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THE 



AMERICAN JOURNAL OF SCIENCE 



[THIRD SERIES.] 



Art. XLV. — The Mathematical Theories of the Earth ; by 

 R. S. Woodward, as Vice-president of Section A, of the 

 American Association for the Advancement of Science, 

 Toronto meeting, Aug. 27 to Sept. 3, 1889. 



The name of this section, which, by your courtesy, it is my 

 duty to address to-day, implies a community of interest among 

 astronomers and mathematicians. This community of interest 

 is not difficult to explain. We can of course imagine a considera- 

 ble body of astronomical facts quite independent of mathemat- 

 ics. 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 without recog- 

 nizing its dependence on mathematics, and we never think of 

 mathematics as a whole without considering its capital applica- 

 tions 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 ref- 

 erence, whereby it is possible to make out the orderly arrange- 

 ment and procession of our solar system and^to gain some ink- 

 ling 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 



Am. Jour. Sci.— Third Series, Vol. XXXVIII, No. 227.— Nov., 1889. 

 22 



