4.32 TRANSACTIONS OF SECTION A. 
first making the deformation according to the first pattern, then going on to make 
the deformation according to the second pattern, and soon. If we begin with a 
pattern, for instance the shape of the earth, which is not a standard pattern, we 
can find out how great a deformation of each standard pattern must be made in 
order to reproduce the prescribed pattern. The method of doing this is the 
method of spherical harmonic analysis. Except in very simple cases the applica- 
tion of it involves rather tedious computations. With much kind assistance and 
encouragement from Professor Turner, I made a rough spherical harmonic 
analysis of the earth’s surface. I divided the surface into 2,592 small areas, rather 
smaller on the average than Great Britain, gave them the value +1, or one unit 
of elevation, if they are above the sea, and the value —], or one unit of depression, 
if they are below the 1,400-fathom line. To the intermediate areas 1 gave the 
value 0. The distribution of the numbers over the surface was analysed for 
spherical harmonics of the first, second, and third degrees, 
Any spherical harmonic of the first’ degree gives us a division of the surface 
into two hemispheres—one elevated, the other depressed. The spherical harmonic 
analysis informs us as to the position of the great circle which separates the two 
hemispheres, and also as to the ratio of the maximum elevation of this pattern 
to the maximum elevation of any other pattern. The central region of greatest 
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elevation of this pattern is found to be in the neighbourhood of the Crimea, and 
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Fig.6. 
the region of elevation contains the Arctic Ocean and the northern and central 
parts of the Atlantic, Europe, Africa, Asia, most of North America, and a small 
part of South America. When the surface is mapped on a rectangle in the same 
way as before, the chart of the harmonic is that shown in fig. 6." The actual dis- 
proportion between the amounts of continental area in the northern and southern 
hemispheres is associated with the result that the central region of elevation, as 
given by the analysis, is about 45° north of the equator; and the extension of the 
Pacific Ocean and adjoining Southern Ocean to much higher southern than 
northern latitudes is associated with the corresponding position of the central 
region of greatest depression about 45° south of the equator. In regard to 
harmonies of the second degree, the spherical harmonic analysis informs us as 
to the ellipticity of the equator and the obliquity of the principal planes of that 
ellipsoid which most nearly represents the elevation of the surface above or its 
depression below the surface of the ocean, or the geoid. The result is an 
equatorial region of depression, which spreads north and south unequally in different 
parts and forms a sort of immense Mediterranean, containing two great basins, and 
separating a northern region of elevation from a southern, The northern region of 
elevation occupies the northern part of the Atlantic Ocean and runs down to and 
across the equator in the neighbourhood of Borneo, The southern region of eleva- 
tion occupies the southern part of the Pacific Ocean, and it runs up to and across 
the equator in the neighbourhood of Peru. The chart of the harmonic is shown in 
1 In this figure, and in the following figures, regions of elevation are shaded, and 
regions of depression are left blank. 
