68 



CHARLES S. SLICHTER 



X x represents the value of gravity at any point distant x from 

 the center of the spheroid on an equatorial radius, and if Y y repre- 

 sents the corresponding quantity for a point on the polar axis, and 

 iig e and^ are the values of gravity at the equator and at the pole 

 respectively, and if a and b are the semi-polar and semi-equa- 

 torial axes, then we have 



X —Ki^. v = gpy 

 a ' y b ' 



Also if P x and P y represent the pressure at the same points, then 



*=?*(— ?)■ 



2 8 * \ b ) ' 



in which p Q is the density of the homogeneous spheroid, and in 

 which the other letters have the same significance as above. 

 The following table gives the pressures at various distances from 

 the center. The unit pressure is a million atmospheres of io 6 

 dynes per sq. cm. 



TABLE II. 



PRESSURES WITHIN HOMOGENEOUS SPHEROIDS OF VARIOUS ECCENTRICITIES. 



The pressures for <?=.5 and for the sphere are shown graphi- 

 cally by the lower curves in Fig. 2. The line OX corresponds to 

 either the polar or equatorial radius, as we may be pleased to 

 consider it, but is represented, of course, as of length 10 in 

 each case. The pressures at any other point in the spheroid 

 can be found by drawing the equipotential surfaces ; for on each 

 of these the pressure is everywhere constant and equal, of course, 



