NEWTON AND THE LAW OF GRAVITATION 



must now take up the steps of his progress somewhat in 

 detail, and state his theories and their demonstration 

 in his own words. Proposition IV., theorem 4, of his 

 Principia is as follows: 



" That the moon gravitates towards the earth, and by 

 the force of gravity is continually drawn off from a 

 rectilinear motion and retained in its orbit. 



" The mean distance of the moon from the earth, in 

 the syzygies in semi-diameters of the earth, is, accord- 

 ing to Ptolemy and most astronomers, 59; according 

 to Vendelin and Huygens, 60 ; to Copernicus, 6oJ ; to 

 Street, 6of ; and to Tycho, 564. But Tycho, and all 

 that follow his tables of refractions, making the re- 

 fractions of the sun and moon (altogether against the 

 nature of light) to exceed the refractions of the fixed 

 stars, and that by four or five minutes near the horizon, 

 did thereby increase the moon's horizontal parallax by 

 a like number of minutes, that is, by a twelfth or 

 fifteenth part of the whole parallax. Correct this 

 error and the distance will become about 6oJ semi- 

 diameters of the earth, near to what others have 

 assigned. Let us assume the mean distance of 60 

 diameters in the syzygies; and suppose one revolution 

 of the moon, in respect to the fixed stars, to be com- 

 pleted in 2yd. yh. 43', as astronomers have determined; 

 and the circumference of the earth to amount to 

 123,249,600 Paris feet, as the French have found by 

 mensuration. And now, if we imagine the moon, de- 

 prived of all motion, to be let go, so as to descend 

 towards the earth with the impulse of all that force 

 by which (by Cor. Prop, iii.) it is retained in its orb, 

 it will in the space of one minute of time describe in 



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