1863.] FEKaussoff — delta of the gauges. 323 



conditions of inequality of surface or of soil, it would flow continu- 

 ously in a straight line ; but any obstruction or inequality whatever 

 necessarily induces an oscillation, and, the action being continuous, 

 the effects are cumulative, as those in the pendulum are discumulative; 

 and the oscillation goes on increasing till it reaches the mean between 

 the force of gravity tending to draw it in a straight line, and the 

 force due to the obstruction tending to give it a direction at right 

 angles to the former. 



If this be so, it will immediately be perceived that the extent or 

 radius of the curves will be directly proportioned to the slope of the 

 bed of the river. If, for instance, a river were flowing down a 

 regular slope, through a perfectly homogeneous soil, with a fall of, 

 say, 10 feet per mile, or 1 in 500, the curves would be so extended 

 as to appear nearly a straight line on the map. With a fall of 1 

 foot per mile, the radius of the curve is, as nearly as I can ascertain, 

 double that of a river with a fall of 6 inches ; and when the fall is 

 about 3 inches per mile, the direct and tangential forces so nearly 

 balance one another that the curves are practically semicircles. In 

 the latter case the chord of the curves is practically four times the 

 width of the river. Thus a river 1000 feet wide would oscillate 

 once in 4000 feet in the general direction of its course, and the ex- 

 tent of its curve, measured along the centre of the stream, is a little 

 more than 6000 feet. Between a fall of 6 inches and 1 foot per 

 mile, the oscillation is, apparently, once in about six times the width ; 

 above a foot it rises to one in ten or twelve, above which it is ex- 

 tremely difficult to find examples uninfluenced by natural obstruc- 

 tions. It need hardly be remarked that these observations apply to 

 rivers when their beds are full, which is the only time when they 

 are shaping their courses *. 



There are a number of other consequences flowing from these, to 

 which I shall not allude here, as they have no direct bearing on the 

 subject in hand, though it would be extremely interesting if they 

 were observed and tabulated ; for not only would these tables enable 

 any one on inspecting a map to calculate approximately the slope of a 

 country, and to estimate the relative importance of every river there 

 delineated, but they would enable the engineer to regulate their 

 courses, and the statistician to predict the result of the changes he 

 sees taking place. To make this clearer, let me take one example. The 

 Austrian engineers have of late years speut enormous sums of money 

 in the attempt to straighten the course of the Danube by cutting off 

 its lateral branches. This has been done by embanking across their 

 mouths with dykes of fascines and piles. For a time this resists, and 

 might resist so long as the river finds some other place where it can 

 readjust its curvature ; but, as these are stopped one after the other, 

 it bursts through the barriers and resumes its old course. The fact 

 is, the Austrians are trying to make the whole body of water flow in 

 curves due only to a portion, and they have hitherto, as might be 

 expected, found this impossible ; had they taken the trouble to calcu- 



* The average width of the Nile between Kouni Ombos and Memphis is 



