THEORY OP TIDES. 
219 
for 1 the lunar tide, h being the primitive lunar variation : and 
for a lake of 9O 0 in breadth, where b = 6210, or for the open 
ocean, the heights become — dL_ h , and ^ (1 J i respectively. It 
would, however, probably be more correct to make the numbers 
14 and 13 somewhat larger, on account of the deficiency of 
velocity observable in almost all the motions of fluids. 
Corollary 2. In this calculation we neglect the attraction of E ^ ect 0 f the 
the parts of the sea already elevated or depressed, so that it sea’s density,, 
would only be strictly accurate if the density of the sea were 
absolutely inconsiderable, and h were *8 or 2 feet. But if the 
earth consisted wholly of a substance not more dense than 
water, the force tending to destroy the level of its surface would 
be only f as great as the disturbing force which would act at the 
same point if the body had assumed the form of equilibrium, 
since f- of the force would be the effect of the attraction of the 
parts actually elevated (Theorem G.) : and the ratio of the forces 
would be the same in every part of the vibration : so that the 
time of a spontaneous oscillation would be increased in the 
subduplicate ratio of the diminution of the force, and the value 
of n diminished in the simple ratio. And if we suppose the 
density of the earth to be about times as great as that of the 
sea, the value of n becomes reduced to 5 f- n> and we find for 
the solar tide of the open sea ‘ 9 —~ } and for the lunar 2 
d — 15*7 d-14-6 
= q ; and having the actual height q, d — — or \ 
the depth 157 and 14*6 miles being the smallest at which the 
I tides could be direct : supposing the sea shallower, they would 
be inverted, the passage of the luminary over the meridian cor** 
responding with the time of low water. 
Corollary 3. We may form a coarse estimate of the effect of R es i stance 
resistance on the height and time of the tides of a given sea by a simple term, 
considering the case of a simple oscillation subjected to a 
resistance proportional to the velocity. Supposing the retarda- 
1 
tion or acceleration of a lunar tide to amount to one lunar hour, 
the arc of the circle appropriate to the vibration becoming 30®, 
