THE TIDES 295 



the mutual attraction of two pieces of lead in his balance. 

 Tidal theory is one strong link in the grand philosophic 

 chain of the Newtonian theory of gravitation. In explain- 

 ing the tide-generating force we are brought face to face 

 with some of the subtleties, and with some of the mere 

 elements, of physical astronomy. I will not enter into de- 

 tails, as it would be useless for those who already under- 

 stand the tidal theory, and unintelligible to those who do not. 

 I may just say that the moon attracts a piece of matter, 

 for example a pound-weight, here on the earth, with a force 

 which we compare with the earth's attraction thus. Her 

 mass is ?V of the earth's, and she is sixty times as far 

 away from the earth's centre as we are here. Newton's 

 theory of gravitation shows, that when you get outside 

 the mass of the earth the resultant attraction of the earth 

 on the pound weight, is the same as if the whole mass of the 

 earth were collected at the centre, and that it varies inversely 

 as the square of the distance from the centre. The same law 

 is inferred regarding the moon's attraction from the general 

 theory. The moon's attraction on this pound weight is 



therefore jjo_ or 28g I ooo of the attraction of the earth 



60x60 



on the same mass. But that is not the tide-generating 

 force. The moon attracts any mass at the nearest parts of 

 the earth's surface with greater force than an equal mass 

 near the centre; and attracts a mass belonging to the re- 

 moter parts with less force. Imagine a point where the 

 moon is overhead, and imagine another point on the sur- 

 face of the earth at the other end of a diameter passing 

 through the first point and the centre of the earth (illus- 

 trated by B and A of FIG. 124, p. 298). The moon attracts 

 the nearest point (B) with a force which is greater than that 

 with which it attracts the farthest point (A) in the ratio of 

 the square of 59 to the square of 61. Hence the moon's at- 

 traction on equal masses at the nearest and farthest points 

 differs by one fifteenth part of her attraction on an equal 

 mass at the earth's centre, or about a 4,320,000^, or roughly, 

 % four-millionth, of the earth's attraction on an equal mass at 

 its surface. Consequently the water tends to protrude 

 towards the moon and from the moon. If the moon and earth 



