126 



LAMBERT: CONSTITUTION OF THE EARTH 



ter due to the pressure of the matter above it computed as for a 

 fluid. The modulus of compressibility is assumed to vary as 

 the square of the density. We naturally expect this modulus, 

 which measures the resistance to compression, to increase rather 

 rapidly with the density, and Legendre's assumption is in accord 

 with this idea and it has the further advantage of leading to 

 fairly simple and manageable mathematical expressions. The 

 density of p at any point whose distance from the center is x 

 (x being expressed in units of the mean radius of the surface), 

 is given by 



Pism{dx) 



P = 



(3) 



X sin 6 

 where Pi is the surface density and is a constant. 



Table i shows the values of the density and also of the hydro- 

 static pressure p in megabars, a megabar being one million 

 dynes per square centimeter or nearly one standard atmosphere. "^ 



TABLE I 

 Density, Pressure, and Modulus of Rigidity according to Legendre's Law. 



" For comparison: Modulus of rigidity of steel = 8 X 10"; of glass 

 10"; of surface rock (average) = 2.4 X 10"; all in C. G. S. units. 



■5 X 



337; also Pratt, Attractions and figure of the earth (4th ed.), p. iii. The starting 

 point here adopted is that of Laplace rather than that of Legendre. 



•5 One megabar = 0.987 standard atmosphere of 76 cm. of mercury at sea-level 

 in latitude 45°. 



