14 THE TIDES. 



from this height is proportional to ps, and therefore to 



08 2w. 



The effect of pressure with such a tide will be extremely 

 small. As it operates to send the water away from its 

 position of greatest elevation, it will so far assist the moon's 

 force without changing the place of high water. 



To estimate the effect of friction, the moon's force being 

 = - R sin 2o>, the velocity v, undisturbed by friction 

 = Fcos 2o> (V being the greatest velocity). If the dis- 

 placement caused by friction is very small, we may take 

 this value of v as a sufficient approximation. The friction, 

 assumed proportional to velocity = Vf cos 2o>, and the 

 velocity begins to be checked when Vf cos 2w = - ZTsin 2&> 



or, tan 2, . - . _ /= _ 700 0/nearl y . 



_tl O^ 



When the displacement (which we shall call 8) is sensible, 

 we shall have as follows : since the velocity is periodic and 

 is a maximum, positive or negative, when w = 8 ; and is = 0, 

 when w- 8 = 45, 135, we may assume fl=Fcos2(w-8). 

 Then friction = fV cos 2 (w - 8) and the net amount of 

 force = - H sin 2w -fV cos 2 (co - 8). Hence 

 H cos 2o> /Fsin 2 ( w - 8) 



~2T~ ~^7~ 



By hypothesis this reaches its maximum, so that it is high 

 or low water respectively, when w = 8, 8 -f P0, 8 + 180. 



m , - ,,, H cos 28 , . 



Iheretore V = ~ - ; and since at these points the 



AT 



net force = 0, we have sin 28 = - = -f G - , and tan 28 



JJ. Zr 



remains as before = - 7000/. The rise of the tide in a sea 

 three miles in depth, will be 2 '4 cos 28 inches. 



