181 



tions of the surface before it returns to normal level. These oscilla- 

 tions are called seiches. Since the currents set up by seiches are 

 never strong, the characteristics of a seiche in a long canal of uniform 

 dimensions, closed at both ends, may be derived from the equations 

 for frictionless flow in such a canal. The frictionless tides and cur- 

 rents in a canal open at the initial end and closed at the other have 

 been derived in equations (251) and (252). If the canal is closed at 

 both ends, the currents at the initial end are zero. Placing a:=0 in 

 equation (252) the equation of the current at the initial end becomes: 



v= — (glc)Ao sin {at-\-ao) tan y 



This current is zero if the speed of the oscillations, a, is such that 

 tan 7=0, or if: 



y=aL/c = ir 



whence : 



a=Trc/L 



The period, T, of these oscillations is therefore, from equation (28), 

 paragraph 49 : 



T=2T/a=2Llc=2LI^'gD (266) 



Thus the period of free oscillation in a canal 5,000 feet in length, 

 and 30 feet in mean depth is 10,000/-y30^=322 seconds = 5K minutes. 



If then the entrance were closed, an oscillation of this period, once 

 started, would continue, like the oscillations of a pendulum, until 

 damped out by friction. 



At a point distant x from the initial end of the canal, and at the 

 time t, the height of the water surface above its normal level, is found 

 by placing 7=7r in equation (251), and is: 



y=Ao cos {at-\-ao) cos (irx /L) (267) 



and the current is, from equation (252) : 



v= — (g/c)Aosm (at-^ao) sin (tx/L) (268) 



At the middle of the canal, x—jiL, so that irx/L=ir/2; and y^O 

 The middle of the canal is then the node of the oscillation. The 

 currents there reach the maximum amplitude of gAo/c. 



Since the current at the initial entrance also is zero when the oscil- 

 lations have such a period that 7=27r, 3t, 4x, etc., similar oscillations 

 with periods of one-half, one-third, one-fourth, etc., of the first may 

 be set up in a canal closed at both ends. These have two, three, 

 four, etc., nodal points respectively. 



