198 



SEE— TEMPERATURE, SECULAR COOLING 



[April 20, 



00 = 46,455° C. = 83,619° Fahr. (4) 



Beginning at the centre with a temperature of 83,600° Fahr., we 

 find for the elliptical distribution of temperature within the earth 

 the values shown in the following table. It is found by calculation 

 that this arrangement of the temperature fulfills the two conditions 

 above specified, namely the elliptical distribution, and the following 

 quantitative criterion : 



= -|[(5y-(if)>.^7'®.=45.ooo(5.5K. ^'^ 



In the second member of this equation the average specific heat of 

 the earth's matter is taken to be 0.2, and the same numerical value 

 is used in evaluating the first member of the expression under the 

 summation sign. 



§ 3. The Laws of Density, Pressure and Theoretical' Rigidity Within 



the Earth. 



Laplace's celebrated law of density for the earth results from an 

 hypothesis introduced into Clairault's general differential equation 

 for the equilibrium of a heterogeneous mass of fluid endowed with 

 a rotatory motion, which permits the integration of the equation in 

 some particular cases, and thus enables the geometer to connect the 

 oblateness of the successive layers of the fluid with the radius of the 

 spheroid, of which the density is supposed to be a function. In 

 default of knowledge Laplace assumed as an hypothesis that the 



