808 



neously from the centre towards the surface, and from the surface 

 towards the centre. He therefore, in determining the laws of den- 

 sity of the shell and the nucleus, restricts his investigations to the 

 latter case, in which the solidification proceeds from the surface to- 

 wards the centre. 



IV. The Forms of the Strata of the Shell 



The author conceives a surface to exist which may be called the 

 effective surface of separation of the perfect fluid of the nucleus and 

 the imperfectly fluid portion adhering to the shell, the form of which 

 surface will depend on the pressures which the fluid exerts. As it 

 may be shown that the pressure of the perfect fluid will not be con- 

 stant, the surface of separation will tend to assume a form different 

 from that of the inner surface of the shell. If we admit that the 

 matter composing the nucleus becomes denser in assuming the solid 

 state, the author concludes that the inner surface of each stratum 

 added to the shell will be more oblate than its outer surface ; and 

 that thus the tendency will always be to render the inner surface of 

 the shell more and more oblate. He then deduces an expression 

 for the ellipticity of the fluid surface. 



V. The principal Moments of Inertia of the Earth. 



From his investigations the author concludes that, as the thick- 

 ness of the shell increases, the difference between the greatest and 

 the least moment of inertia of the earth also increases ; which con- 

 clusion is independent of any knowledge of the absolute laws of 

 density of the earth's interior. 



VI. On the existeyice of a Solid Nucleus within the Earth, 



The conclusion arrived at here i^, that if a solid nucleus existed, 

 as the pressure on it would be continually diminishing, while its 

 temperature would remain nearly constant, this nucleus, instead of 

 increasing in magnitude, would tend to return to its original fluid 

 state. 



VII. The directions of the Fissures in the Shell which )night be pro- 

 duced by the action of the pressures in Section I. 



The author states that the tendency of the variable pressure is in 

 the first instance to produce fissures parallel to the equator ; that 

 when such a fissure was once commenced the tendency would be to 

 propagate it along a parallel of latitude, until the force of the ten- 

 sions became sufficiently lessened by the separation of the extended 

 portion of the shell; and that similar fissures would be formed si- 

 multaneously and symmetrically on each side of the equator. Sub- 

 sequently, as may readily be deduced from Mr. Hopkins's investiga- 

 tions, the tendency will be to form fissures at right angles to those 

 previously existing. If, however, the constant pressure were far 

 greater than the variable, the directions of the fissures would be go- 

 verned chiefly by accidental causes ; but if a fissure commenced, it 



