240 PROFESSOR A. E. H. LOVE ON THE 



the harmonics of the first degree have ratios anywhere near to those given in the 

 table of 60, the great circle along which the harmonic inequality of the first degree 

 vanishes has a pole somewhere in south-eastern Europe and the opposite pole in the 

 Pacific Ocean. The inequality is positive in Europe, most of Asia, Africa, North 

 America, the northern and central parts of the Atlantic Ocean, and the Arctic 

 regions. The effect of a gradual diminution of the coefficients of the harmonics of 

 the first degree would be a gradual emptying of the Pacific Ocean, accompanied 

 by a rise of sea-level around the shores of the Atlantic Ocean (except towards 

 the southern parts of Africa and South America) and around the northern and 

 western parts of the Indian Ocean. It has been held that such an effect has 

 taken place and constitutes the reason for the difference between a " Pacific coast " 

 and an " Atlantic coast." The ratios of the coefficients of the various harmonics 

 of the second degree for the two distributions considered in 56-60 are widely 

 divergent, but they agree in leading to negative values for the harmonic inequality 

 of the second degree in the regions contained within oval curves which lie within 

 the basin of the PaciBc, and also in the antipodal regions. In a large part of the 

 Pacific region the harmonics of the first and second degrees reinforce each other ; 

 in the antipodal region they are antagonistic. Diminution of the coefficients of 

 the harmonics of the second degree would be manifested by a fall of sea-level in 

 the Pacific, and also in a region antipodal to some part of the Pacific. It may not, 

 perhaps, be altogether fanciful to see in the gradual reduction of area of the " Central 

 Mediterranean Sea " of Mesozoic and Tertiary times f the effect of a continual 

 reduction of those coefficients of harmonic inequalities of the second degree which 

 represent ellipticity of the equator and obliquity of the principal planes. Whether 

 these conjectures as to the particular regions which may have been affected are 

 acceptable or not, it can safely be said that the effects of changes in the harmonic 

 inequality of the first degree, and in those of the second degree which we are now 

 considering, would be progressive in the same sense at the same place. They would 

 be manifested in a tendency of the sea to fall in certain regions and to rise in certain 

 complementary regions and gradually to flood wide areas. The gradual character 

 of the positive movements of the strand-line, by which wide areas have been sub- 

 merged, has been emphasized by STJESS. J 



The surface of the lithosphere is nearly an oblate spheroid which does not coincide 

 precisely with an equipotential under gravity modified by the rotation ; it is less 

 oblate than the geoid. The surface of a shallow ocean covering an oblate spheroidal 

 planet, whose outer surface is not exactly an equipotential surface, is an oblate 

 spheroid, and its ellipticity is a certain multiple of the ellipticity of the surface of the 

 planet. The ratio of the two ellipticities depends partly on the rigidity of the planet, 



* E. SCESS, ' The Face of the Earth ' (Translation), vol. 2, Oxford, 1906, p. 553. 

 t Ibid., pp. 258, 299. 

 \ Ibid., p. 543. 



