104 Professor A. E. H. Love [March 6, 



as we have it at the earth's surface, e would be about five hundred 

 thousand atmospheres. Owing to the great pressures in the interior, 

 the strength of the materials of the earth is on the average much 

 greater than the strength of granite at the surface. The critical value 

 of the fraction ^?/e is about ;V5. The value for the earth in its 

 present state is about 0'81, which is far removed from the critical 

 value. The value for the earth if its strength all through were that 

 of granite is about ;^-5. If it were bigger and less compact, so that 

 its average density was :> ' o instead of 5 • 5, and its strength all through 

 were that of granite, the value would be about 1'75-. but, if the 

 strength were that of sandstone, it would be about 3 "2. It seems 

 quite probable that if the earth was once less compact, and conse- 

 quently less strong, than it is now, its condition might have been 

 critical, and that the centre of gravity might then have taken up an 

 eccentric position. It is natural to examine other planets from the 

 same point of view. If Mars with his actual density had a strength 

 all through equal to that of granite, the value of p/e for him would 

 be very small (0*03). This result suggests that any elevations and 

 depressions which may exist on the surface of Mars are not due to 

 eccentric position of the centre of gravity. [The numbers were 

 thrown on the screen.] 



We conclude that the eccentric position of the earth's centre of 

 gravity, like the ellipticity of the equator, may be a survival from a 

 past state in which this inequality was greater than it is now. The 

 pear-shaped figure has been traced to the interaction of two sorts of 

 causes : the eccentric position of the centre of gravity and the causes 

 which give rise to the ellipsoidal figure, among them the rotation. 

 The inequality specified by harmonics of the third degree must there- 

 fore have been at one time less prominent than it is now, in compari- 

 son with the inequalities specified by harmonics of the first and second 

 degrees. In attempting to trace the general effects of this change in 

 the relative prominence of the various inequalities, we must observe 

 in the first place that the ellipticity of the meridians, which is one 

 of the characters of the harmonic of the second degree, is subject to 

 fluctuations owing to the diminishing speed of the earth's rotation. 

 As the speed of the rotation diminishes the equatorial protuberance 

 of the surface of the ocean diminishes, and so does the equatorial 

 protuberance of the surface of the earth. The equatorial protuber- 

 ance is greater for the ocean, and the excess tends to diminish, so 

 that there is a constant tendency for the ocean to inundate the Arctic 

 and Antarctic regions ; but this tendency must be checked from time 

 to time by subsidences in equatorial regions, for the equatorial pro- 

 tuberance of the earth's actual figure must be progressively diminished. 

 The changes that have taken place in the shape and size of the ellip- 

 soidal inequality are therefore of great complexity, but fortunately the 

 actual influence of this inequality upon the distribution of continent 

 and ocean is not very great, and we ca-u form a fairly satisfactory notion 



