A HISTORY OF SCIENCE 



its fall i5 T V Paris feet. For the versed sine of that arc 

 which the moon, in the space of one minute of time, 

 would by its mean motion describe at the distance of 

 sixty semi-diameters of the earth, is nearly i5 T V Paris 

 feet, or more accurately 15 feet, i inch, i line f . Where- 

 fore, since that force, in approaching the earth, increases 

 in the reciprocal-duplicate proportion of the distance, 

 and upon that account, at the surface of the earth, is 

 60 x 60 times greater than at the moon, a body in our 

 regions, falling with that force, ought in the space of 

 one minute of time to describe 60 x 60 x 15^ Paris 

 feet ; and in the space of one second of time, to describe 

 15-^ of those feet, or more accurately, 15 feet, i inch, 

 i line f. And with this very force we actually find 

 that bodies here upon earth do really descend; for 

 a pendulum oscillating seconds in the latitude of 

 Paris will be 3 Paris feet, and 8 lines J in length, as 

 Mr. Huygens has observed. And the space which a 

 heavy body describes by falling in one second of time 

 is to half the length of the pendulum in the duplicate 

 ratio of the circumference of a circle to its diameter 

 (as Mr. Huygens has also shown), and is therefore 15 

 Paris feet, i inch, i line ^. And therefore the force 

 by which the moon is retained in its orbit is that very 

 same force which we commonly call gravity ; for, were 

 gravity another force different from that, then bodies 

 descending to the earth with the joint impulse of both 

 forces would fall with a double velocity, and in the 

 space of one second of time would describe 30^ Paris 

 feet; altogether against experience." l 



All this is beautifully clear, and its validity has never 

 in recent generations been called in question; yet it 



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