220 
THEORY OF TIDES. 
Actual mag 
tudeof'tfie 
resistance. 
the cosine of this arc will be *866, and the height will be *866, 
, (Th. B.) for the open sea, andd = ; Thus if 
d— 14*6 v r 9—1-96 
the height were 2 or —2, d would be 730 or 7 37 , while the 
formula independent of resistance, would give only 
q — 2'263 
6 45, a negative value of d being impossible. If h were —3, 
with this resistance, d would be 8'83. The sine of 30° being 
*5, the resistance, when greatest, would be equal to half th® 
greatest accelerating force. 
ii> Corollary 4. If the bottom of the sea were perfectly smooth 
and horizontal, we might form some idea of the resistance 
opposed to the tides from the phenomena of rivers and pipes ; 
but on account of the great irregularity of form, we can only 
infer that the resistance must be incomparably greater than that 
which is thus determined. The horizontal velocity is most 
readily deduced from the effect of the inclination, which gene- 
rates a force varying according to the law of the pendulum, 
and producing, therefore, a velocity, which, when greatest, is 
to that which would have been produced by the whole force 
uniformly continued for the same time, as the radius is to on* 
fourth of the circumference : the sine of the inclination, which 
expresses the force, is also to the whole height divided by the 
breadth, as one fourth of the circumference to the radius : so 
that the greatest velocity becomes precisely equal to that which 
would be produced in the same time by a uniform force, 
expressed by the height of the tide divided by the breadth : 
and for the solar tide in the open sea, we have a force expressed 
by the sine — operating for three hours, which is 
equivalent to the force of gravity operating for , and 
will generate a velocity of 5 = -i^-== ~ in a second, 
or, if q be supposed equal to 1 foot, about 4 - of an inch. Now 
it appears from the experiments of Dubuat and others (Phil. 
Trans. 1808,) that the resistance may be expressed in inches of 
pressure by the formula f a~v * + 2c -Lv, where, for 
considerable depths, a =» ’0000413, and c = 'OOOOCg or 
perhaps 
