238 PROFESSOR A. E. H, LOVE ON THE 



which this inequality is 10 per cent, of its maximum above zero. It is to }>e observed 

 that an inequality expressed by harmonics of uneven degrees has numerically equal 

 values with opposite signs at antipodal points, and therefore the area on the sphere 

 within which such an inequality is positive is equal to the area within which it is 

 negative. But this equality of positive and negative areas does not hold when the 

 harmonics of the second degree are present. A rough calculation showed that the 

 zero line of the inequality illustrated in fig. 3 divides the surface of the sphere into 

 two unequal areas, and the inequality is negative in the larger area. The excess of 

 the negative area above the positive is nearly 10 per cent, of the whole surface. 

 The heavy line in fig. 3 corresponds more nearly than the other lines to the 

 principle by which geographers construct the contour-line at mean-sphere-level. The 

 diagram in fig. 3 suggests many features of the outline of the continental block, and 

 there can be no doubt that the coefficients could be adjusted so as to secure a better 

 agreement.* It seems best, however, to record the results as they are. For the sake 

 of comparison a rough map of the world is added (fig. 4). The heavy continuous line 

 is the outline of the continental block at mean-sphere level, and the fine continuous 

 line is the coast-line. I have not attempted to draw the map with minute accuracy, 

 and have omitted many small islands and some small enclosed patches of deep sea, 

 because the object aimed at is a comparison of the general features of the map of 

 the world with those of the diagram in fig. 3. The map is drawn by taking the 

 longitude east of Greenwich and the latitude of any point as the Cartesian 

 co-ordinates of the corresponding point of the map. Fig. 3 is drawn in the same way. 

 The defects of the arrangement in fig. 3, considered as representing the shape of 

 the continental block, are sufficiently obvious, the chief being the absence of any 

 indication of an Arctic ocean, and the almost complete submersion of South America. 

 On the other hand, the fact that even tolerable agreement in so many respects is 

 obtained from a spherical harmonic analysis of the extremely simple distribution 

 detailed in the table of 56 may be regarded as a confirmation of the theory which 

 led us to assume that harmonics of the first, second, and third degrees shoiild be 

 predominant. 



Geological Implications of the Theory. 



62. The results appear to admit of a geological interpretation. We have adduced 

 dynamical reasons for the hypothesis that the lithosphere consolidated in a shape 

 which may be described as an ellipsoid with three unequal axes, with its centre 

 of gravity displaced from its centre of figure, and with a wrinkle upon its surface 

 expressed by spherical surface harmonics of the third degree ; and we have found that 

 the figure of the lithosphere now, as determined by difference of level above or below 



* The coefficients r, t, a, b, c are especially sensitive to changes in the assumed distribution in the Arctic 

 and Antarctic regions where the actual distribution is least known. 



