226 
THEORY OF TIDES. 
verse of C ; and this form D must be combined with the vir- 
tual variation of the horizon corresponding to the primitive tide, 
in such a manner as to produce a result agreeing in its position 
with the actual tide, and such as is represented by the curve 
AE for the direct, or AF for the inverted tide : and this willob- 
. viously happen if the primitive variation be represented by the 
space included between AE or AF and DC, the resistance GH 
being propdrlional to the. sine of the displacement HI or HK, 
and the height of the result LE or LF, on which the true 
height LM immediately depends, to its cosine : the true max- 
imum at M following that of the space AEL> and preceding 
that of FGH, as has already been shown by a different me- 
thod. 
It may be remarked, that since the resistance probably varies 
with the depth, the retrograde motion of the waters will be 
more impeded than the direct, and a very slow, although per- 
haps an imperceptible, current from east to west will thus be 
established, its velocity being always less than that which is 
sufficient to produce an equality of resistance in the different 
directions. 
Effect of re- Scholium 2. It has been observed, in corollary 6 , that the 
the velocity of ^ me water may perhaps be modified by the resistances 
a wave. opposed to the passage of the tides from the open ocean into 
the ports at which they have been observed. And indeed 
without a mature consideration of the subject, it would have been 
natural to speak with less hesitation of the effect of resistance 
in retarding the propagation of an undulation through a fluid. 
In reality, however, this retardation appears to be very inconsi- 
derable, if it exists at all, at least where the height of the wave 
is moderate in proportion to that of the fluid. We may sup- 
pose AM to be the figure of an undulation advancing simply in 
a channel of a given depth, with a resistance proportional to 
the velocity, which may again be represented by the virtual 
elevation of the wave C, which must always accompany the 
original undulation AM in its progress, and must, therefore, 
constantly tend to produce the same motions in the particles of 
the fluid as a real wave of the same magnitude 5 for the figure 
of 
