August i, 1907] 



NA TURE 



331 



way of regarding it would be as a surface with ridges 

 and furrows. From a place in the South Atlantic there 

 run three ridges : one north-westwards across America, a 

 second north-eastwards across Africa and Asia, and the 

 third southwards over the Antarctic continent, continuing 

 northwards across Australia nearly to Japan. From tht 

 Sea of Okhotsk there run three furrows : one south-west- 

 wards across Japan, the Malay Peninsula, and the Indian 

 Ocean ; a second south-eastwards across the Pacilic ; and 

 the third northwards over the Arctic Ocean, continuing 

 southwards by way of the Atlantic. Harmonics of the 

 first and third degrees have in common the character of 

 giving depression at the antipodes of elevation ; the har- 

 monics of the second degree give depression at the anti- 

 podes of depression and elevation at the antipodes of 

 elevation. The maxima of the harmonics of the first and 

 third degrees are found to be rather greater than the ma.xi- 

 mum of the harmonic of the second degree. Of three 

 quantities to be added together the two larger ones agree 

 in giving depression at the antipodes of elevation ; a result 

 which is in accordance with the fact that most continents 

 have oceanic antipodes. 



When we superpose the effects represented by all the 

 various harmonics of the first, second, and third degrees, 

 so as to make, as it were, a composite photograph of all 

 the various elevations and depressions represented by them 

 severally, each in its appropriate amount as determined 

 by the harmonic analysis, we find the curve shown in 

 Fig. 14 as the theoretical curve of separation between 

 regions of elevation and depression which are approximately 

 equal in area. I showed before a smoothed curve (Fig. 3) 

 which 1 proposed to lake as representing ihp facts to be 



Flq. I4-. 



accounted for. The resemblance of the two curves seems 

 to be striking. Incidentally it has been noticed how the 

 prominent features of the distribution of continent and 

 ocean are associated with the presence of various harmonics. 

 As regards the contour of the great ocean basins, we 

 seem to be justified in saying that the earth is approxi- 

 mately an oblate spheroid, but more nearly an ellipsoid 

 with three unequal axes, having its surface furrowed 

 according to the formula for a certain spherical harmonic 

 of the ihird degree, and displaced relatively to the geoid 

 towards the direction of the Crimea. 



As regards the amount of elevation and depression in 

 different parts, the agreement of the theory with the facts 

 is not so good. The computed elevation is too small in 

 Southern Africa, Brazil, and the southern part of South 

 America, too great in the .Arctic regions, to the south of 

 of Australasia, and in the Mediterranean region. There 

 are manv reasons why we could not expect the agreement 

 to be very good. One is the roughness of the method of 

 harmonic analysis that was used. But there is also the 

 fact that many causes must have contributed to the shap- 

 ing of our actual continents and oceans besides those which 

 have been taken into account in the theory. It appears, 

 however, that the broad general features of the distribution 

 of continent and ocean can be regarded as the consequences 

 of simple causes of a dynamical character : eccentric posi- 

 tion of the centre of gravity, arising from a past state of 

 inadequate resistance to compression, an inherited tendency, 

 so to speak, to an ellipsoidal figure, associated with the 

 attraction of the moon in a bygone age, the rotation, and 

 the interactions of these various causes. 



In attempting to estimate the bearing of the theory on 



NO. Tg^'o, VOL. 76] 



geological history we must be guided by two considerations. 

 The first is that the earth is not now gravitationally un- 

 stable. From observations of the propagation of earth- 

 quake shocks to great distances, we can determine the 

 average resistance to compression, and we find that this 

 resistance is now sufficiently great to keep in check any 

 tendency to gravitational instability. The eccentric position 

 of the centre of gravity must be regarded as a survival 

 from a past state in which the resistance to compression 

 was not nearly so great as it is now. The second guiding 

 consideration is that, according to the theory, the in- 

 equalities which are expressed by spherical harmonics of 

 the third degree are secondary effects due to the interaction 

 of the causes which give rise to inequalities expressed by 

 harmonics of the first and second degrees. We should 

 expect, therefore, that the inequalities of the third degree 

 would be much smaller than those of the first and second 

 degrees ; but the harmonic analysis shows that the three 

 inequalities are entirely comparable. We must conclude 

 that the harmonics of the first and second degrees which 

 we can now discover by the analysis are survivals from a past 

 state, in which such inequalities were relatively more 

 important than they are now. Both these considerations 

 point in the same direction, and they lead us to infer that 

 certain s.-Bcular changes may have taken place in the past, 

 and may still be going on. Sixty-nine years ago Charles 

 Darwin wrote : " The form of the fluid surface of the 

 nucleus of the earth is subject to some change the cause 

 of which is entirely unknown, and the effect of which is 

 slow, intermittent, but irresistible." Forty-two years later 

 Sir George Darwin showed that any ellipsoidal inequality 

 in the figure must be gradually destroyed by an irreversible 

 action of the same nature as internal friction or viscosity. 

 The same may be said of a stale in which the centre of 

 gravitv does not coincide with the centre of figure whtn 

 the resistance to compression is great enough to keep in 

 check the tendency to gravitational instability. The state 

 would be changed gradually in such a way as to bring 

 the centre of gravity nearer to the centre of figure. .\ 

 symptom of such changes might be the occurrence of great 

 subsidences in the neighbourhood of the Crimea, where 

 we found the maximum of the first harmonic. Such sub- 

 sidences are supposed by geologists to have taken place in 

 rather recent times. Symptoms of the diminution of the 

 inequalities expressed by harmonics of the second degree 

 would be found in the gradual disappearance of seas 

 forming part of the great depression which was described 

 above as a sort of immense Mediterranean (r/. Fig. 7), in 

 the destruction and inundation of a continent in the 

 northern .Atlantic and in a gradual increase of depth of 

 the Southern Pacific. The disappearance of seas from a 

 vast region surrounding the present Mediterranean basin, 

 and containing the Sahara and Southern Asia as far east 

 as the Himalayas, is one of the best ascertained facts in 

 geological history ; and the belief in the destruction of a 

 north Atlantic continent is confidently entertained. In 

 parts of the Southern Pacific a depression represented by 

 harmonics of the third degree is superposed upon an 

 elevation represented by harmonics of the second degree, 

 and we should therefore expect to find the depth of the 

 ocean to be increasing gradually in this region. The 

 region in question is that of the coral reefs and coral 

 islands, such as Funafuti, and the result is in accord with 

 Darwin's theory of the formation of coral reefs. So far 

 as the general distribution of the mass within the earih 

 is concerned, the reduction of the inequalities of the first 

 and second degrees would seem to have already proceeded 

 very far ; for we are assured by geodesists that harmonics 

 of the first degree, and those of the second degree which 

 do not represent the effect of the rotation, are far from 

 prominent in the figure of the geoid— much less prominent 

 than we found them to be in the distribution of continent 

 and ocean. We infer that the inequalities of the first 

 and second degrees must have been progressively diminished 

 in comparison with those of the third degree. The general 

 result of such changes would be a gradual diminution of 

 the depths and extents of the oceans which correspond 

 with the harmonics of the first and second degrees, and a 

 compensating increase in the depths and extents of the 

 oceans which correspond with the harmonic of the third 

 degree. To see the character of the changes which wuuld 



