NATURE 



[August i, 1907 



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 descrip- 

 tion 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 harmonics of the third degree are not so 

 familiar. There are pssenlially four of them, each specify- 



Flg.8. 



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. The existence of an Antarctic continent and an 

 .Arctic Ocean is specially associated with the presence of 

 this harmonic, and the disproportion of the continental 



Fiq.9, 



areas in the northern and southern hemispheres is also 

 connected with it. The second of the harmonics of the 

 third degree, the tesseral harmonic of rank i, gives us 

 a division of the surface into six half-zones by means of 

 a complete meridian circle and the parallels of latitude 

 about 27° north and 27° south. Alternate half-zones are 

 depressed and elevated as shown in Fig. g. The combined 

 effect represented by the zonal harmonic and the tesseral 



of combining these two harmonics because they represent 

 the particular effects that would be produced by the inter- 

 action of two causes — the rotation, and the eccentric posi- 

 tion of the centre of gravity. The third type of harmonics 

 of the third degree, the tesseral harmonic of rank 2, gives 

 us a division of the surface into octants by means of the 

 equator and two complete meridian circles. Alternate 

 octants are elevated and depressed as show-n in Fig. 11. We 



Fig.) I. 



can name the octants where there is elevation : Asia, Aus- 

 tralasia, North .America, South America. The harmonic 

 of this type is certainly prominent. It is specially asso- 

 ciated with the skew position of .South .America to the 

 east of North America. The fourth type of harmonics of 

 the third degree, the sectorial harmonic, gives us a division 

 of the surface into six sectors by means of three complete 

 meridian circles. Alternate sectors are depressed and 



Fig.12. 



elevated as shown in Fig. 12. The soiuhwaid tapering ol 

 Africa is specially associated with the harmonic of this 

 tvpe. The combined effect of all the harmonics of the 

 third degree is shown in Fig. 13. It represents the sphere 

 deformed into a sort of irregular pear-shaped surface. The 

 stalk of the pear is in the southern part of Australia and 

 contains Australasia and the Antarctic continent. This is 

 surrounded on all sides but one (towards South America) 



Fig. 10 



harnionii of rank 1 is a furrowed surface with an .Arctic 

 region of depression extending southwards in the direction 

 of the .Atlantic, a zone of elevation which runs across the 

 Atlantic, South America, and Africa, and then turns north- 

 wards at either end, a zone of depression with the same 

 kind of contour, and an Antarctic region of elevation which 

 extends northwards in the direction of .Australasia. These 

 regions are shown in Fig. 10. 1 have recorded the result 



N). 1970, VOL. 76J 



bv a zone of depression, the waist of the pear. This, 

 again, is surrounded on all sides but one (towards Japan) 

 by a zone of elevation, the protuberant part of the pear ; 

 and finally we find the nose of the pear in the central 

 Atlantic between the Madeiras and the Bermudas. 1 do 

 not, however, wish to emphasise the resemblance of the 

 surface to a pear or any other fruit, but prefer to describe 

 it as an harmonic spheroid of the third degree. Another 



