AND ON THE DIURNAL INEQUALITY. 
3 
the attempts to draw the cotidal lines of the Atlantic and Pacific. But it appears 
unlikely that this supposition rightly represents the mode in which the waters of the 
Atlantic and Pacific obey the action of the sun and moon. 
7 . If it be asked what other mode of operation of the lunar and solar forces upon 
the ocean can be conceived, different from this progressive wave which is expressed 
by means of cotidal lines; an answer immediately suggests itself, that a stationary 
undulation, corresponding in its period with the period of the moon’s aj)parent revolu- 
tion, from meridian to meridian (that is, a lunar half-day), is a possible mode of mo- 
tion for a fluid under such circumstances. By a “stationary undulation,” I mean a 
motion such as that which takes place in a vessel of water, when one side is suddenly 
lifted from rest, and then set down again. When this is done, the water oscillates, 
the surface rising alternately on the raised side and on the other, and the middle 
line of the surface neither rises nor falls. In this case the oscillation is free, de- 
pending on the dimensions of the fluid only : but if the fluid were subject to peri- 
odical forces, such as an attracting body passing over it at equal intervals of time, it 
might perform forced oscillations of the same kind ; and in this case, the period of 
the oscillation would necessarily, in the ultimate condition of the fluid, be the same 
as the period of the forces. 
8. The lunar attraction passes over every wide ocean once in every lunar half-day; 
and it is conceivable that such an ocean, under the influence of the lunar forces, should 
perform, every lunar half-day, such a stationary oscillation as has been described. On 
this supposition, we should have a regular tide at its eastern and western shore, but no 
tide in the middle part ; and in such a case there would be no 
cotidal lines. The ocean would be divided into two portions 
or areas by a line of no tide (AB) ; and these two areas would 
each have the tide over the whole area at the same time, 
the two times differing by six lunar hours. For instance, if 
the time of high water on the eastern shore, ACB, were one 
o’clock, the time of high water on the western shore, ADB, 
would be seven o’clock. This might be expressed by distinguishing the two spaces 
by shading, and marking them I. and VII. respectively. (See fig. 1.) 
9. But this cannot be a representation of the state of 
the tides of oceans generally, at least as to their littoral 
spaces. For we know by observation that, along large 
tracts of the shores of all seas, the tide does travel 
progressively, in such a manner that its course in those 
parts may be represented by a series of cotidal lines. 
And if the shore be broken by shallow inlets and bays, 
the tide must, by the laws of fluids, travel progressively up these recesses. In such 
cases, we may properly represent the state of the tides by such a diagram as before, 
bordered with a series of cotidal lines representing the course of the tide into the 
B 2 
Fig. 2. 
Fig. 1. 
A 
