Part I.— THE THEORY OF FISHER. 



GENERAL EQUATIONS. 



A definite form for the development of the theory has been initiated by- 

 Fisher,^ on the basis essentially of three main suppositions as to the prop- 

 erties of the ideal earth-substance. These are: (1) that the path of com- 

 pression traversed by any particular element of the mass is identical as far 

 as it goes with that defined by the relation between density and pressure 

 within the earth in its final state; (2) that pressure and density are related 

 as specified by the classic law of Laplace; (3) that rise of temperature dur- 

 ing compression is proportional to increase of compressional energy, or of 

 work done to produce compression. 



For critical purposes it will be necessary to undertake a close scrutiny of 

 these assumptions, as to their agreement with pertinent observed data, and 

 also, in the light of general thermodynamic laws, of their consistency with 

 each other, or at least of the exact interpretation to be accorded them in order 

 to assure consistency. But in view of their close affiliation with the stand- 

 points adopted in many previous studies of the constitution of the earth's 

 interior, it will be worth while to develop their consequences in some detail. 



The pressure density law, proposed by Laplace,^ has been used by many 

 writers on geophysics, partly it would seem on account of its mathematical 

 convenience, being the only one which reduces equation (6) to linear form. 

 It is based on the condition 



^=hp ;i=const. (20) 



dp 



which, when applied to the compression of an individual portion of the 

 mass, gives 



P=^(P'-P^') (21) 



and for equations (12) and (14) the particular forms 



^^h {p-p,y (22) 



2 p 



s=h{p-p,) (23) 



Assumption (1), however, which gives s = ku, allows the use of the relation 

 (20) in the differential equation (6) or (11), which reduces to 



the appropriate solution being 



sin ^ 



P==Po 



P=qr (25) 



» Rev. O. Fisher. On Rival Theories of Cosmogony. Am. J. of Sc, xi, 1901, p. 414. 

 * Laplace, Mecanique Celeste, book xi, chap. iv. 

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