304 Astronomical and Nautical Collections. 
be rather original than derivative, not excepting the most widely 
extended oceans. There are, however, other considerations, which 
limit, in some measure, the probable magnitude of a resistance 
varying either accurately or very nearly in proportion to the square 
of the velocity; and the chief of these is the time of high water at 
the spring and neap tides, which must be very differently affected 
by such a resistance, since it must necessarily cause a much greater 
acceleration or retardation of the spring tides than of the neap 
tides. Hitherto it has only been observed that, in particular ports, 
the greatest tides have happened the earliest; but no accurate 
comparison of the times of high and low water have been made in 
a sufficient variety of circumstances to authorise our forming any 
general conclusion of this kind. It might indeed be supposed, that 
this diversity of the relative time of high water might be modified 
and concealed by a difference of velocity in the progress of the 
different tides from their source in the ocean to the places of ob- 
servation, according to the different degrees of resistance opposed 
to them: but, if we can depend on a mode of calculation which has 
occurred to us, the velocity, with which a wave or tide is propa- 
gated, is not materially affected by a resistance of any kind, its 
magnitude only being gradually reduced, and even its form re- 
maining little altered by this cause, when the resistance is nearly 
proportional to the velocity ;” although, as the form of a wave is 
evidently altered in approaching the shore, its summit advancing 
more rapidly than its basis, till it falls over and the wave breaks, 
so a tide remote from the ocean is generally observed to rise some- 
what more rapidly than it falls. 
** Another limitation of the magnitude of a resistance, varying as 
the square of the velocity, is the modification of the apparent pro- 
portion of the solar to the lunar force, which must arise from it 
Tn assuming that the comparative magnitudes of the tides in the 
open sea must be precisely the same with those of the disturbing 
forces which occasion them, astronomers have hitherto neglected 
two very material circumstances; one, the effect that a greater 
approach of the frequency of the spontaneous oscillations, to the 
solar or lunar period, must have in augmenting the respective tide ; 
