S 4 THE IMPROVEMENT OF RIVERS. 



curvature of the axis of the bed varied in a gradual and continuous manner, and every 

 abrupt change of curvature was accompanied by an abrupt change of depth. 



These relations existed only in those portions of the river where the length of 

 sinuosities, that is, the distance betwivn two consecutive points of inflection, was neither 

 too great nor too small. Where these relations did not exist? the channel was formed 

 of isolated trenches separated one from the other by shoals or bars which soon reformed 

 after they had been removed by dredging. 



Using these facts as a basis on which to reason, M. Fargue formulated the following 

 rules: 



i st. In order that the channel may be stable and permanent, it is necessary that 

 each bank present a succession of curvilinear arcs, alternately concave and convex, 

 and connecting right lines formed by the prolonged direction of parts of the banks 

 where the curvature changes directions. 



ad. In order that the channel may he deep, it is necessary that the polygon 

 formed by these right alignments have angles and sides neither too great nor too small. 



3d. In order that the channel may be regular it is necessary that the curvilinear 

 arc have gradual curves, that is, approaching a curve whose curvature is nothing at 

 its inflection, grows in a continuous manner up to a certain maximum, and decreases 

 afterward to again become nothing at the 'following inflection. 



4th. The spacing of the banks should vary with two elements, the distance and 

 the curvature, to wit: on the one hand, the width at the point of inflection should 

 increase going down stream, and on the other hand, between two consecutive points 

 of inflection the width should grow with the curvature and present toward the 

 apex a maximum which is the greater as the curvature of the apex is greater. The 

 width increases then, according to a periodical law, in such a manner that the bed is 

 found widened toward the apex of the curves and restricted in the region where the 

 curvature changes its direction. 



5th. In this same region the points of inflection of the two banks should not be 

 in the same transverse profile. The one where the concavity is changed to convexity 

 should be above that where the inverse change is made, at a distance which seems to 

 depend only on the width at the point of inflection. 



In the note from which the foregoing extracts have been made it is stated by 

 M. Fargue that the pass above Caudrot has presented constantly for forty years depths 

 varying from 10.7 to 13.12 feet; that of Mondiet, which between 1852 and 1866 had only 

 30 inches depth, in 1 886 had 6.56 feet ; part of this increase was accomplished by dredging, 

 but it was accompanied by a correction of the outline of the left bank under the rules just 

 laid down. With a single dredging in twenty years the depth has remained between 

 4.3 and 6.6 feet. In another pass the depth has been increased by this process and 

 maintained constantly. 



There is one fact in connection with these improvements worthy of note. In that 

 portion of the river having these contracting works the bed has eroded at the upper 



