46 NORMAL FORCE LEAST EFFECTIVE. 



same direction (towards M E) at either side of the sphere, 

 its constant tendency will be to heap up the waters to- 

 wards the point vertically under the moon, and towards 

 the antipodes of that point. 



In like manner the normal force may be seen to be 

 nothing at the points 0,0,0,0 (fig. 6), 55 on either side 

 of the line ME, and gradually to increase as a force 

 acting outwards at all lesser angles included in that 

 space, thus tending to raise the waters vertically under 

 the attracting body ; whilst beyond the angle of 55 it 

 ceases to be an outward, and becomes an inward force, 

 thus depressing the waters within that space. So that 

 its whole force, whether in drawing out or pressing in, 

 unites with the tangential element in lifting the waters 

 at the opposite points of the sphere, vertically under 

 the moon. 



On a hasty inspection of the figures above given, it 

 may seem that the rise of the waters is greatly due to 

 the normal element of the force, because the lines in- 

 dicating its amount are drawn proportionally longer 

 than those representing the tangential, and are more 

 in the direction of the attracting body. But the re- 

 verse is really the case. For the normal element, 

 pulling vertically, or in direct opposition to gravity, 

 is almost wholly neutralized by the enormous dispro- 

 portion between its strength and that of its opponent, 

 as will be evident if we compare their amounts. It 

 is found by calculation that the maximum normal 

 force is only -000,000,1056 x gravity, that is, about 

 100 oVo? crth. f the weight of water. If therefore the 

 sea be supposed to be 10 nautical miles, or 10,000 



