* 
156 L. Nickerson on the Periodic action of Water. 
is actually formed, and the water of amplitude flows to and 
bounds from the foot of the stream. Bidone discovered 
law, and Belanger has applied to it a formula. 
The general formula which relates to this action we may 
gather from what proceeds. If 4 be the height of the remou 
just before greatest action, h—h,= height at the beginning 
the lull that succeeds. The velocities are then 
Y=, — Y, 
And the times = t= |—*2, s, and s, being spaces due to th 
two velocities combined with the time, ¢, of the vibration. Or 
the time of one vibration is equal to the time in which water falls 
perhaps another set similar to those on ordinary dams & 
tions, I am only prepared to recapitulate the foregoing exaniil 
y 
2d, The same would be true if there were no backwatel; 
the stream retained its mean velocity unretarded, obtaining ¥ 
the sine = sine’, as before, or wlfen the surface becomes pa 
with the bed; and again, should the pool be:so filled as 0 ™®” 
the bed become parallel with the surface.’ 
* After the horizontal lin ine i i which 
surface of a pool just on the point of running over its dam. is found, and te wa 
begins to flow over, the longitudinal outline of the surface changes from re at som! 
° 
the form or nature of the weir. i oe ee a a 
state of motion past sf civil a law for the periodic action at 
