240 Prof. H. Hennessy on the 



always continued to maintain, and which forms the cumulative 

 result of the investigations in the text of this paper. In a 

 Report to the Royal Irish Academy on " Experiments on the 

 Influence of the Molecular Influence of Fluids on their Motion 

 when in Rotation/' p. 57*, I referred to a proof obtained by 

 me of the result alluded to, and I now may be allowed to 

 submit this proof to those interested in the question. 



(2) Let us suppose the earth to consist of a solid spheroidal 

 shell, composed of nearly similar spheroidal strata of equal 

 density, and having the ellipticities of the inner and outer 

 surfaces small and nearly equal. The shell is supposed to be 

 full of liquid and to rotate around its polar axis. Under these 

 conditions the attraction of an exterior body would tend to 

 produce pressure between the fluid nucleus and the inner 

 surface of the shell. Whatever may be the direction of this 

 pressure, it can be resolved into a force normal to the shell's 

 surface and into forces in its tangent plane. The normal force 

 might be effective in causing a deformation of the shell, or, if 

 the latter were rigid, it would be destroyed by the shell's re- 

 sistance. If friction existed between the materials of the 

 shell and the fluid of the nucleus, the resolved forces in 

 the tangent plane would tend to change the motion of the 

 shell from the motion it would have if empty. But if no 

 friction and no adhesion existed between the particles of the 

 liquid and the shell's nearly spherical surface, and if the 

 particles of the liquid are free from viscidity and internal 

 friction among themselves, this purely tangential component 

 could exercise no influence on the motions of the shell. If 

 the solid envelope containing fluid was bounded by planes 

 such as a prismatic vessel or box, it is manifest that unequal 

 normal pressures on the faces of such prism would tend to 

 produce couples, and thus possibly rotations. Such a case has 

 been considered by Professor Stokes, and he has shown that 

 a rectangular prism filled with fluid will have the same motion 

 as if the fluid was replaced by a solid having the same mass, 

 centre of gravity, and principal axes, but with much smaller 

 moments of inertia corresponding to these axes. But in a 

 continuously curved and nearly spherical vessel, the normal 

 pressure arising from disturbance of the liquid could not pro- 

 duce the same results. The tangential components of the 

 forces acting at the surface of the liquid could, in this case, be 

 alone effective, and if no friction or viscidity existed at this 

 surface such tangential action would totally disappear. The 

 conclusion of Mr. Hopkins's first memoir is, that if the ellip- 

 ticity of the inner and outer surfaces of the solid shell were 

 * Proceedings of K. I. A., 2nd series, vol. iii. Science. 



