Mathematical Theories of the Earth. — Woodward. 269 
Of all the subjects and objects of common interest to us the earth 
will easily rank first. The earth furnishes us with a stable foundation 
for instrumental work and a fixed line of reference, whereby it is pos- 
sible to make out the orderly arrangement and procession of our solar 
system and to gain some inkling of other systems which lie within 
telescopic range. The earth furnishes us with a most attractive store 
of real problems: its shape, its size, its mass, its precession and 
nutation, its internal heat, its earthquakes and volcanoes, and its ori- 
gin and destiny, are to be classed with the leading questions for astron- 
omical and mathematical research. We must of course recognize the 
claims of our friends the geologists to that indefinable something 
called the earth's crust, but, considered in its entirety and in its rela- 
tions to similar bodies of the universe, the earth has long been the 
special province of astronomers and mathematicians. Since the times 
of Galileo and Kepler and Copernicus it has supplied a perennial stim- 
ulus to observation and investigation, and it promises to tax the 
resources of the ablest observers and analysts for some centuries to 
come. The mere mention of the names of Newton, Bradley, d'Alem- 
bert, Laplace, Fourier, Gauss, and Bessel calls to mind not only a long 
list of inventions and discoveries, but the most important parts of 
mathematical literature. In its dynamical and physical aspects the 
earth was to them the principal object of research, and the thorough- 
ness and completeness of their contributions toward an explanation of 
the "system of the world" are still a source of wonder and admiration 
to all who take the trouble to examine their works. 
A detailed discussion of the known properties of the earth and of the 
hypotheses concerning the unknown properties, is no fit task for a 
summer afternoon; the intricacies and delicacies of the subject are 
suitable only for another season and a special audience. But it has 
seemed that a somewhat popular review of the state of our mathemat- 
ical knowledge of the earth might not be without interest to those 
already familiar with the complex details, and might also help to 
increase that general interest in science, the promotion of which is one 
of the most important functions of this association. 
As we look back through the light of modern analysis, it seems 
strange that the successors of Newton, who took up the problem of the 
shape of the earth, should have divided into hostile camps over the 
question whether our planet is elongated or flattened at the poles. 
They agreed in the opinion that the earth is a spheroid, but they 
debated, investigated, and observed for nearly half a century before 
deciding that the spheroid is oblate rather than oblong. This 
was a critical question, and its decision marks perhaps the most 
important epoch in the history of the figure of the earth. The New- 
tonian view of the oblate form found its ablest supporters in Huyghens, 
Maupertuis, and Clairaut, while the erroneous view was maintained 
with great vigor by the justly distinguished Cassinian school of astron- 
omers. Unfortunately for the Cassinians, defective measures of a 
