228 Royal Society: — Prof. J. Thomson on the Origin 



(pp. 405, 406); a large addition to the articles on Infinitesimals 

 (pp. 40-43); and a new article on the direction of the normal in 

 Vectorial Coordinates (pp. 230-233). The additions of most import- 

 ance, however, are two — an appendix containing a brief geome- 

 trical discussion of the chief properties of the Cartesian Oval 

 (pp. 411-416), and the account of Boiling Curves or Eoulettes. 

 In the second edition the subject fills about _ten pages at the end 

 of the chapter on tracing Curves ; in the present edition these ten 

 pages are expanded into a separate chapter (XIX.) of twenty nine 

 pages, which gives a fairly complete view of the questions suggested 

 by cycloids and analogous curves, such as might be looked for in 

 a work which professedly treats of the Theory of Plane Curves, 

 together with some kinematical applications. On the whole it is 

 plain that these additions are not such as to change very materially 

 the general character of the work ; they serve, however, to render 

 it somewhat more complete, and to make it still more worthy of the 

 attention of every student of geometry. 



XXXI. Proceedings of Learned Societies. 

 ROYAL SOCIETY. 



[Continued from p. 153.] 



May 4, 1876.— Capt. F. J. O. Evans, E.X., C.B., Vice-President, 



in the Chair. 

 ^HE following communication was read : — 

 -*■ " On the Origin of Windings of Rivers in Alluvial Plains, with 

 Rt marks on the Plow of Water round Bends in Pipes." By Pro- 

 fessor James Thomson, LL.D., P.P.S.E. 



In respect to the origin of the windings of rivers flowing through 

 alluvial plains, people have usually taken the rough notion that 

 when there is a bend in any way commenced, the water just rushes 

 out against the outer bank of the river at the bend, and so washes 

 that bauk away, and allows deposition to occur on the inner bank, 

 and thus makes the sinuositv increase. But in this thfw overlook 



the hydraulic principle, noi generally Known, tnm a stream liowing 

 along a straight channel and thence into a curve must flow w T ith a 

 diminished velocity along the outer bank, and an increased velocity 

 along the inner bank, if we regard the flow as that of a perfect 

 fluid. In view of this principle, the question arose to me some 

 years ago: — Why does not the inner bank wear away more than 



