AND THEORY OF THE HEAVENS. 49 



is the law demonstrated under the regulation of which 

 this force extends from the centre of the system to the 

 remote regions. It always decreases inversely, as the 

 squares of the distances from the centre increase. This 

 rule flows in the same infallible way from the time which 

 the planets take at their various distances for their 

 revolutions. These times, their periods of revolution, 

 are always as the square root of the cubes of their mean 

 distances from the sun ; and from this it has been 

 deduced that the force which impels these heavenly 

 bodies to the centre around which they revolve, must 

 diminish in the inverse ratio of the square of their 

 distance. 



This same law that rules the planets, in so far as they 

 revolve around the sun, is also found in the smaller 

 systems, namely, those constituted by the moons moving 

 around their own planets. The times of their revolution 

 are in like manner proportional to their distances, and 

 establish the same relation of the falling force towards 

 the planet as that to which the planet is subjected in its 

 relation to the sun. All this is established beyond ques- 

 tion by the most certain mathematics, and by means of 

 indisputable observations. Thus arises the idea that this 

 falling force is the very same impulse which is called 

 gravity on the surface of the planet, and which, starting 

 from the planet, gradually diminishes with the distances, 

 according to the law indicated. This is seen from a 

 comparison of the quantum of gravity upon the surface 

 of the earth with the force that drives the moon towards 

 the centre of its orbit, which shows the same relation as 

 attraction does in the whole universe; that is to say, the 

 gravity or weight is in the inverse ratio of the square 



