122 
SHIDY. 
diurnal and diurnal waves, they will often enable us to ex¬ 
plain the causes of the tides in large lakes, or in portions of 
the sea, and to foretell the approximate time and height of 
high or low water. In a small but deep enclosed body of 
water the surface keeps nearly perpendicular to the lines of 
gravity as disturbed by the moon—that is, the tide approxi¬ 
mately obeys the corrected equilibrium theory. As exam¬ 
ples of this we have the eastern portion of the Mediterranean 
sea, Lake Superior, and less accurately Lake Michigan. 
The slope upon which the surface of the water temporarily 
lies when the maximum disturbing forces are acting in equa¬ 
torial regions is, for the mean moon, only 0.017 second, or 
one vertical unit to about 12 million horizontal units. This 
gives the range of tide on the coast of Syria and at Sicily as 
about half of a foot, and the force diagrams indicate that it 
should be high water about 9 o’clock by the moon at Syria, 
and 6 hours earlier at Sicily, the time meridian being that 
of the middle of the sea under consideration, which range 
and times of tide are in practical accordance with observa¬ 
tions. As applied to Lake Superior, it gives a theoretical 
range of tide at Duluth of one and a half inches, and the 
time of high water at about 2 hours 45 minutes by the moon, 
both of w T hich agree almost exactly with observations. 
In applying the force diagrams to any portion of the 
ocean, the wave length is computed by Lagrange’s formula: 
A' =s t j / gh feet, 
where r is the periodic time of the forces, which may be 
assumed to be 12.4206 solar hours for the semidiurnal waves 
and 24.8412 solar hours for the diurnal waves; g is the accel¬ 
eration of gravity, which may be assumed to be 32.1722 feet 
per second, and h is the undisturbed depth of the water in 
feet. Substituting these numerical values and extracting 
the square root of the value for g , we obtain for the length 
of the wave: 
A == 41.714 V h nautical miles for the semidiurnal wave ; 
X == 83.429 i/ h nautical miles for the diurnal wave. 
