$ 1 73 ] Extension of Gravity to the Moon 219 



distance of the m;)on (which is 60 times the radius of the 



earth, or 20,000,000 feet); that is, it is 3>3 - ^- 



60 x 2^,000,000' 



which reduces to about TTTr . Consequently, if the law of 

 the inverse square holds, the acceleration of a falling body 

 at the surface of the earth, which is 60 times nearer to the 



centre than the moon is, should be -. or between 



no 



32 and 33 ; but the actual acceleration of falling bodies 

 is rather more than 32. The argument is therefore 

 satisfactory, and Newton's hypothesis is so far verified. 



The analogy thus indicated between the motion of the 

 moon round the earth and the motion of a falling stone 

 may be illustrated by a comparison, due to Newton, of the 

 moon to a bullet shot horizontally out of a gun from a 

 high place on the earth. Let the bullet start from B in 

 fig. 71, then moving at first horizontally it will describe a 

 curved path and reach the ground at a point such as c, 

 at some distance from the point A, vertically underneath 

 its starting-point. If it were shot out with a greater velocity, 

 its path at first would be flatter and it would reach the 

 ground at a point c' beyond c ; if the velocity were greater 

 still, it would reach the ground at c" or at c'" ; and it 

 requires only a slight effort of the imagination to conceive 

 that, with a still greater velocity to begin with, it would miss 

 the earth altogether and describe a circuit round it, such 

 as BDE. This is exactly what the moon does, the only 

 difference being that the moon is at a much greater distance 

 than we have supposed the bullet to be, and that her 

 motion has not been produced by anything analogous to 

 the gun ; but the motion being once there it is immaterial 

 how it was produced or whether it was ever produced in 

 the past. We may in fact say of the moon " that she is a 

 falling body, only she is going so fast and is so far off that 

 she falls quite round to the other side of the earth, instead 

 of hitting it ; and so goes on for ever." * 



In the memorandum already quoted ( 169) Newton 

 speaks of the hypothesis as fitting the facts " pretty 

 nearly"; but in a letter of earlier date (June 2oth, 1686) 



* W. K. Clifford, Aims and Instruments of Scientific Thought. 



