242 Prof. H. Hennessy on the 



By analytical transformations, which are fully given by 

 Poisson in his memoir, Sur la rotation de la Terre autour de son 

 centre de Gravity and other writers, it finally appears that the 

 variations of 6 and yjr depend on equations in which a factor 

 enters of the form 



2C-A-B 



C 



where A, B, C are the three principal moments of inertia of 

 the earth. In a spheroid of revolution A = B, and the factor 



becomes ^ p — -. As precession depends essentially on the 



variation of the angle tjr, it follows that the complete expres- 



C— A 



sion of the factor — ^ — is of primary importance. 



(4) Mathematicians, during the past two centuries, have de- 

 voted much attention to the question of the figure of a rota- 

 ting mass of fluid, with especial reference to the explanation 

 of the spheroidal figures of the Earth and her sister planets. 

 Solutions of this problem have been presented, especially by 

 Clairaut, Legendre, Laplace, Gauss, Ivory, Jacobi, and Airy; 

 and it is not a little remarkable that in applying these solu- 

 tions to the case of the Earth every one of these investigators 

 has not only supposed the Earth to have been originally in a 

 fluid state, but that the particles of the mass retained the same 

 positions after solidification had taken place. This tacit or 

 openly expressed assumption of the unchangeable position of 

 the particles of the original fluid mass on their passage to a 

 complete or partial state of solidity lies at the root of the whole 

 question of the Earth's structure. For the first time in the 

 treatment of the physico-mathematical problem, I distinctly 

 discarded this assumption, and I affirmed that the position of 

 the particles of matter, on passing from the state of fluidity to 

 solidity, must assume positions in conformity with mechanical 

 and physical laws. In this way the hypothesis of the Earth's 

 primitive fluidity became more simple and much more 

 rational ; for it was as manifestly absurd to assume that the 

 particles of the fluid mass, on passing into a solid state of con- 

 sistence, retained their original positions, as it would be to 

 assume that if the whole Earth became liquified the positions 

 of its particles would be unchanged. The corrected and sim- 

 plified hypothesis is also fruitful in important results; but it is 

 singular that, as far as I am aware, no mathematician seems 

 to have understood or appreciated its bearing on the physical 

 structure of the Earth, except M. Plana, by a remark in a 

 memoir published by him towards the close of his career. 



