90 GREAT MEN OF SCIENCE 



focus. The law of gravitation is thus shown to hold for 

 any two masses of the planetary system; they attract one 

 another with forces proportional to the two masses, and in- 

 versely proportional to the square of the distance between 

 them. 



Newton already regards as a conclusion of this the 

 existence of disturbances, exerted by the planets upon one 

 another through their mutual forces, and thus going beyond 

 the laws of Kepler. He considers in particular the influence 

 of the gravitational force between the sun and the earth's 

 moon upon the path of the latter, and is able to give a full 

 explanation of the irregularities in the motion of the moon. 

 If the law of gravitation is true for any two masses whatever, 

 it must also be true for any two parts of the earth; and there- 

 fore for a body on the earth's surface, and the whole mass of 

 the earth. The resulting force upon the body, which is 

 known as its weight, must be the resultant of all the single 

 forces acting between the given body and all single parts of 

 the earth, in accordance with their masses and the square of 

 their distance. This brings Newton to calculate the result- 

 ing forces for spherical masses such as the earth, and partly 

 also for non-spherical. He finds that the resulting force for 

 any point outside the sphere has exactly the magnitude and 

 direction that it would have if the whole mass of the sphere 

 were concentrated at its centre. The attractive force inside 

 the sphere is given by another law; here the force decreases 

 as we approach the centre of the sphere, in simple proportion 

 to the distance from the centre; from this we know the force 

 of gravity in the interior of the earth. Newton thus arrives 

 at a correct comparison between gravity on the earth's surface 

 and that acting upon the moon, the latter being calculated 

 from the centrifugal force of the moon, and hence from the 

 distance and period of rotation of the latter. It is found, 

 that making use of the size of the earth's radius, first deter- 

 mined in Newton's time with sufficient accuracy, that in 



