446 G. H. Darwin— Influence of Geological Changes 



it would not be so to considerable departures from the figure 

 of equilibrium, such as would arise from a wandering of the 

 pole of figure from its initial position; and that readj 

 to an approximate form of equilibrium probably take place, at 

 considerable intervals of time, impulsively by means of earth- 

 quakes. Such periodical adjustments would not sensibly 

 modify the geographical path of the principal axis as due to 

 terrestrial deformation. But it is held that during the con- 

 solidation of the earth there must have been great iiu-t 

 the geographical position of the poles. Throughout the rest of 

 the inquiry, however, the hypothesis of the earth's sensible 

 rigidity, together with the possibility of more or less rare 

 impulsive readjustments to the figure of equilibrium, is adhered 

 to. In consequence of these results dynamical considerations . 

 may be dismissed, and it only remains to consider the kinemati- 

 cal question of the change in the earth's principal axes due to 

 any deformation of its shape. 



2. Formulae for this end are here found, and are adapted for 

 numerical calculation. It is assumed, in the first place, that 

 the deformation is such that there is no change in the strata of 

 equal density ; and accordingly all suppositions as to the 

 nature of the internal changes accompanying geological up- 

 heaval and subsidence are set aside. 



3. The forms of continent and depression are next inv«8*3r 

 gated, which, for the transport of a given quantity of matter 

 from one part of the earth's surface to another, would cause the 

 maximum deflection of the principal axis of greatest moment- 

 subject, however, to the condition that the layer excavated or 

 piled up shall nowhere exceed a given small fraction of the 

 earth's radius. 



It is shown that the continents and depressions must be of uni- 

 form height and depth ; there must be two of each, all - 

 one another; that each has one of its own kind diam 

 opposite to it ; that they are in shape sphero-conics, formed by 

 the intersection of a certain elliptic cone with the sphere; 

 that the centers of the four sphero-conics are all on the same 

 complete meridian and all in latitude 45°. A table of numeri- 

 cal results depending on the values of certain elliptic functions 

 is given. 



4. In this part an endeavor is made to collect evidence as to 

 the extent to which the earth may have undergone deformation 

 from geological changes. The object is to discover what are 

 the largest areas over which there has been a consentaneous rise 

 or fall, and what is th imoant of that rise or 

 fall ; also to determine how the erosion of the land and the sea 



• affect the local excesses or deficiencies of matter on the earth's 

 surface. The areas and amounts of elevation and subsidence 



