are far 
within the limits of their probable errors. This shows, as was anticipated, that practically 
no error of the position angle was present. 
We have now to deal with the question, How are these remarkable differences 
between the two groups to be interpreted? Is their cause indeed to be sought for in 
the sun itself? We are, of course, not yet in a position to attempt an answer to this 
question, but there is a probability of the solar origin of this phenomenon, for which I 
should like to give some reasons. First, we have to take into consideration that the 
observations have been made throughout by the same observer, with the same entirely 
unaltered instrument, and at the same place,—that means, under the same atmospheric 
conditions. While it must be granted that deficiencies in the instrument and in the 
method of observation, or the personal perception of the line-displacements, which may 
be different for different observers, but most of all atmospheric conditions, which shall 
be discussed later—that all these circumstances may vitiate the results, there seems, 
however, to be no reason for the assumption that these influences should have altered 
so decidedly from one year to the next. 
Secondly, that a real change of the rotation must have taken place from the one 
group to the other seems to be indicated by a significant peculiarity of the angular 
velocities which have been derived from the linear velocities v contained in Table I. 
By multiplying the values of v by sec. 8, 6 being the heliographic latitude, we obtain 
numbers which obviously must be proportional to the angular velocities. This computa- 
tion having been made, the values were plotted down in fig. 4, again for both groups 
separately. At first glance we recognise the retardation of the angular velocity from 
the equator towards the poles, but it will be remarked that the amount of this retarda- 
tion during the second period is considerably smaller than during the first. The most 
significant fact, however, appears to be this: if in both groups the values of the curve 
for corresponding latitudes are subtracted from the equatorial velocity, these differences 
can be made to agree perfectly if the values for 1901-2 are multiplied by the factor 0°4. 
This result seemed to me so remarkable that I decided to test its correctness by a special 
investigation, including also the results of Professor Dunir’s observations. 
First of all I endeavoured to find an empirical formula which should represent the 
angular velocities in every group in a satisfactory manner. After various attempts at 
representing these velocities in the usual way by the sine and cosine functions of the 
heliographic latitude, the method had to be abandoned, as my observations could be 
represented only by extremely complicated expressions of such a form. Accidentally, 
however, I arrived at a formula very different from those hitherto used, which satisfies 
the observations in all three groups with a high degree of accuracy, and which has the 
further advantage of being extremely simple. This formula can be expressed in the 
following way— 
E=a—be*, 
where € is the angular velocity in latitude 6, and a, b and ¢ are constants. When 
