THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



DECEMBER 1862. 



■ 



LV. Tests of the Truth of the Fluid Theory of the Figure of the 

 Earth. By Archdeacon J. H. Pratt*. 



1. HHHE calculation of the figure of the earth on the fluid 

 JL theory proceeds upon the hypothesis that the earth at 

 one time consisted of a heterogeneous mass of incompressible 

 fluid or semifluid materials revolving round a fixed axis, and 

 that these materials arranged themselves in layers nearly sphe- 

 rical in form ere the mass, or at any rate its surface, became 

 solid as at present. The law of density of the layers is assumed 



to be represented by A — , a being the mean radius of any 



layer, and A and q constants. Though this is an assumed law, 

 it has not been chosen at random, but has been selected for good 

 reasons. 



2. The following are some of the results flowing from this 

 hypothesis. The layers are all spheroidal, with a common centre 

 and axis ; their ellipticities are related by the equation 



3 1 



I 2 2 I 



e q z cr z' 



e 



V 



O 9 



q~ix z 



e and a being the ellipticity and semi-axis major of the surface, 

 and e' and a the same of any other layer; also 



<7 a j_i c l a 4. 



2 = 1-7-^-, sal- 



tan (/a* tan qa 



* Communicated by the Author. 



t These formulce may be gathered from any book on this subject. I 

 have derived them from my treatise c On the Figure of the Earth/ second 

 edition, p. 76* . 



PMl Marj % S. 4. Vol. 24, No. 103. Dec. 1 SG2. 2 B 



