322 The Rev. W. Whewell on the mean Level of the Sea. 



nel are not in equilibrium at any moment. And this is quite 

 consistent with mechanical principles ; for the difference of 

 pressures in different parts of the channel is precisely the 

 force by which the tide-wave is transferred along the channel. 

 These oscillations of the pressure and of the surface, corre* 

 spond to each other; being respectively the changes of force 

 and the motion produced. But the deviations above and 

 below the mean pressure and the mean surface, balance each 

 other in the course of a few hours. If the mean surface 

 were not a level surface, the mean pressures would not be in 

 equilibrium, and there would be in one part of the fluid a 

 permanent resulting excess of mean pressure ; which excess 

 would tend to carry the fluid from the place where its mean 

 level was highest, and to restore the mean surface to a level, 

 just as if the fluid were at rest. 



This being understood, it will not be difficult to see what 

 will be the state of the levels of high, low and mean water 

 under any supposed circumstances of a port. 



If the water be deep enough, and the surface of low water 

 not much contracted, the motions of the high-water surface 

 and of the low-water surface will be nearly equal, and the 

 mean water will be at the constant height of the level surface : 

 this is the case at Liverpool, as I have shown from Captain 

 Denham's observations in my Twelfth Memoir on the Tides 

 (in the Phil. Trans. 1840). 



If the surface of low water be much contracted, the volume 

 of water subtracted from the mean state of the sea in or- 

 der to make low water, will (in the interior of the port) be 

 nearly equal to the volume added, in order to make high 

 water ; and as the horizontal surface is smaller, the depth will 

 be greater : this is the case at Plymouth ; where, as I have 

 shown in my Tenth Memoir, the motions of the low-water sur- 

 face are greater than those of the high-water surface. 



If the inlet be a river, in which, by various causes, the tide- 

 wave is gradually extinguished in its progress upwards, and 

 in which, without the tide, the water would flow towards the 

 sea, the high water will be most nearly a level surface, and 

 the mean water line will slope towards the sea. This is the 

 case in the river Thames, in which, as appears by the re- 

 searches of Messrs. Rennie, the surface of high water is 

 nearly a level surface, while the low water surface slopes 

 considerably. 



Finally, if in consequence of shallowness, or a bar, the water 

 cannot run out to the level of low water in the sea, the height 

 of apparent low water will be constant, and the apparent mean 

 water will be charged with half the changes of the high water 



Bearing in mind these results, it will be easy to reply 



