1-C 



On the Fluid Theory of the Figure of the Earth. 507 



T 27r 1— c \—c 



= j 2<fy . F(/*, «), as ^-, j™, ... all vanish. 



= 47rF(yt6 ; &>), as F(/4, &)) is independent of yjr. 



This is the celebrated theorem of Laplace, on which his pow- 

 erful analysis is based. 

 Calcutta, October 8, 1862. 



LXVIII. Postscript to a Paper " On Tests of the Truth of the 

 Fluid Theory of the Figure of the Earth. 3 ' By Archdeacon 

 J. H. Pratt*. 



A STILL better hypothetical re-arrangement of the mass of 

 the earth, with a view to test the fluid theory, is the following. 

 All we know a priori regarding the mass is this, that the external 

 surface is an oblate spheroid of ellipticity g-i^, that the mean 

 density is twice that of the surface, and that the materials are 

 arranged in more or less spherical strata about the centre. Sup- 

 pose, then, that we conceive that the external spheroidal form 

 has not been derived from a former state of fluidity, but from 

 the constant action of the centrifugal force removing the parts 

 discharged by weathering upon the surface towards the equator, 

 and that the interior is not necessarily arranged according; to the 

 fluid law. Conceive the mass made up as follows — of a homo- 

 geneous spheroid of the same density as the superficial parts of 

 the earth, with the remainder of the mass distributed through it 

 in some unknown arrangement. That arrangement, as one of 

 our data shows, cannot depart much from that of spherical 

 shells around the centre. I will assume, in the first instance, 

 that this is the arrangement, and will find the effect on the pen- 

 dulum. It is clear that, as the density of the surface is half the 

 mean density of the earth, the mass of the homogeneous spheroid 

 will be half the mass of the earth, and the remainder will be half 

 also. Hence the potential of the earth's mass under this new 

 arrangement will be 



»- 1 ?* 1 ?(-?)(i-*)+e 



?(«-?)G-4 



E lEs 



7 + 2 



* Communicated bv the Author. 



