Rigidity of the Earth. 503 



the observations of latitudes. A comparison o£ this with the 

 results in (57), (62), and (66) leads to the conclusion that the 

 earth is much more rigid than steel. 



But the amplitude of the variation in latitude whose period is 

 430 days is only 0"'15 according to Chandler, a quantity 

 which is within the limits o£ observation in determinations of 

 latitudes. When it is remembered that two elaborate series 

 of observations to determine the constant of aberration, 

 namely those of Professor Doolittle of Philadelphia and 

 Professor Pees of Columbia College, New York, give results 

 differing by 0"*09, it is clear that a large number of careful 

 observations have to be reduced to discover a small variation 

 of amplitude 0"'15, or even to prove that it exists. Another 

 drawback is that Chandler's reduction gives an annual varia- 

 tion with nearly as large an amplitude. Considering these 

 things it is highly desirable that the existence of the 430-day 

 variation of latitude should be confirmed by other evidence. 



That such a variation of latitude should exist is very 

 probable. It could arise from changes of form of the earth. 

 These changes shift the earth's axis of greatest moment of 

 inertia, so that, even if this axis once coincided with the axis 

 of rotation the formation of a mountain system would cause 

 a relative displacement. For example, the upheaval of the 

 Himalayas and the Thibetan tableland from the general 

 body of the earth might displace its axis of figure 

 by over 200". If the upheaval took place slowly then the 

 axis of rotation would be constantly pursuing the axis of 

 figure in consequence of the viscosity of the earth and tidal 

 friction, so that the angle between them would always be 

 small *. 



But the variation of the axis of rotation itself causes the 

 centrifugal forces (which are equivalent to a negative tidal 

 force) to change their direction relative to the earth's body. 

 If the axis of rotation is describing a cone in the earth's body 

 then the alteration in the centrifugal forces causes a tide in 

 latitude 45°. If we think of a spheroid as the surface of 

 equilibrium under the earth's rotation, this spheroid always 

 has the axis of rotation as its axis. If then the axis of rota- 

 tion describes a cone of semi-vertical angle 6 about the earth's 

 axis of figure in 430 days, then the ellipse of section of this 

 spheroid by any meridian plane of the earth oscillates back- 

 ward and forward in its own plane through 26 in 430 days. 

 This obviously causes a tide whose crest is in latitude 45°. 

 To show this analytically let the earth's axis of figure be 



* See the paper " On the Influence of Geological Changes on the 

 Earth's Axis of Rotation," Sir G. II. Darwin's Scientific Papers, vol. iii. 



2 L 2 



