346 On the nearly Spherical Arrangement of the Mass of the Earth. 



whole mass, and the arrangement of the mass E would obviously 

 be according to the fluid law throughout. Suppose any part of 

 this to become solid, retaining this law of arrangement, the 

 equilibrium of the free fluid-surface would remain undisturbed. 

 Now consider the effect upon the free-fluid surface of any rear- 

 rangement of this solid part within its own limits. The result- 

 ant effect of this change in the arrangement of the attracting 

 matter upon the fluid-surface would be a force which might at 

 particular points of the surface equal zero, but which would in 

 general vary from point to point of the surface. The equili- 

 brium of the fluid would therefore be disturbed by this change 

 of arrangement. It will be obvious from this, that no departure 

 of the arrangement of the attracting mass from that of the fluid 

 law, even in the solid parts of the mass, will allow the free sur- 

 face to retain its form. Hence if the outer surface is one of 

 equilibrium all the strata are so too; and, as the fluid theory 

 shows, they are all spheroids of small ellipticity. 



The more nearly, therefore, geodesy and pendulum experi- 

 ments bring out the mean form of the earth, represented by the 

 level surface, to be that of a spheroid, the more nearly spheroidal 

 are the strata. This is a logical consequence of the free surface 

 being held in equilibrium and having its form regulated by the 

 attraction of the whole mass. It does not prove how much or 

 how little of the mass is fluid, if, indeed, any part of it is ; but 

 it shows that (if the surface is a spheroid of equilibrium) the 

 arrangement of the whole mass must be that peculiar one, and 

 no other, which coincides precisely with the fluid arrangement 

 in every part of the mass. If, then, the value of e obtained from 

 geodesy, when substituted in the formula for V, or rather in that 

 derived from it for gravity, makes it accord with the result of 

 pendulum experiments, we have a very strong evidence that the 

 superficial parts of the earth/ s mass have the equilibrium form, 

 and consequently that the whole mass throughout, solid or not, 

 is arranged according to the fluid law. No more convincing 

 Pargument, short of an absolute knowledge of the fact, could be 

 / produced to show that the earth's mass has derived its arrange- 

 ment and form from having once been in a fluid condition — 

 especially as no other conceivable cause than rotation acting on 

 a fluid mass could have made the interior of the mass in every 

 stratum bulge out towards the equator, and in every part by the 

 precise quantity required by the fluid theory. 



J. H. Pratt. 

 Murree, August 1, 1863. 



