218 
THEORY OF TIDES. 
Example. 
ing at rest in the vertical line about which its point ofsuspension 
vibrates, and will consequently follow the motion of the tempo- 
rary horizon in the same manner as the pendulum follows the 
vibration of its point of suspension, either with a direct or 
retrograde motion according to circumstances : the operation of 
the forces concerned being perfectly analogous, whether we 
consider the simple hydrostatic pressure depending on the 
elevation, or the horizontal pressure derived from the inclina- 
tion of the surface, or the differential force immediately pro* 
ducing elevation and depression, depending on the variation of 
the horizontal pressure, and proportional to the curvature of the 
surface. We have only to determine the time of spontaneous 
oscillation (ss) either in the open sea, or in any confined chan- 
nel or lake of known dimensions, and we may thence immedi- 
ately infer the magnitude of the solar or lunar tide, supposing 
the resistance inconsiderable j and supposing the resistance 
given, we may obtain by approximation a sufficiently correct 
idea of its effects. 
Corollary 1. Neglecting, in the first place, the resistance, we 
may suppose a lake or sea to be contained between opposite 
coasts in the direction of the meridian, and call its breadth in 
the direction of the equator b, and its depth d, both in miles ; 
then the time required for the complete oscillation of such a 
lake will be — - — ,in hours : and the square of this time will 
140 Jd 
h 2 
he to the square of half a solar day (©) a?. to 144, or as 
n lytjood 
I; 2 to 2830000^, :: 1 ; n (Pr. A. Sch. 2.) and n = 2830000 d ; 
b 2 and n — = , which is the multiplier for 
n— l 2830000d— 6 2 r 
determining the excursion of the pendulum from that of the 
point of suspension, or the true height of the tide from the 
variation of the form of equilibrium : so that if b be considered 
as a circular arc, the height at the eastern and western shores 
will be S b — — ' 3 °°. — — • h , h being the whole height of the 
primitive solar variation, and in the same manner taking half a 
lunar instead of half a solar day, we have S I b — 30.->ooo od — h , 
* SOSOOOOd — bb 
or 
