APPLICATION OF MATHEMATICS IN METEOROLOGY. 223 
been announced to be about 25.80 days—that is, one day 
shorter than the period observed at the solar equator, 
which is the smallest period that can be seen on the surface 
of the sun. Is it probable that at the earth the angular 
velocity should be much larger than the greatest vis¬ 
ible on any part of the photosphere? We may note 
in regard to the several discussions of this subject that 
the relative motion of the earth’s atmosphere, which car¬ 
ries with it the thunderstorms, the aurora, and the elec¬ 
tric potential, has not been eliminated from the computed 
periods. This should de done, and it would result in length¬ 
ening the 25.80-day period considerably. Several of these 
solutions have been executed by least-square methods in one 
form or another, and the fact that there has been a general 
* failure to come to any agreement as to the true period of the 
sun’s rotation influenced me to employ a simple computation 
and tabular exhibit of the facts, which would exhibit the 
periodic events as they occur. On laying down the azimuth 
angles of the deflecting vectors of the earth’s magnetic field in 
long tables, a marked periodic phenomena became evident, 
and it persisted through the series of 15 years over which 
the work was extended. Now, while it was easy to note 
the general features of this periodic action and to mark the 
dates of transition in azimuth, the periodic recurrence was 
attended in general by an irregular sliding backward and 
forward through short intervals on both sides of the mean, 
causing a lap of a day or two on each side of the average 
periodic time. The actual dates were marked down, an 
approximate period and epoch was assumed, the system of 
residuals was determined between the observed and computed 
dates, and then the adjustment of the assumed period and 
epoch was made by least squares. It is undoubtedly proper 
to apply least squares to these data. This unsteady action 
in the 26.68-day period is like that occurring in the 11-year 
sun-spot period, which has similar irregularities, some indi¬ 
vidual periods being longer and some shorter than the aver¬ 
age, but from these one can compute the mean period, as 
