188 THE MATHEMATICAL THEORIES OF THE EARTH. 



ill a siiif^le hypothesis, involving- only one assumption in addition to 

 that of original fluidity and the law of gravitation. This assumi)tion 

 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 rela- 

 tive 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 densitj'^ 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 surpassing 

 the crushing strength of steel at the depth of a few miles and amount- 

 ing at the center to no less than 3,000,000 atmospheres. The infer- 

 ences, then, as distinguished from facts, are that the mass of the Earth 

 is very nearly symmetrically disposed about its center of gravity, that 

 pressure and density except near the surface are mutually dependent, 

 and that the earth in reaching this stage has passed through the fluid 

 or quasiHuid state. 



I^ater writers have suggested other hypotheses for a continuous dis- 

 tribution of the earth's mass, but none of them can be said to rival the 

 hypothesis of Laplace. Their defects lie either in not postulating a di- 

 rect connection between density and pressure or in ])ostulating a con- 

 nection which implies extreme or impossible values for these and other 

 mechanical properties of the mass. 



It is clear, from the positiveness of his language in frequent allusions 

 to this conception of the earth, that Laplace was deeply impressed with 

 its essential correctness. " Observations," he says, " prove incontesta- 

 bly that the densities of the strata (couches) of the terrestrial si)heroid 

 increase from the surface to the center,"* and "the regularity with 

 which the observed variation in length of a second's pendulum follows 

 the law of squares of the sines of the latitudes proves that the strata 

 are arranged symmetrically about the center of gravity of the earth."t 

 The more recent investigations of Stokes, to which allusion has already 

 been made, forbid our entertaining anything like so contideut an opin- 

 ion of the earth's primitive fluidity or of a symmetrical and continuous 

 arrangement of its strata. But, though it must be said that the suffl- 

 ciency of Laplace's arguments has been seriously impugned, we caa 

 hardly think the [)robability of the correctness of his conclusions has 

 been iiroportionately diminished. 



* "Enfin il (Newton) rt'giinle la terre comuie homogeue, ce qui est contraire aax 

 observations, qui prouveut incontestablement que les deu8it<5s des couches du 8ph6- 

 roide terrestre croissent de la surface an centre." Mecanique Ct^leste, Tome V, p. 9. 



t "La r^gularitd avec laquelle la variation observoe des longueurs du pendule h 

 secondes suit la loi du carr^' du sinus do la latitude i)rouve que ces couches sont dis- 

 posoes r(^gulit"^roniont autoiir du centre de gravity de la terre et que leur forme est ^ 

 pen pros oUiptiqueet de n'^volution." Ibid., i>. 17. 



