THE FIGURE OF THE EARTH. 13 



tho solid and fluid matter on the outer crust of the 

 earth." Although while it is not improbable, judging from 

 geological data, that the incidental alterations which are 

 readily brought about in the fused portions of the interior 

 of the earth, when they are moved by a change of position of 

 the masses, may even modify the geometrical surface by pro- 

 ducing curvature of the meridians and parallels in small 

 spaces, and at very widely separated periods of time ; the 

 physical surface of the oceanic parts of our globe is peri- 

 odically subjected to a change of place in the masses, occa- 

 sioned by the ebbing and flowing (or in other words the 

 local depression and elevation) of the fluid element. The 

 inconsiderable amount of the effects of gravity in continental 

 regions may indeed render a gradual change inappreciable to 

 actual observation ; and according to Bessel's calculation, in 

 order to increase the latitude of a place by a change of only 

 1", it must be assumed that there is a transposition in the 

 interior of the earth of a mass, whose weight (its density 

 being assumed to be that of the mean density of the earth) is 

 that of 7296 geographical cubic miles.* However large the 

 volume of this transposed mass may appear to us when we 

 compare it with the. volume of Mont Blanc, or Chimborazo, 

 or Kintschindjinga, our surprise at the magnitude of the 

 phenomenon soon diminishes when we remember that our 

 terrestrial spheroid comprises upwards of 1696 hundreds of 

 millions of such cubic miles. 



Three different methods have been attempted although 

 with unequal success for solving the problem of the figure of 

 the earth whose connection with the geological question of 

 the earlier liquid condition of the rotating planetary bodies 

 was known at the brilliant epoch of Newton, Huygens 

 and Hooke.* These methods were the geodetico-astro- 



5 Bessel, Ueber den Einfiuss der Vcrdnderungen ties Erdkorpers auf die 

 Polhohen, in Lindeuau und Bohnenberger, Zeitschi ift fur Astronomic. 

 Bd. v, 1818, s. 29. " The weight of the earth, expressed in German 

 pounds=9933 x 10. 21 , and that of the transposed mass = 947 x 10. 14 ." 



6 The theoretical labours of that time were followed by those of 

 Maclaurin, Clairaut, and d'Alembert, by Legendre and by Laplace. 

 To this latter period we may add the theorem advanced by Jacobi, in 

 1834, that ellipsoids of three unequal axes may, under certain conditions, 

 represent the figures of equilibrium no less than the two previously- 

 indicated ellipsoids of rotation. See the treatise of this writer, whose 



