TIDES AND THE RIGIDITY OF THE EARTH 5 



ceding turn. This movement of the Moon causes an inequality 

 in the tide-raising force with a period of a fortnight and this in- 

 equality in the force affects the observable height of the tide with 

 an inequality of the same period. It is as if, in addition to the 

 tide that comes in twice a day, there were a tiny tide that comes 

 in twice a month. The method of harmonic analysis of tidal 

 observations can draw out from a long series of observations 

 the amount of this tiny tide, just as a suitably tuned resonator 

 can pick out one of the component tones of a musical instrument 

 or of an orchestra. Now the amount which the fortnightly 

 oceanic tide would have if the Earth were absolutely rigid 

 can be calculated. The result that it may be calculated by 

 the so-called "equilibrium theory" was first asserted on 

 insufficient grounds, then denied on the basis of a more 

 rigorous investigation and finally proved by taking account 

 of a circumstance neglected in that investigation. The adven- 

 tures of this result form a curious chapter in the history of 

 science but must be omitted here. It is now well established. 

 The comparison of the observed and calculated values is one of 

 the methods available for determining the height of earth-tides. 

 Clearly, if the observed value be nearly equal to the calculated, 

 the Earth yields but little ; if the observed value be much less 

 than the calculated, the Earth yields a good deal. In the 

 former case it is very stiff or of great rigidity, in the latter the 

 rigidity is small. If the Earth were fluid inside there should 

 be very little fortnightly tide. As a matter of fact, the observed 

 value is nearly two-thirds of the calculated. This result forms 

 an essential part of the famous argument invoked by Lord 

 Kelvin to prove that the Earth cannot consist of a molten fiery 

 core covered over with a thin solid crust. 



This argument is greatly strengthened when it is found 

 to be confirmed by others derived from a study of other 

 phenomena than the fortnightly tide. The attraction of the 

 Moon tends to draw a pendulum to one side. The force 

 available for this purpose is not the full amount of the Moon's 

 attraction but the difference between the amounts of this 

 attraction at the centre of the Earth and at the place where 

 the pendulum is hung ; and of this difference the horizontal 

 component only can affect the direction in which the pendulum 

 hangs or the apparent vertical. The maximum amount of the 

 available force being only about one eleven-millionth of gravity, 



