vii LAW AND PRINCIPLE 171 



called gravity ; does this force extend beyond the earth 

 to the moon, and if so, will it account for the motion of 

 our satellite around the earth ? 



A stone dropped from a height upon the earth's 

 surface falls 193 inches in a second ; how far would it 

 fall in the same time if it were dropped from the distance 

 of the moon ? Assuming that the centre of attraction 

 may be regarded as at the centre of the earth, the moon 

 is sixty times farther away from this point than is the 

 earth's surface. The force would, therefore, be not 

 60 times less but 60x60, or 3,600 times less, for it 

 diminishes according to the square of the distance. To 

 make an accurate calculation of the amount, however, 

 requires a correct knowledge of the distance from the 

 earth's centre to the surface, that is, of the earth's 

 radius. 



Taking the value accepted in 1666, Newton calculated 

 that the moon would fall toward the earth by 44 

 thousandths of an inch in a second ; in other words, 

 this is the amount by which the path of the moon 

 should deviate from a straight line in a second in order 

 to describe its curved path around the earth in a month. 

 The amount by which the moon actually swerves from 

 a rectilinear path in a second is 53 thousandths of 

 an inch, so Newton saw that the calculated result did 

 not agree with what was then considered to be fact. 

 The discrepancy between theory and observation " in- 

 duced him to abandon the subject, and pursue other 

 studies with which he had been previously occupied." 



Not until 1684 did he " resume his thoughts concerning 

 the moon." A few years before that time an accurate 

 determination of the size of the earth had been made by 

 Picard, and this gave a more correct value of the length 

 of the earth's radius than had previously been accepted. 



