OF CENTRAL FORC F>. 4^ ' 



But upon this supposition the earth and moon would LFCT. 

 soon come together : and to be sure they would, if they ^x-x'-x 

 had not a motion round their common center of gravity, 

 to create a degree of centrifugal force sufficient to ba- 

 lance their mutual attraction. This motion they have : 

 for as the moon goes round her orbit every month, at 

 the distance of 249,000 miles from the earth's center, and 

 of 234,000 miles from the center of gravity of the earth 

 and moon, so does the earth go round the same center 

 of gravity every month at the distance of COOO miles 

 from it ; that is, from it to the center of the earth. 

 Now as the earth is (in round numbers) 8000 miles in 

 diameter, it is plain that its side next the moon is only 

 $000 miles from the common center of gravity of the 

 earth ana moon ; its center 6000 miles distance there- 

 from ; and its farther side from the moon 10,000. 

 Therefore the centrifugal forces of these parts are as 

 2000, 6000, and 10,000 ; that is, the centrifugal force of 

 any side of the earth, when it is turned from the moon, 

 is five times as great as when it is turned towards the 

 moon. And as the moon's attraction (expressed by the 

 number 6000) at the earth's center keeps the earth from 

 flying out of this monthly circle, it must be greater than 

 the centrifugal force of the waters on the side next her; 

 and consequently, her greater degree of attraction on 

 that side is sufficient to raise them ; but as her at- 

 traction on the opposite side is less than the centrifugal 

 force of the water there, the excess of this force is 

 sufficient to raise the water just as high on the opposite 

 side. To prove this experimentally, let the bar D C 

 (in page 47) with its furniture be fixed upon the whirl- 

 ing board of the machine (page 33) by pushing 

 the pin P into the center of the board ; which pin is in 

 the center of gravity of the whole bar with its three balls 

 *,/, g. and moon 3f. Now if the whirling-board and 

 bar be turned slowly round by the winch, until the ball 



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