NEWTON AND THE LAW OF GRAVITATION 



any satellite, in proportion to the quantity of its 

 matter, did gravitate towards the sun with a force 

 greater than Jupiter in proportion to his, according to 

 any given proportion, suppose d to e ; then the distance 

 between the centres of the sun and of the satellite's 

 orbit would be always greater than the distance be- 

 tween the centres of the sun and of Jupiter nearly in 

 the subduplicate of that proportion : as by some com- 

 putations I have found. And if the satellite did grav- 

 itate towards the sun with a force, lesser in the propor- 

 tion of e to d, the distance of the centre of the satellite's 

 orb from the sun would be less than the distance of 

 the centre of Jupiter from the sun in the subduplicate 

 of the same proportion. Therefore, if at equal dis- 

 tances from the sun, the accelerative gravity of any 

 satellite towards the sun were greater or less than the 

 accelerative gravity of Jupiter towards the sun by one- 

 one-thousandth part of the whole gravity, the distance 

 of the centre of the satellite's orbit from the sun would 

 be greater or less than the distance of Jupiter from 

 the sun by one one-two-thousandth part of the whole 

 distance that is, by a fifth part of the distance 

 of the utmost satellite from the centre of Jupiter ; an 

 eccentricity of the orbit which would be very sensi- 

 ble. But the orbits of the satellites are concentric to 

 Jupiter, and therefore the accelerative gravities of 

 Jupiter and of all its satellites towards the sun, at equal 

 distances from the sun, are as their several quantities 

 of matter; and the weights of the moon and of the 

 earth towards the sun are either none, or accurately 

 proportional to the masses of matter which they con- 

 tain. 



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