Rigidity of the Earth. 501 



series of observations indicates an ellipticity of the equi- 



potential surface relative to the earth of magnitude 0*57 ~-, 



and the latter series indicates an ellipticity of 0'493 ^- . The 



former of these agrees almost exactly with the ellipticity in 

 (82) calculated for the rigidity 4 x 10 s grams per square 

 centimetre, rather less half the rigidity of steel. The latter 

 ellipticity corresponds to a still smaller rigidity. 



Tidal Observations. — The evidence from observations on 

 ocean-tides is in very good agreement with Dr. Hecker's 

 observations. Due to the moon's action there are two small 

 tides with periods of a month and half a month respectively. 

 It is considered probable that these long-period tides occur 

 at the same places as the corresponding tides on the solid 

 earth under the oceans. That is, these ocean-tides do not lag 

 behind the solid tides to any appreciable extent. Suppose t 

 is the calculated height of one of these ocean-tides on a 

 perfectly rigid earth, the mutual attraction of the disturbed 

 water being neglected. Now from a discussion of a large 

 number of tidal observations W. Schweydar * finds that the 

 actual height of the tide is 0*62 t. But assuming the density 

 and rigidity which gave the result in (82), and allowing for 

 the mutual attraction of the disturbed water as well as for 

 the depression of the solid by the water-tide I have calculated 

 that the height of the ocean-tide would be 0'682 t. Now {82) 

 shows that when the mutual attraction of the disturbed water 

 and the depression of the solid is neglected, the height of 

 the tide is 0'569 t. In arriving at the result 0'682 t, how- 

 ever, I have supposed that the ocean covers the whole earth, 

 whereas it only covers about two-thirds of it. If we only 

 allow, in the actual case, half the increase due to the mutual 

 attraction of the water and the depression of the solid we get, 

 as the height of the water-tide, 0*625 i, which agrees almost 

 exactly with the observed tide. Thus tidal observations also 

 indicate that the rigidity of the earth is about half that of 

 wrought iron. 



Evidence from Variation of Latitudes. 



If the earth is not spinning about its axis of greatest 

 moment of inertia then, by theorems proved in rigid 

 dynamics, its axis of rotation describes a cone in the earth 

 itself with the axis of greatest moment of inertia as the axis 



* Beitrage zur Geophysik, Bd. ix. 1907. 

 Phil. Mag. S. 6. Vol. 22. No. 130. Oct. 1911. 2 L 



