1908] on the Figure and Constitution of the Earth. 103 



Australia and the Antarctic continent. The defects of the computed 

 map admit of an interpretation connecting them with geological 

 events. The conclusion appears to be warranted that the main 

 features of the shape of the earth can be regarded as due to the 

 causes which would give rise to inequalities expressed by spherical 

 harmonics of the first, second, and third degrees. [Statement illus- 

 trated by four maps shown as slides.] 



I proceed to explain how the three inequalities are accounted for, 

 and I take first the harmonic of the second degree, characterised by 

 ellipsoidal figure and antipodal continents. [A table showing the 

 characters of the harmonics was thrown on the screen]. The ellip- 

 soidal figure means that there is ellipticity of the equator as well as 

 ellipticity of the meridians. The ellipticity of the meridians is due 

 to the rotation ; and the fact that both the Arctic and the Antarctic 

 regions are parts of the continental region, shows that the ellipticity 

 is rather greater for the mobile waters of the ocean than it is for the 

 very rigid earth, as we should expect. The ellipticity of the equator 

 is more difficult to account for. It has been suggested that it may be 

 a survival from the state of the earth at the time when the moon had 

 but recently broken away. If the inequality of the first degree, 

 characterised by the eccentric position of the centre of gravity, could 

 be accounted for, it would be easy to account for the inequality of the 

 third degree, answering to the pear-shaped figure, by the interaction 

 of the causes which give rise to harmonics of the first and second 

 degrees. A rotating body with its centre of gravity at a distance from 

 its centre of figure would have its surface deformed in an unsym- 

 metrical way. The denser parts would recede from the axis more 

 than the rarer parts, and the surface would get an inequality specified 

 by a spherical harmonic of the third degree, or it would become pear- 

 shaped. It remains to account for the eccentric position of the centre 

 of gravity. The only dynamical theory which has been put forward 

 to account for this is the theory of gravitational instability. Accord- 

 ing to this theory the earth was once, when it was less compact than 

 it is now, what may be called too heavy for its strength. If this were 

 the case it would sway to one side, just as a plank, set up on end, and 

 held fast at the bottom, may be too long to stand straight up, and 

 then it bends over to one side. It has been shown to be probable that 

 this condition of things would arise if a certain fraction, here denoted 

 by p/e, approaches a certain critical value. The heaviness of the 

 planet is specified appropriately by the pressure that would be exerted 

 at its centre by the superincumbent material if the density were the 

 same all through. This pressure is denoted by p. In the case of the 

 earth, jt? is about one and three quarter millions of atmospheres. The 

 appropriate measure of the strength is the elastic resistance called into 

 play when waves of compression travel through the substance. This 

 elastic resistance is denoted by e. [Definitions of p and e were thrown 

 on the screen.] If the substance were granite, in the same condition 



