TIDES AND THE RIGIDITY OF THE EARTH 7 



change in the attraction of the Earth or a genuine alteration 

 of gravity, due to the attractions of the tidal protuberances 

 and the loss of attraction that accompanies the tidal flattening. 

 This additional force, the genuine alteration of gravity, may 

 be described as the u change of attraction." It is easy to see 

 that it acts so as to reinforce the Moon's force. The observed 

 result is interpreted in the statement that the force due to 

 tilting exceeds the change of attraction by an amount equal 

 to about one-third of the Moon's force. Now if we knew the 

 force due to tilting, we should know how much the surface 

 is tilted and thence how much the Earth yields to the tide- 

 raising forces. If we knew the change of attraction, we 

 could then use the result obtained by observing the deflexion 

 of the horizontal pendulum to infer the force due to tilting 

 and thence, as before, find the amount by which the Earth 

 yields. But the pendulum result will not tell us how much 

 the Earth yields, because all it can possibly give is the 

 difference between two forces ; what we want to know is the 

 magnitude of one of them. Observations of the fortnightly 

 tide cannot give us any additional information. They can 

 only tell us what the horizontal pendulum tells us. 



The ambiguity of the interpretation to be put upon the 

 results obtained from observations of the fortnightly tide and 

 of the behaviour of horizontal pendulums should make us 

 cautious about accepting statements as to the rigidity of the 

 Earth, when such statements are founded upon observations 

 of these kinds only. It is true that Lord Kelvin proved long 

 ago that, if the Earth were homogeneous and incompressible, 

 it would have to be as rigid as steel to make the observable 

 height of the fortnightly tide as much as two-thirds of that 

 calculated by the equilibrium theory. The fact that the 

 observed height is of about this amount does not enable us 

 to infer that the actual Earth, which is neither homogeneous 

 nor incompressible, is as rigid as a ball of steel. To obtain 

 sufficient evidence for a judgment on this matter it is neces- 

 sary to have recourse to a different kind of observations and 

 the observations that have proved effective have to do with a 

 phenomenon that has no obvious relation to tides or the lunar 

 deflexion of gravity — the phenomenon of variation of latitude. 

 It has been known for a long time that the latitudes of places 

 on the Earth's surface are not quite fixed or, what comes to 



