THE TIDES 117 



Supposing the moon's attractive force were not at work, 

 then at a given point on the surface of the ocean the attraction 



of the earth would be /2 . 



Assuming the moon to act, then this pull is lessened, and 

 to assume a position of equilibrium the water moves away 

 from the earth to a distance /i, so that it is now r'+h away 



from the earth's centre. Gravity at this point is , , , 2 - 

 Consequently, the diminution is 



r 2 (r + h) 2 r* 



Omitting infinitesimal calculations, this gives 



J_ M 



r' 2 '' r' 



that is, of the total attraction of the earth, but the tide- 



producinp- force is _ ; 



8945000 



2/2 I 



50 that ~P =- 8 94 5o5o' 



since r / 



and the height of the tide due to the moon is only 356 milli- 

 metres. A similar calculation for the sun shows that its 

 attractive force produces a tide of 164 millimetres, so that the 

 moon's attractive force is 2*171 times that of the sun, or, 

 roughly, as u is to 5. 



Lord Kelvin devised a method for the harmonic analysis 

 of the tides. In this method the tide-wave, considered with 

 reference to the time when it reaches a given point of the earth's 

 surface and to its height at that point, is made up of the super- 

 position of a series of waves of different amplitudes and 



