1008] on the Figure and Gonstitution of the Earth. 



101 



some approach to symmetry, and on the whole widening as they go. 

 [Map shown by slide.] From this discussion we conckide that the 

 surface of the earth presents all the types of inequalities which can 

 be specified by spherical harmonics of the third degree or represented 

 by pear-shaped figures. Since each of the types gave us elevation in 

 Australia and antipodal depression in the central Atlantic, we must 



Fig. 3. 



not entertain a prejudice in favour of Australia as a sort of stalk for 

 a pear-shaped figure. We shall find that it is better to regard it as 

 a part of the protuberant ring of such a figure. 



I will not proceed to describe the spherical harmonics of the fourth 

 and higher degrees, because it is possible to go some way towards 

 accounting theoretically for the existence of inequalities of the first 

 three degrees, but not for those of higher degrees, and, if we found 

 these to exist, we should have to infer that they are not due to gravi- 

 tational causes, but to local tectonic accidents. We know that the 

 actual shape, whatever it may be, can be reproduced by combining 

 harmonics of all degrees ; but, if we find that a fair approximation to 

 the actual shape can be obtained by taking those of the first three 

 degrees only, we may conclude that the main features of the shape 

 are due to gravitational causes. If the depth of the sea, or height of 

 the land, at every point were accurately known, we could use a definite, 

 straightforward and very laborious, mathematical process to determine 

 the proportions in which the various harmonics must be combined in 



