4 
HAYFORD. 
instrument which the geodesist claims rather than the 
astronomer. 
For ten years past there has been marked activity in in¬ 
vestigating this question along two lines. One class of in¬ 
vestigators worked by the inductive method, and slowly 
built up empirical mathematical expressions for the observed 
facts as to the variations, independently of any theory as to 
their causes. For this purpose they used many series of old 
observations, made at various fixed observatories, but not 
primarily for this purpose. In addition they have used 
many modern series of observations, made with zenith tele¬ 
scopes, for this special purpose. It has been shown that the 
motion of the pole in the past may be represented with con¬ 
siderable accuracy as a combination of two motions, each 
circular, one with a mean period of about 428 days and the 
other with a period of one year. A still closer approxima¬ 
tion is obtained by assuming that the amplitude and epoch 
of each of these motions is subject to a periodic variation. 
A somewhat closer agreement between the mathematical 
curves and the observations is secured when elliptical paths 
are substituted for the circular paths above referred to. The 
net result of the investigations by the inductive method has 
been certain mathematical expressions which closely repre¬ 
sent the known facts of the past, but there is great uncer¬ 
tainty as to how far into the future these mathematical 
expressions may be extended, because their basis is wholly 
empirical. 
The progress made along this empirical line of investi¬ 
gation has been due to Prof. S. C. Chandler, of Harvard, 
more than to any other one man or, possibly, any group of 
men. His results have been published as the investigations 
proceeded, in the Astronomical Journal, and form an ex¬ 
ceedingly interesting series, not only on account of the 
remarkable success attained, but because of the ingenuity 
and skill shown in devising methods of investigation which 
are independent of any theoretical basis. 
