Production of Tides, Mechanically Considered. 177 



produced by the moon in the respective portions of the 

 earth considered — a., b, and c. 



The total mass of the moon is about one-eigfhtieth of that 

 of the earth, and her mean distance about 240,000 miles 

 (Newcomb). The moon is thus distant about GO semi- 

 diameters of the earth. Whatever may be the earth's 

 attractive force on a small mass at its surface, the moon's 

 attractive force is g^oth of ^^th of ^th of this force — the 

 earth's attractive force. The tide-'producinrj force of the 

 moon (in part) is, hov^ever, only as the difference between 

 ^th of ^th of -g^y th and g^oth of g^st of -^jst of the earth's 

 attractive force on a small mass at its surface. The 

 calculation is too tedious to go through, and it is only 

 required to have some idea of the magnitude. It will 

 suffice here, therefore, to say that the tide-producing power 

 of the moon is very much less than a millionth of the power 

 of the earth to draw a small mass at its surface towards its 

 centre. 



The tide-inoducing force of the moon being so small 

 compared to the power of the earth to draw a mass at its 

 surface towards its centre, how can it possibly pull up from 

 the surface of the earth a portion of its liquid sm^face ? It 

 is impossible for a very small force to lift up a small mass 

 when there is a vast force pulling it down. The moon, 

 however, certainly produces the tides. The only question 

 is, how? 



Now, water is slightly com.pressible, and the pressure of 

 the upper portion of the oceans is very great on the lower 

 portions. If this pressure were weakened, as by the action 

 of the moon, the elasticity of the water would cause the 

 ocean to swell up where the pressure was relieved. If my 

 memory serves me rightly, Mr. Murray, of the '* Challenger 

 Exploring Expedition," in a lecture at Edinburgh, estimated 

 that if the force of gravity of the earth were to be suspended, 

 the waters of the ocean would swell up, raising the water- 

 level over the earth by 500 feet. Now the tide-iDroducing 

 power of the moon reduces the force of gravity of the earth, 

 and thus relieves the pressure of the water of the ocean 

 under the moon. The ocean, owing to the elasticity of the 

 water, swells up, and a tide is produced. 



Is the elasticity of the water sufficiently great to produce 

 the actual tide of, say four feet in the open ocean ? 



The relief of pressure here producible by the moon is less 

 than one-millionth of the pressure produced by the force 



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