SIR ISAAC NEWTON 69 



matter less than the thousandth part of the whole, had any such been. 

 But, without all doubt, the nature of gravity towards the planets 

 is the same as towards the earth. . . . Moreover, since the satellites 

 of Jupiter perform their- revolutions in times which observe the 

 sesquiplicate proportion of their distances from Jupiter's centre — 

 that is, equal at equal distances. And, therefore, these satellites, 

 if supposed to fall towards Jupiter from equal heights, would de- 

 scribe equal spaces in equal times, in like manner as heavy bodies do 

 on our earth. . . . If, at equal distances from the sun, 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 of d to e; then the distance between the cen- 

 tres of the sun and of the satellite's orbit would be always greater than 

 the distance between the centres of the sun and of Jupiter nearly in the 

 sub-duplicate of that proportion; as by some computations I have 

 found. And if the satellite did gravitate towards the sun with a 

 force, lesser in the proportion of e to d, the distance of the centre of 

 the satellite's orbit from the sun would be less than the distance of 

 the centre of Jupiter from the sun in the sub-duplicate of the same 

 proportion. Therefore if, at equal distances from the sun, the ac- 

 celerative gravity of any satellite towards the sun were greater or 

 less than the accelerative gravity of Jupiter towards the sun but one 

 i-iooo 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 1-2000 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 

 be very sensible. But the orbits of the satellite are concentric to 

 Jupiter, and therefore the accelerative gravities of Jupiter, and of all 

 its satellites towards the sun, are equal among themselves. . . . 



But further; the weights of all the parts of every planet towards 

 any other planet are one to another as the matter in the several parts ; 

 for if some parts did gravitate more, others less, than for the quantity 

 of their matter, then the whole planet, according to the sort of parts 

 with which it most abounds, would gravitate more or less than in 

 proportion to the quantity of matter in the whole. Nor is it of any 

 moment whether these parts are external or internal ; for if, for 

 example, we should imagine the terrestrial bodies with us to be 



