October 25., 1907] 



SCIENCE 



535 



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 disproportion between 

 the amounts of continental area in the 

 northern and southern hemispheres is as- 

 sociated with the result that the central 



tion occupies the northern part of the At- 

 lantic Ocean and runs down to and across 

 the equator in the neighborhood of Borneo. 

 The southern region of elevation occupies 

 the southern part of the Pacific Ocean, and 

 it runs up to and across the equator in the 



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 asso- 

 ciated with the corresponding position of 

 the central region of greatest depression 

 about 45° south of the equator. In re- 

 gard to harmonics 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 depres- 

 sion 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 eleva- 



"In this figure, and in the following figures, 

 regions of elevation are shaded, and regions of 

 depression are left blank. 



Fiq.7. 



neighborhood of Peru. The chart of the 

 harmonic is shown in Pig. 7. The equa- 

 torial regions of elevation given by the 

 analysis are near the ends of a diameter, 

 as we should expect. 



It has not been necessary to enter into a 

 minute description of the harmonics of the 

 first and second degrees, because they 

 represent very simple things— a shifting of 

 the surface to one side and a distortion of 

 it into an ellipsoid. The harmonies of the 

 third degree are not so familiar. There 

 are essentially four of them, each specify- 

 ing a standard pattern of deformation. 

 The first of these, the zonal harmonic, gives 

 us a division of the surface into two polar 

 caps and two zones by means of the equator 

 and the parallels of latitude about 51° 

 north and 51° south. Alternate zones are 

 depressed and elevated, as shown in Fig. 8. 



F"ig8 



