34:2 B. S. Woodward — Mathematical Theories of the Earth. 



distribution, and of the pressures that exist at great depths ? 

 Two facts, namely, the mean density and the surface density 

 are roughly known ; and a third fact, namely, the precession 

 constant, or the ratio of the difference of the two principal 

 moments of inertia to the greater of them, is known with 

 something like precision. These facts lie within the domain 

 of observation and require only the law of gravitation for 

 their verification. Certain inferences also from these facts 

 and others have long been and still are held to be hardly less 

 cogent and trustworthy, but before stating them it will be well 

 to recall briefly the progress of opinion concerning this general 

 subject during the past century and a half. 



The conception of the earth as having been primitively fluid 

 was the prevailing one among mathematicians before Clairaut 

 published his Theorie de la Figure de la Terre in 1743. By 

 the aid of this conception Clairaut proved the celebrated theo- 

 rem which bears his name, and probably no idea in the 

 mechanics of the earth has been more suggestive and fruitful. 

 It was the central idea in the elaborate investigations of 

 Laplace and received at his hands a development which his 

 successors have found it about equally difficult to displace or to 

 improve. From the idea of fluidity spring naturally the hydro- 

 statical notions of pressure and level surfaces, or the arrange- 

 ment of fluid masses in strata of uniform density. Hence 

 follows, also, the notion of continuity of increase in density 

 from the surface toward the center of the earth. All of the 

 principal mechanical properties and effects of the earth's mass, 

 viz : the ellipticity, the surface density, the mean density, the 

 precession constant, and the lunar inequalities, were correlated 

 by Laplace in a single hypothesis, involving only one assump- 

 tion in addition to that of original fluidity and the law of 

 gravitation.* This assumption relates to the compressibility of 

 matter and asserts that the ratio of the increment of pressure 

 to the increment of density is proportional to the density. 

 Many interesting and striking conclusions follow readily from 

 this hypothesis, but the most interesting and important are 

 those relative to density and pressure, especially the latter, 

 whose dominance as a factor in the mechanics of celestial 

 masses seems destined to survive whether the hypothesis 

 stands or falls. The hypothesis requires that while the density 

 increases slowly from something less than 3 at the surface to 

 about 11 at the "center of the earth, the pressure within the 

 mass increases rapidly below the surface, reaching a value sur- 

 passing the crushing strength of steel at the depth of a few 

 miles and amounting at the center to no less than three million 

 atmospheres. The inferences, then, as distinguished from the 



* Mecanique Celeste, Tome 5, Libre xi. 



