in the Air and in the Sea. 



105 



sider, not the absolute motion of each particle, but only the re- 

 lative motion of the particles with respeet to the earth's centre. 

 Hence we have not to do with the whole of the attraction which 

 any heavenly body exerts on the earth ; the difference between 

 the forces with which the earth's centre and the point of its sur- 

 face to be considered are attracted gives the limits for our consi- 

 deration. Thus, e.g., the point which has the sun or the moon in 

 the zenith is nearer to this heavenly body than the centre of the 

 earth ; and the difference of the attraction upon these two points 



■ u , , . 319500 319500 -. \, , , 



might be expressed by ^3399)2 - (23400) 2 SUn ' y 



li 



for the moon. The second quantity is equal 



80(59) 2 80(60) 2 

 to about 2 \ times the first ; and from this we infer that although 

 the attraction of the sun is 168 times that of the moon, yet the 

 difference between the attraction of a point at the surface and 

 the centre of the earth by the moon is greater than the same by 

 the sun ; and therefore the effect produced by her attraction 

 upon the currents of air and sea must also be greater. 



For all other heavenly bodies this difference is so slight that 

 we need not take it into consideration. 



Supposing that the circle AC ED (fig. 2) represents the 



Fig. 2. 



earth, L the place of the centre of the moon or sun, and that k 

 denotes the difference between the attraction of a point at the 

 surface and the centre of the earth. The point A is attracted 

 more strongly than the centre by the quantity k v Now, as this 

 attraction in the half of the earth turned towards the sun or 

 moon acts in the opposite direction to the earth's attraction, 

 g — k x will express the weight of any particle in the point A, the 

 earth's gravitation being denoted by^. At the point B the dif- 

 ference between the attraction of it and the centre will be some- 

 what less. Let us call this difference & 2 ; then the weight at 

 the point B may be expressed by g — k 2 . cosLB6; for here the 



