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XLIX. The Mass of the Earth is arranged in nearly spherical strata 

 around its centre ; and if the outer surface be a spheroid of equi- 

 librium, then all the strata are so also, whether they acquired 

 that form from once being fluid or not. By Archdeacon J. H. 

 Pratt. 



To the Editors of the Philosophical Magazine and Journal, 



Gentlemen, 



T has been asserted that all we know with any certainty 



I 



regarding the constitution of the earth's mass is contained 

 in the following facts derived from observation and experiment : 

 (1) That the level-surface obtained by geodesy, to which the 

 plumbline is everywhere perpendicular, is almost exactly a sphe- 

 roid, of small ellipticity, about vVg-th, and coincides very nearly, 

 if not exactly, with the mean surface of the earth. (2) That the 

 force of gravity is nearly the same on all points of the surface, 

 and changes, in passing from place to place, almost exactly as 

 the change in the square of the sine of the latitude. (3) That 

 the mean density is nearly equal to 5*66 times the density of 

 water. It has been said that any notions we have of the inte- 

 rior arrangement of the mass are altogether theoretical. In 

 connexion with this subject it has also been stated that nothing 

 can be gathered from pendulum experiments (and therefore from 

 the value of gravity and the ellipticity thence deduced) regarding 

 the fluid arrangement of the earth's mass. There appears to me 

 to have been some confusion of ideas on this subject. My pre- 

 sent object is to show that the first of the three facts I have 

 enumerated above leads logically to the two following results : — 



I. That the earth's mass is, as a matter of fact, arranged in 

 nearly spherical layers of equal density about the earth's centre. 



II. That if we assume, as is generally done, that at least the 

 mean exterior surface of the earth is a spheroid of equilibrium, 

 then it follows as a necessary consequence that the forms of all 

 the interior strata are also spheroids of equilibrium, and follow 

 the fluid law, whether they are fluid or not now, or ever were so, 

 in part or in whole. 



1. The earth's mass } as a matter of fact, consists of nearly sphe- 

 rical strata of equal density about the earth's centre. 



2. Let r, 6, co be polar coordinates to any point on the earth's 

 surface, the centre being origin (cos 6=p)' } r', 6', co 1 coordinates to 

 any point in the interior (cos r =/j,'), p- the density at that 

 point; a the mean radius of the surface; r = a-\-ct . u, u being a 

 function of /n and co, and a a small fraction, because the surface 

 is nearly spherical. Then the potential of the whole mass for 



