502 Mr. J. Prescott on the 



of the cone. If the earth were perfectly rigid the axis of 



A 



rotation would describe its cone in the earth in -^ — ^ days, 



where A is the earth's moment of inertia about its symmetrical 

 axis and C its moment of inertia about an equatorial diameter. 

 But if the earth behaved like a liquid its form would adjust 

 itself so that the axis of rotation would be the axis of figure, 

 and there would consequently be no wandering of the axis of 

 rotation. Owing to the imperfect rigidity of the earth its 

 form would partly adjust itself to the rotation so that the 

 axis of figure at any instant is displaced from what we may 

 call the permanent axis of figure towards the axis of rotation. 

 If the instantaneous axis of figure is displaced a fraction /of 

 the whole distance between the permanent axis of figure and 

 the axis of rotation, then the latter axis will describe its cone 



1 A A 



in the earth in - — >, -r — ~ days. Now the quantity -r — p 



is involved in the theory of the precession of the earth's axis, 

 and observations tell us that its value is about 305. The 

 shifting of the axis of spin would be manifested by an 

 apparent variation of all latitudes. It is believed that 

 observations do indicate a variation whose period is 430 days. 

 A comparison of this with the calculaled period gives 

 /= 0-291. 



The alteration of form of the earth is due to centrifugal 

 force, and since this is similar to a negative tidal force, at 

 least on an incompressible earth, it follows that calculations 

 made for tidal forces can be applied to centrifugal forces also. 

 Now the distribution of land and water over the globe 

 shows that the earth's figure is very nearly an equilibrium 

 figure, and consequently we may assume that the extent to 

 which the earth actually yields to the components of centri- 

 fugal force perpendicular to the permanent axis is the same 

 as if the earth were liquid. The yielding of the earth a 

 fraction /of what a liquid earth would yield indicates that it 

 would yield to a tidal force to the same extent as to this 

 periodic centrifugal force. Now owing to rotation the 



ellipticity of the earth's surface is known to be about ^— , 



and when centrifugal force is represented as a tidal force the 



quantity — in our calculations is about ^kt:. Thus the 

 g 290 



earth, when behaving as a liquid^ has an ellipticity 



290 ha 



^. — , and under the action of a tidal force of long period 



it has an ellipticity 0'291 X ^ — or 0*281 — , according to 

 1 J 300 g g ; n 



