222 
BIGELOW. 
afford concrete examples of the most profound questions in 
theoretical physics. 
THE THEORY OF LEAST SQUARES IN SOLAR PHYSICS. 
When we come to solar physics the case is even more 
troublesome. There we have at an enormous distance from 
us an immense mass of seething matter at very high temper¬ 
atures. From observations on the surface phenomena of the 
sun, the inference is inevitable that all the intractable con¬ 
ditions which on the earth render it difficut to apply the 
probability theorem are there multiplied in their complexity. 
The recurrences of the spots, faculse, and prominences on the 
surface of the sun are simply resulting products of very com¬ 
plex processes going on in the interior, and in the circulation 
attendant upon the readjustments of its thermal equilibrium. 
If the solar radiation falling on the earth’s tropical zones 
produces the observed complex circulation of the atmos¬ 
phere with its interdependent current systems, how much 
more should this be true in the sun’s circulation. By so 
much more will it be impractical to apply correctly the 
least-square theorems or the potential theorem, as Professor 
Schuster has attempted to do in various ways. We must 
for the present, until the true nature of the physical prob¬ 
lem is understood, approach the solution by more simple, 
practical methods. It only paralyzes the efforts of students 
to have negative results derived from mathematical analysis 
laid down as decisive, and the only effect is to hinder such 
advances as can properly be made by the simpler graphical 
or numerical methods. Take, for example, the rotation 
period of the sun, which has been determined many times 
from the recurrence of various terrestrial and solar events. 
On the surface of the sun we observe a synodic period of 
26.68 days at the equator, a longer period of 27.30 days at 
latitude 12°, and still longer periods at higher latitudes up 
to 35°, beyond which the movement is unknown. There is 
evidence that the period varies also in altitude as well as in 
latitude. Now, several periods in the terrestrial field have 
