410 Archdeacon Pratt on the Fluid Theory 



By making qa. = 140° 45', =2*4576 in arc, the theory gives the 

 ellipticity of the surface equal to shs** which is remarkably 

 near t ^— and j^r, the last determination by geodesy and pen- 

 dulum experiments. (See Preface to the volume of the ' British 

 Ordnance Survey/ and p. 453 of Humboldt's ' Cosmos/ vol. iv. 

 part 1.) 



3. My present object is to test the general correctness of the 

 distribution of the earth's mass which the fluid theory leads to, 

 by showing what effect will be produced upon the formula for 

 the variation of gravity, and therefore upon the computed num- 

 ber of vibrations of a seconds' pendulum, by a change in the 

 arrangement of the materials. Problems of this description are 

 of such difficulty, that I am of course very much restricted in 

 selecting a readjustment so as to make the calculation possible. 

 If the earth has not derived its figure from having been once 

 fluid, we know no more of its internal structure than that its 

 mean density is twice that of the superficial parts ; that the 

 average arrangement of the materials must be pretty uniform 

 around the centre, as gravity in all parts of the world tends 

 nearly towards the geometrical centre of the earth ; and that the 

 increase of gravity in passing from one place to another changes 

 very much as the square of the sine of the latitude does. The 

 arrangements which I suggest as tests are, under these circum- 

 stances, as likely to be true, as to their resultant effect upon the 

 surface } as any other arrangement which might be tried. 



First test : the ellipticity of some of the strata changed, 



4. The diagram represents a section of the earth's mass 

 through the poles N and S. ABCD and abed are two layers 

 or spheroidal surfaces bounding a shell of the mass, of one-fifth 

 of the radius in thickness, that is, 800 miles. The first change 

 I imagine to take place is this. All the strata of this shell lose 

 their ellipticity and become spherical; at A and C the mass 

 swells up, as it were, and increases the density of the inner parts 

 of the outer crust in A A' and C C; and at b and d the mass 

 penetrates the inner nucleus as far as^b ! and d' 3 A'B CD and 

 aVcd} being circles, and the other curves oblate ellipses f. In 

 this way the total mass is not altered; but the mass belonging 

 to the shell no longer attracts as a spheroidal shell, but as a mass 

 consisting only of spherical layers, which may therefore be con- 

 sidered as concentrated in the centre of the earth. This change 



* On the Figure of the Earth, second edition, p. 78. 

 f AA' and C C, as well as b V and del', are drawn too large in the dia- 

 gram. A A' should be about ^ihrth of ON, and bb' should be about 



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