4()8 FOURTH REPORT — 1834. 



The conclusions from the preceding observations, arc, 



1st, That the greatest velocity is at the surface : 



2ndly, That the velocity (which at first diminishes insensibly 

 downwards,) decreases rapidly towards the bottom, in a ratio de- 

 pendent on the nature of the bed : 



3rdly, That supposing two right lines to pass through the 

 extremity of four ordinates, determined by experiment, and 

 conveniently chosen in the curve, which should pass through 

 all the points obtained, the ordinates of these right lines, cor- 

 responding to the velocities observed in the other points, will 

 differ little in the numerical expression of these velocities : 



4thly, That the point of intersection of two right lines which 

 each partial surface of partial motion circumscribes, has for its 

 ordinate a numerical value which differs very little from the 

 mean velocity expressed by the quotient of the sui'face of mo- 

 tions divided by the depth of the water : 



5thly, That the mean velocities resulting from the preceding 

 observations are greater than the mean velocities deduced from 

 the velocity of the surface by means of the formula adopted for 

 gauging streams : 



6thly, That the position of the ordinates, which expresses 

 the mean velocity of each surface of partial motion, is nearer 

 the bottom than the surface, or frds of the depth, reckoning 

 from the surface, and ^ the depth when the bottom is very 

 regiUar. 



Forms of the Surface of Rivers. 



Opinions vary very much on this subject ; some maintain 

 that the surface is convex, others concave, and others horizontal. 

 M. de Fontaine finds the form of the surface to vary accordingly 

 as the river is rising, falling, or slack. 



After explaining in detail the principles which have guided him 

 in regulating the course of the Rhine between Basle and Lau- 

 terbourg, a distance of 194,490 metres, M. de Fontaine gives 

 the following Table as the probable results of the action of the 

 river when turned into the new course. 



