THE MATHEMATICAL THEORIES OF THE EARTH.* 



By RoBER'j' Simpson Woodward. 



The name of this section, which by your courtesy it is my duty to ad- 

 dress today, implies a community of interest amongst astronomers and 

 mathematicians. This community of interest is not difficult to explain. 

 We can of course imagine a considerable body of astronomical facts 

 quite independent of mathematics. We can also imagine a much larger 

 body of mathematical facts quite independent of and Isolated from 

 astronomy. But we never think of astronomy in the large sense with- 

 out recognizing its dependence on mathematics, and we never think of 

 mathematics as a whole without considering its capital applications in 

 astronomy. 



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 possible 

 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 prob- 

 lems ; its shape, its size, its mass, its precession and nutation, its internal 

 heat, iisearthcjuakes, 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 something called the earth's crust, but con- 

 sidered in its entirety and in its relations to similar bodies of the uni- 

 verse, the Earth has long been the special province of astronomers and 

 mathematicians. Since thetimes of Galileo and Kepler and Copernicus 

 it has supi)lied a perennial stimulus to observation and investigation, 

 and it promises to tax the resources of the ablest observers and anal- 

 ysts for some centuries to come. The mere mention of the names of 

 Newton, Bradley, d'Alembert, Laplace, Fourier, Gauss, and Bessel, calls 

 to mind not only a long list of inventions and discoveries, but the most 



* Vice-presidential address before the section of Mathematics and Astronomy of 

 the American Association for the Advancement of Science at the Toronto meeting, 

 August, 1889. (From the Froceedinga Am. Assoc. Adv. Sci., vol. xxxviii.) 



183 



