226 A Short History of Astronomy [Cn. ix. 



force exerted on it by the earth. Since the earth produces 

 the same acceleration in all bodies at the same place, 

 it follows that the masses of bodies at the same place are 

 proportional to their weights^ thus if two bodies are com- 

 pared at the same place, and the weight of one (as shewn, 

 for example, by a pair of scales) is found to be ten times 

 that of the other, then its mass is also ten times as 

 great. But such experiments as those of Richer at Cayenne 

 (chapter VIIL, 161) shewed that the acceleration of falling 

 bodies was less' at the equator than in higher latitudes ; 

 so that if a body is carried from London or Paris to 

 Cayenne, its weight is altered but its mass remains the 

 same as before. Newton's, conception of the earth's 

 gravitation as extending as far as the moon gave further 

 importance to the distinction between mass and weight ; 

 for if a body were removed from the earth to the moon, 

 then its mass would be unchanged, but the acceleration 

 due. to the earth's attraction would be 60 x 60 times less, 

 and its weight diminished in the same proportion. 



Rules are also given for the effect produced on a 

 body's motion by the simultaneous action of two or more 

 forces.* 



-VA further principle of great importance, of which only 

 very indistinct traces are to be found before Newton's 

 time, was given by him as the Third Law of Motion in 

 the form : " To every action there is always an equal 

 and contrary reaction ; or, the mutual actions of any two 

 bodies are always equal and oppositely directed." Here 

 action and reaction are to be interpreted primarily in the 

 sense of force. If a stone rests on the hand, the force with 

 which the stone presses the hand downwards is equal to 

 that with which the hand presses the stone upwards ; if 

 the earth attracts a stone downwards with a certain force, 

 then the stone attracts the earth upwards with the same 

 force, and so on. It is to be carefully noted that if, as 

 in the last example, two bodies are acting on one another, 

 the accelerations produced are not the same, but since force 



* The familiar parallelogram offerees, of which earlier writers had 

 had indistinct ideas, was clearly stated and proved in the intro- 

 duction to the Princtpia, and was, by a curious coincidence, published 

 also in the same year by Varignon and Lamt. 



