on the Earth's Axis of Rotation. 445 



the ellipsoid; A+at, A+bt, C+ct the principal moments of 

 inertia at the time t. Then it is shown that the secular effect 

 on tbe obliquity of the ecliptic, as resulting from the motion of 

 the principal axes in the body (which constitutes the first part 

 of the solution), is given by the equation 



and as resulting from the change in the impressed forces, due 

 to the change of shape of the body (which constitutes the second 

 part), is given by 



dd n. a+ft-2c 

 dt ' 2n C-A ' 

 The former part may be neglected compared with the latter. 

 But from such geological changes as we are entitled to assume 

 in the case of the earth, the total change in the obliquity of the 

 ecliptic must be exceedingly small. Even gigantic polar ice- 

 caps during the Glacial period could not have altered the posi- 

 tion of the arctic circle by so much as three inches ; and this is 

 the most favorable redistribution of matter on the earth's sur- 

 face for producing that effect. Thus the obliquity of the 

 ecliptic has remained sensibly constant throughout geological 



It ia also shown that, during any gradual deformation of the 

 . the instantaneous axis of rotation will always remain 

 sensibly coincident with the principal axis of figure. 



In the course of the work by which the previous results are 

 attained there is shown to be a small inequality in the motion 

 of the instantaneous axis, in consequence of which that axis 

 describes a circle with uniform velocitv, and is coincident with 

 the axis of figure every 306th day (in the earth). This circle 

 touches the - of figure is traveling 



in consequence of the deformation of the earth's shape. The 

 diameter of the circle is shown in a particular case (not unfavor- 

 able to produce a large effect) to be less than t \/'. But 

 although t > to be so small, it is of interest 



some length. It is shown that, if the earth 

 be not quite rigid, this inequality might have the effect of 

 modifying the path of the axis of figure in the body, m con- 

 sequence of readjustments to a figure of equilibrium. 



Various hypotheses as to the power of adjustment are con- 

 sidered, and the paths of the instantaneous and principal axes 

 in the precession of a viscous spheroid undergoing deformation 

 are found. , ., , ... 



It is maintained that although the earth may be sensibly rigid 

 to the tidally deforming forces exercised by the sun and moon, 



