76 CHARLES S. SLICHTER 



Now if the change in pressure that has taken place is 4 per cent., 

 we may place 



d£ _ 4 

 p 100 



and, since c is small in comparison with/, 



dp , d p 2 



— £ = ^ -f — n = * 



p / 100 



in which ?z is a number with a small average value. Therefore, 

 we may assume that, on the average, the change in density is 

 about half the change in pressure. Taking the ratio as one-half, 

 we can compute the change in volume of the spheroid for a 

 given change in internal pressure, since, of course, volume is 

 inversely proportional to density. I have placed results of this 

 computation in the line 18 of Table I. 



The decrease in the size of the earth due to the increase of 

 internal pressures must likwise reduce the extent of the outer 

 surface. If v and s represent the volume and surface of the 



s P here > ds , dv 



S V 



or, for small changes, the chanere in surface is two-thirds the 

 change in volume. This gives a reduction in surface amounting 

 to about 1.3 per cent, for the spheroid ^= .5, and .85 per cent, for 

 the spheroid e = .4, or, in square miles, a reduction in surface of 

 about 2,700,000 square miles, and 1,700,000 square miles respect- 

 ively. 



The compressibility of matter under high pressure and high 

 temperature cannot be said to be known experimentally. Thomp- 

 son and Tait, however, on page 415 of Part II, estimate for the 

 average material at the surface of the earth, the compressibility 

 that must theoretically follow from Laplace's law, and give as 

 the result : 



Melted lava, by Laplace's law - - 4.42 



They also give actual experimental determinations of com- 

 pressibility as follows: 1 



1 If the radius of the earth, 6.37 X io 8 , be divided by each of these numbers and if 



