338 R. S. Woodward — Mathematical Theories of the Earth . 



heat, its earthquakes and volcanoes, and its origin and destiny, 

 are to be classed with the leading questions for astronomical and 

 mathematical research. We must of course recognize the 

 claims of our friends the geologists to that indefinable some- 

 thing called the earth's crust, but, considered in its entirety 

 and in its relations to similar bodies of the universe, the earth 

 has long been the special province of astronomers and mathe- 

 maticians. Since the times of Galileo and Kepler and Copern- 

 icus if has supplied a perennial stimulus to observation and in- 

 vestigation, 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' Alembert, La- 

 place, 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 as- 

 pects the earth was to them the principal object of research, 

 and the thoroughness 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 delica- 

 cies 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 mathematical 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 ob- 

 served for nearly a half century before deciding that the sphe- 

 roid 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 Newtonian view of the 

 oblate form found its ablest supporters in Huyghens, Mauper- 

 tuis, and Clairaut, while the erroneous view was maintained 

 with great vigor by the justly distinguished Cassinian school of 

 astronomers. Unfortunately for the Cassinians, defective meas- 

 ures of a meridional arc in France gave color to the false theory 

 and furnished one of the most conspicuous instances of the de- 

 terring effect of an incorrect observation. As you well know 



