INTRODUCTION. 175 



GENERAL EQUATIONS; NOTATION; NUMERICAL CONSTANTS. 



The following notations will be used throughout, and special values of 

 the variable referring to the center and surface of the earth denoted by sub- 

 scripts 0, 1, respectively: 



< = tinie. (P = loss of potential energy in con- 



r = distance from center. traction from infinity. 



x = rlr^. £-= total energy of compression. 



,0 = density. e = energy of compression per unit- 



p = pressure. mass. 



w = mass within radius r. J = mechanical equivalent. 



A; = constant of gravitation. fl^ = modulus of cubic compression. 



9' = acceleration of gravity. a = specific heat. 



y = gravitation potential. ^ = temperature. 



X = conductivity. 



Numerical values are given, unless otherwise stated, in terms of the units 

 centimeter, gram, second, and centigrade degree, for convenience in using 

 published data on the absolute values of the physical constants; and are 

 based chiefly on the following assumed constants, unless expressly stated : 



Total radius ri = 6.370X10' mean density (0^ = 5.516 



surface gravity g'i = 981 



From these are obtained the folio wins;: 



•■b- 



volume = 1.083X10" total mass 77^1 = 5.972X10" fc = 6.665XlO-« 



Further are assumed: 



Pi = 2.70 to 2.75 (estimated average for surface-rock) 

 J = 4.2 X 10^ Hi = about 4 X 10" (t^ = about 0.2 /^ = about 0.005 



As stated above, it is necessary to supplement the general hypothesis by 

 certain assumptions as to the physical properties of the earth-substance, in 

 particular the form of the characteristic thermodynamic surface : 



F(j),p,d)=0 (!) 



and the form of the intrinsic energy, conveniently an expression of the type: 



eH{p,d) (2) 



The fundamental equations forming the basis of the theory may then be 

 grouped in two classes, related to two curves, not necessarily identical, on 

 the surface (1). The first curve belongs to the actual distribution of the 

 physical magnitudes within the earth at a given time, its projection in the 

 'p-p plane being determined in parameter form by the values of p and p as 

 functions of r. The second curve corresponds to the path of compression 

 traversed by a particular mass of the substance from the time of its deposi- 

 tion to the time when the growth of the planet is complete, and is practi- 

 cally an adiabatic curve if the accretion and consequent compression are 

 relatively rapid, as is here supposed. 



