THE TIDES 117 



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

 then at a given point on tlie surface of the océan the attraction 



of the earth would be - ,7,. 



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 h, so that it is now r'+/i away 



from the earth's centre. Gravity at this point is i—^rr^' 



Consequently, the diminution is — 



I 



n 



;-[-aj 



Omitting infinitésimal calculations, this gives — 



I 2h 



.'2 



r 



2/j 

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

 r 



producing force is „ ; 



^ ^ 8945000 



1 2h I 



so that — / = o - — » 



r 8945000 



since r' = 63703ooM, 



/i= 0-356 M, 



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

 mètres. A similar calculation for the sun shows that its 

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

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

 roughly, as 11 is to 5. 



Lord Kelvin devised a method for the harmonie analysis 

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

 référence 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 séries of waves of différent amplitudes and 



