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Mr. G. H. Darwin on the Influence of [Nov. 23, 



velocity, and is coincident with the axis of figure every 306th day (in 

 the earth). This circle touches the meridian along which the axis of 

 figure is travelling in consequence of the deformation of the earth's 

 shape. The diameter of the circle is shown in a particular case (not un- 

 favourable to produce a large effect) to be less than y-y-g-". But although 

 this inequality appears to be so small, it is of interest and is discussed 

 at some length. It is shown that, if the earth be not quite rigid, this 

 inequality might have the effect of modifying the path of the axis of 

 figure in the body, in consequence of readjustments to a figure of 

 equilibrium. 



Various hypotheses as to the power of adjustment are considered, and 

 the paths of the instantaneous and principal axes in the precession of a 

 viscous spheroid undergoing deformation are found. 



It is maintained that although the earth may be sensibly rigid to the 

 tidally deforming forces exercised by the sun and moon, it would not be 

 so to considerable departiu'es from the figure of equilibrium, such as 

 would arise from a wandering of the pole of figure from its initial 

 position ; and that readjustments to an approximate form of equilibrium 

 probably take place, at considerable intervals of time, impulsively by 

 means of earthquakes. 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 consolidation of the earth 

 there must have been great instability in the geographical position of the 

 poles. Throughout the rest of the inquiry, howeyer, 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 dis- 

 missed, and it only remains to consider the kinematical question of the 

 change in the earth's principal axes due to any deformation of its shape. 



2. Tormulse for this end are here found, and are adapted for numeri- 

 cal 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 accord- 

 ingly all suppositions as to the nature of the internal changes accompany- 

 ing geological upheaval and subsidence are set aside. 



3. The forms of continent and depression are next investigated, 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 uniform 

 height and depth ; there must be two of each, all similar to one another ; 

 that each has one of its own kind diametrically opposite to it ; that they 

 are in shape sphero-conics, formed by the intersection of a certain 

 elliptic cone with the sphere ; that the centres of the four sphero-conics 



