226 PROFESSOR A. E. H. LOVE ON THE 



a nature that these surfaces are nearly oblate spheroids. If the lithosphere were 

 exactly iu the form of an oblate spheroid, and its centre of gravity coincided with its 

 centre of figure, it would either lie entirely within the geoid or would protrude from 

 it symmetrically at the North and South Poles. Owing to the rigidity of the 

 lithosphere the ellipticity produced in the geoid by rotation would be slightly greater 

 than that produced in the lithosphere, and thus there is a tendency to lay bare the 

 polar regions ; but, since the land of the globe does not consist of two circular islands 

 at the poles, there are other deviations from sphericity, both of lithosphere and geoid, 

 and the relative amounts of these at different places can be expressed by the difference 

 of radii drawn from the centre of gravity. According to the theory which has been 

 here advanced this difference of radii should be, at least in its general features, 

 expressible as a sum of spherical harmonics of the first, second and third degrees. 



54. It is easy to verify the presence of some of these harmonics. The effect of 

 a term of the first degree would be to make the lithosphere protrude from the geoid 

 towards one side. If this term were the only one, the land of the globe would form 

 a circular island or continent. It is the fact that most of the land is in one 

 hemisphere. The great circle of the globe which contains most land has a pole 

 situated between Orleans and Le Mans* (latitude 48 N., longitude 30' E.). Again, 

 the zonal harmonic of the third degree vanishes at three circles, one being a great 

 circle. If this term were the only one, the land of the globe would consist of 

 a circular island surrounded by a belt of ocean in one hemisphere, and in the 

 antipodal hemisphere there would be a circular ocean surrounded by a ring of land. 

 This arrangement corresponds to two features of SOLLAS' description of the Earth's 

 surface. The nearly symmetrical breaking at three places of the belt and three of 

 the ring, which he also noticed, indicates the presence of the sectorial harmonic of the 

 third degree. If we refer to the polar axis, instead of any other morphological axis, 

 the presence of the zonal harmonic of the third degree is indicated by the existence 

 of an Antarctic continent, and by the fact that most of the land of the globe is north 

 of the Equator. The harmonic of the third degree and second rank, referred to the 

 polar axis, vanishes at the Equator and at four meridians symmetrically placed. If 

 this term were the only one, then, in two northern quadrants there would be land, 

 and also in the two alternate southern quadrants, an arrangement which suggests 

 Central Asia and North America as the land quadrants of the northern hemisphere, 

 Australia and South America as those of the southern. 



Spherical Harmonic Analysis of tlie Distribution of Land and Water. 



55. By such arguments as the foregoing, and by some trials with small numerical 

 coefficients for the various harmonics, I had convinced myself that many features of 

 the distribution of land and water could be represented by means of harmonics of the 

 third degree, when Professor H. H. TURNER suggested to me the advisability of 



* E. BRUCKNER, 'Die feste Erdrinde und ihre Formen,' Wien, 1897. 



