H. S. Woodward — Mathematical Theories of the Earth. 353 



however, in the elaboration of such theories. Roche,* Dar- 

 winf and others have done much to remove the nebulosity of 

 Laplace's nebular hypothesis. Poincare^: and Darwin§ have 

 gone far toward bridging the gaps which have long rendered 

 the theory of rotating fluid masses incomplete. Poincare has 

 in fact shown us how a homogeneous rotating mass might, 

 through loss of heat and consequent contraction, pass from the 

 spheroidal form to the Jacobian ellipsoidal form, and thence, 

 by reason of its increasing speed of rotation, separate into two 

 unequal masses. Darwin, starting with a swarm of meteorites 

 and gravitation as a basis, has reached many interesting and in- 

 structive results in the endeavor to trace out the laws of evo- 

 lution of a planetary system. | But notwithstanding the splen- 

 did researches of these and other investigators in this field, it 

 must be said that the real case of the solar system, or of the 

 earth and the moon, still defies analysis ; and that the me- 

 chanics of the segregation of a planet from the sun, or of a 

 satellite from a planet, if such an event has ever happened, or 

 the mechanics of the evolution of a solar system from a swarm 

 of meteorites, are still far from being clearly made out. 



Time does not permit me to make anything but the briefest 

 allusion to the comparatively new science of mathematical 

 meteorology, with its already considerable list of well defined 

 theories pressing for acceptance or rejection. Nor need I say 

 more with reference to those older mathematical questions of 

 the tides and terrestrial magnetism, than that they are still un- 

 settled. These and many other questions, old and new, might 

 serve equally well to illustrate the principal fact this address 

 has been designed to emphasize, namely, that the mathematical 

 theories of the earth already advanced and elaborated are by 

 no means complete, and that no mathematical Alexander need 

 yet pine for other worlds to conquer. 



Speculations concerning the course and progress of science 

 are usually untrustworthy if not altogether fallacious. But, 

 being delegated for the hour to speak to and for mathemati- 

 cians and astronomers, it may be permissible to offer, in closing, 



* Essai sur la Constitution et L'Origine du Systeme Solaire, par M. Edouard 

 Roche. Memoires de L'Academie des Sciences et Lettres de Montpellier, tome 

 vift, 187:1 



f Oq the Precession of a Viscous Spheroid aud on the remote History of the 

 Earth, Phil. Trans., Part II. 1879 ; On the secular changes in the Elements of 

 the Orbit of a Satellite revolving about a tidally distorted Planet, Phil. Trans., 

 Part II, 1880; On the Tidal Friction of a Planet ai tended by several Satellites, 

 and on the Evolution of the Solar System, Phil. Trans., Part II, 1881. 



\ Sur L'Equilibre d'une Masse Fluid auiine d'un mouvement de rotation, Acta 

 Mathematica, vol vii, 1 .>85. 



§ On Figures of Equilibrium of Rotating Masses of Fluid, Phil. Trans., vol. 

 187, 1887. 



|| On the Mechanical Conditions of a Swarm of Meteorites and on Theories of 

 Cosmogony, Phil. Trans., vol. 180, 1889. 



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

 23 



