i8i] Mass: Action and Reaction 227 



is measured by the product of mass and acceleration, the 

 body with the larger mass receives the lesser acceleration. 

 In the case of a stone and the earth, the mass of the 

 latter being enormously greater,* its acceleration is enor- 

 mously less than that of the stone, and is therefore (in 

 accordance with our experience) quite insensible. 



181. When Newton began to write the Principia he had 

 probably satisfied himself ( 173) that the attracting power 

 of the earth extended as far as the moon, and that the 

 acceleration thereby produced in any body whether the 

 moon, or whether a body close to the earth is inversely 

 proportional to the square of the distance from the centre 

 of the earth. With the ideas of force and mass this result 

 may be stated in the form : the earth attracts any body with 

 a force inversely proportional to the square of the distance 

 from the earths centre, and also proportional to the mass of 

 the body. 



In the same way Newton had established that the 

 motions of the planets could be explained by an attraction 

 towards the sun producing an acceleration inversely pro- 

 portional to the square of the distance from the sun's 

 centre, not only in the same planet in different parts of its 

 path, but also in different planets. Again, it follows from 

 this that the sun attracts any planet with a force inversely 

 proportional to the square of the distance of the planet 

 from the sun's centre, and also proportional to the mass 

 of the planet. 



But by the Third Law of Motion a body experiencing an 

 attraction towards the earth must in turn exert an equal 

 attraction on the earth ; similarly a body experiencing an 

 attraction towards the sun must exert an equal attraction 

 on the sun. If, for example, the mass of Venus is seven 

 times that of Mars, then the force with which the sun 

 attracts Venus is seven times as great as that with which 

 it would attract Mars if placed at the same distance ; and 

 therefore also the force with which Venus attracts the 

 sun is seven times as great as that with which Mars would 

 attract the sun if at an equal distance from it. Hence, in 

 all the cases of attraction hitherto considered and in 



* It is between 13 and 14 billion billion pounds. Sec chapter x. 

 219. 



