70 CHARLES S. SLICHTER 



neous spheroids of eccentricities .5 and .4 were known, a com- 

 putation of pressures would require the neglect of the squares of 

 the ellipticities, which, in the case of ellipticities so large, 

 would give results poorly compensating for the labor involved. 

 I have, therefore, contented myself with two rough processes of 

 approximation. 



The pressure within a sphere in which the density is that of 

 the Laplacian law can readily be computed by direct integra- 

 tion. 1 The result may be expressed as follows: 



r „„n / sin 2 n (2.460O \ . 



p = go |_ 2 • 73S8J I- — — — 0.396] atmospheres. 



In this formula,/ is the pressure in atmospheres of 10 6 

 dynes per square cm. each, at the fractional distance n from the 

 center of the earth, the radius being taken equal to unity for 

 convenience. The bracket [2.7388 | indicates the logarithm of 

 a factor, and g Q is the value of gravity at the surface. 



Returning now to Fig. 1, it will be noticed that I have rep- 

 resented a section of the spheroid and two spheres, in contact 

 at N. We shall suppose that the spheroid A is heterogeneous, 

 with Laplace's law of density, and that sphere B is a sphere of 

 same volume, same density, and the same law of density as the 

 spheroid A. The sphere C is inscribed within the spheroid A, 

 and has, I shall suppose, the same mean density and the same 

 law of density as the latter. Then it is easy to see, since the 

 law of density is such that the density increases towards the 

 center, that the pressure at the center of the sphere C must 

 be less than the pressure at the center of the spheroid A. 

 Likewise, for the same law of density, the pressure at the point 

 of the sphere B is greater than the pressure at the center 

 of the spheroid A. The pressures at the point within the 

 spheres can be obtained by the formula above given, and as the 

 pressure at the center of the spheroid is intermediate in value to 

 those thus obtained, its value becomes approximately deter- 

 mined. 



1 See Osmond Fisher, Physics of the Earth's Crust, p. 32. 



