222 
THEORY OF TIDES. 
resistance, even in a sea of a form perfectly regular, would pro- 
bably be greater than is inferred from the formula for pipes and 
rivers, published in the Phil. Trans. 
Effec v Corollary 5. We are next to inquire what would be the 
natural resist- . 
ance on the effect of a considerable resistance, varying as the square ot the 
tides aDd limar velocit f> on com P ounj d tide, produced by the combination of 
the lunar and solar forces ; and the calculations in Theorem D. 
will serve to illustrate this case as it is found in nature. The 
first remarkable consequence of such a resistance is the alteration 
of the comparative magnitudes of the forces concerned : the 
extent of the oscillations being diminished by the resistance, the 
diminution will be greater where the resistance is greater for a 
given velocity, and the spring tides will bear a smaller propor- 
tion to the neap than if there were no resistance, so that the 
apparent inequality of the solar and lunar forces will be greater 
than their true inequality. We must, however, remember in 
making this calculation, that the proportion of the tides is by no 
means precisely the same with that of the disturbing forces of 
the luminaries, but may differ from it more or less on account 
of the difference of the periods, according to the depth of the 
ocean, and the form and magnitude of the seas and lakes con- 
cerned. For example, taking n = -§- and r , or since 
n ■= JL. , d == IO 2 miles, the greatest resistance being supposed 
for the solar tide equal to of the greatest propelling force; it 
appears that under these circumstances, if the true spring and 
neap tides are generally as 2 to I , which seems to be very nearly 
their true proportion, the tides which would happen if the 
resistance were annihilated, would be in the proportion of 4*3 67 
to 2*055, and the primitive forces exciting these tides, instead 
of 6*422 and 2*312, would be 6*422 - — and 2*312 - , or 
n n 
in the proportion of 5*158 to 2*312, or 2*208 to 1. It is obvious 
therefore, that without a more correct knowledge of the depth of 
the sea, and the resistances to its motion, than we possess, it is 
impossible to form any accurate estimate of the proportion of 
the solar and lunar forces from the tides, even if we suppose our 
observations to be exempt from the operation of any of those 
local 
