THE MATHEMATICAL THEORIES OF THE EARTH, 197 



precisely, w iietber the Earth may uot be at once highly plastic under 

 the action of long-coutiiiaed forces and highly rigid under the action 

 of periodic forces of short period, it is pretty certain that some years 

 must elapse before the arguments will be convincing to all concerned. 

 The difficulties appear to be due principally to our profound ignorance 

 of the properties of matter subject to the joint action of great pressure 

 and great heat. The conditions which exist a few miles beneath the 

 surface of the earth are quite beyond the reach of laboratory tests as 

 hitherto developed, but it is not clear how our knowledge is to be im- 

 proved without resort to experiments of a scale in some degree com- 

 parable with the facts to be explained. In the mean time, therefore, we 

 may expect to go on theorizing, adding to the long list of dead theories 

 which mark the progress of scientific thought with the hope of attain- 

 ing the truth uot so much by direct discovery as by the laborious process 

 of eli'.ninating error. 



When we take a more comprehensive view of the problems presented 

 by the Earth, and look for light on their solution in theories of cosmog- 

 ony, the difficulties which beset us are no less numerous and formidable 

 than those encountered along special lines of attack. Much progress 

 has recently been made, however, in the elaboration of such theories. 

 Koche,* Darwin. 1 and others have done much to remove the nebulosity 

 of Laplace's nebular hypothesis. Poincare | and Darwin § have gone far 

 towards bridging the gaps which have long rendered the theory of ro- 

 tating 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 instructive 

 results in the endeavor to trace out the laws of evolution of a planetary 

 system. II But notwithstanding the splendid 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 moon, still defies analysis; and 

 that the mechanics of the segregation of a planet from the sum, or of a 

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



* Essai 8ur la Coustitutiou et I'origiue da systeiue solaire, par M. fidouarrl Roche. 

 Mmioires de V Academie des Sciences et Lettres de Montpellier, Tome viii, 1873. 



t Ou the Precession of a Viscous Spheroid aud ou the remote History of the Earth, 

 Phil. Trans., Part ii, 1879. Ou the secular changes in the Elemeuts of the Orbit of a 

 Satellite revolving about a tidally distorted Planet, Phil. Trans., Part ii, 1880. On 

 the Tidal Friction of a Planet attended by several Satellites, and on the Evolution of 

 the Solar System, Phil. Trans., Part ii, 1881. 



i Sur I'equilibre d'une masse fluide animde d'uu mouvement de rotation. Acta 

 Mathematica, vol. 7, 1885, 



$ On figures of Equilibrium of Rotating Masses of Fluid, Phil. Trans., vol. 178, 1887. 



II On the Mechanical Conditions of a Swarm of Meteorites aud on Theories of Cos- 

 mogony, Phil. Trans., vol. 180, 1889. 



