284 NEWTON S PRINCIPIA. 



If the depth be very great we have 



/ 9 *&amp;gt; 

 v = V |~ very nearly, 



and when the wave is very long, 



v = V g h very nearly. 



The former of these results is not the same as Newton s, 

 but the general conclusion will be unaltered. The exact 

 result may, however, be obtained by Newton s reasoning, 

 if we slightly change the value assumed for I and take 



The second result admits of an easy demonstration, 

 which we shall speak of in another place. 

 [See NOTE YIIL] 



