RECENT PROGRESS IN GEODESY. 
5 
Another class of investigators has worked from the stand¬ 
point of pure theory. Their endeavor has been to furnish 
an adequate explanation for the observed facts. Up to the 
time when the latitude was shown, by direct observation, to 
be subject to periodic variations, one of the fundamental as¬ 
sumptions upon which astronomical computations were based 
was that the latitude of a given point on the earth’s surface 
is invariable. Pure theory, indeed, indicated that the lati¬ 
tude of a point should be subject to a periodic variation of 
small amplitude with a period of about 305 days. Special 
investigations had failed to reveal a variation having that 
period, and astronomers had fallen back to the dogma of in¬ 
variability. Theorists are now confronted with the neces¬ 
sity of accounting for a period of about 428 days instead of 
305. It is known that any movements of the earth’s crust 
and of the water and air in response to a displacement of the 
pole of figure from the pole of rotation have the effect of 
lengthening Euler’s period. It has been shown that any dif¬ 
ference in the equatorial radii also has a tendency to increase 
the theoretical period to correspond more nearly with the 
fact. The known atmospheric and oceanic currents have 
also been appealed to for an explanation. It has also been 
shown that it is not impossible that such impulsive forces as 
are concerned in earthquakes and volcanoes may produce 
some of the effects observed. The net result, however, of the 
investigations of theorists has been a series of partial expla¬ 
nations, no one of which stands all the tests which have been 
applied to it. Each fails, either by furnishing a law of mo¬ 
tion which differs essentially from the observed facts or by 
being quantitatively inadequate. 
This was the situation when the International Geodetic 
Association formulated and adopted a plan for determining 
the actual motion of the pole during a series of years with the 
highest attainable accuracy. The observations, in conformity 
with the plan devised by them, were actually begun in the 
latter part of 1899, and it is proposed to continue these ob¬ 
servations uninterruptedly for at least five years. The plan 
