194 POPULAR LECTURES AND ADDRESSES. 



quarter, at treble distance the force is reduced to 

 one-ninth part. Suppose we compare forces at the 

 distance of one million miles, then again at the 

 distance of two and a half million miles, we have 

 to square the one number then square the other, 

 and find the proportion of the square of the one 

 number to the square of the other. The forces are 

 inversely as the squares of the distance, that is the 

 most commonly quoted part of the law of gravita- 

 tion ; but the law is incomplete without the first 

 part, which establishes the relation between two 

 apparently different properties of matter. Newton 

 founded this law upon a great variety of different 

 natural phenomena. The motion of the planets 

 round the sun, and the moon round the earth, 

 proved that for each planet the force varies 

 inversely as the square of its distance from the 

 sun ; and that from planet to planet the forces on 

 equal portions of their masses are inversely as the 

 squares of their distances. The last link in the 

 great chain of this theory is the tides. 



(2) Tide-Generating Force. And now we are 

 nearly ready to complete the theory of tide- 

 generating force. The first rough view of the case, 

 which is not always incorrect, is that the moon 

 attracts the waters of the earth towards herself and 

 heaps them up, therefore, on one side of the earth. 

 It is not so. It would be so if the earth and moon 

 were at rest and prevented from falling together 

 by a rigid bar or column. If the earth and 



