Astronomical and Nautical Collections. 303 
Dubuat, we ought to expect a yery different result, since, accord- 
ing to Dubuat’s formula, the resistance, in the case of a tide of any 
moderate magnitude, must far exceed the moving power. From 
this result, however, nothing can be concluded with certainty, ex- 
cept that the formula is extremely defective with respect to great 
depths and slow motions; yet we may infer from it, as a probable 
conjecture, that the resistance must be great enough to produce 
some perceptible effects, and even that it must be greater than 
would be expected from another mode of calculation founded on 
the same experiments, (PAil. Trans. 1808; Suppl. Enc. Br, Art- 
Hyprautics,) which would give the proportion of the greatest re- 
sistance to the greatest moving force only as 4 of the height of the 
tide, increased by about ten feet, to the whole depth of the ocean 
concerned, at least on the supposition of a uniform depth and a 
smooth bottom, which indeed must be far from the truth; since 
he inequalities of the bottom of the sea must tend very greatly to 
increase the resistance, especially that part of it which varies as 
the square of the velocity. 
““ Now it has been demonstrated, (Nich. Journ. Illustr. Cel. 
Mech. Suppl. E. Br. Art. Trpzs,) that a resistance, simply propor- 
tional to the velocity, would not disturb the perfect regularity of 
the oscillations concerned, and that it would only retard them when 
direct, and accelerate them when inverted, by the time correspond- 
ing” to a certain arc, of which the tangent is to the radius, as the 
velocity due to half the length of the pendulum synchronous with 
the periodical force is to the yelocity at which the resistance he. 
comes equal to the force of gravity, and as the length of the pen- 
dulum synchronous with the spontaneous oscillation to the dif- 
ference of the lengths of these two pendulums conjointly. ‘ Nor 
will the displacement produced by an equal mean resistance, vary- 
ing as the square of the velocity, be materially different ; the body 
or surface merely oscillating a little about its mean place, in con. 
sequence of the different distribution of the resistance. 
“ Here, then, we have another source of very great diversities in 
the times of the tides, according to the dimensiuns of the seas con- 
cerned, even in those parts in which the tides may be supposed to 
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