56 



having the same side CBD always turned towards S, it 

 is obvious that it turns once round an axis CD in going 

 once round its orbit, and that CD is perpendicular to the 

 plane of its orbit. But if the sphere also rotates on an- 

 axis AB inclined to the plane of the orbit, whilst any 

 force, however small, tends to make it rotate about the 

 axis CD, then AB will gradually approximate to CD, and 

 finally coincide with it. 



III. PKOGKESSIVE CHANGE IN THE FORM OF THE EARTH. 



If a spheroid of equilibrium, NQSE (Fig. 10), contract 

 uniformly in lines perpendicular to its surface, a new 

 spheroid, N'Q'S'E', is produced of a greater degree of 

 excentricity. For if CQ be the semi-transverse, and CN 

 the semi-conjugate axis of the elliptical section NQSE of 

 the spheroid, and if from these there be taken the equals 

 NN' and QQ', the remainder CQ' has to the remainder 

 CN' a greater ratio than CQ to CN, therefore the 

 excentricity of the spheroid is increased. 



But if the spheroid, rotating on an axis, contract in 

 size, its velocity of rotation will be increased : this in- 

 crease of velocity would tend to increase its excentricity. 

 Now, it is barely possible that the increased excentricity 

 due to the contraction, should be precisely the same as 

 the increase of excentricity due to the increased speed of 

 rotation ; in that case the spheroid would still be one of 

 equilibrium, notwithstanding the alteration of its form. 



But if the increase of excentricity arising from contrac- 

 tion, is greater than that arising from the increased 

 speed, the effect will be an accumulation of matter in the 

 equatorial region, an increase of pressure on the internal 

 mass, and a tendency to subsidence into the northern and 

 southern hemispheres. A change of form is then neces- 

 sary to restore equilibrium. This may not take place 

 uniioxnAj per gradum / for if there be a resistance from a 



