The Windings of Rivers 345 



figure of eight (8). When a figure of eight is combined with 

 steady forward motion so that both are travelled over in the 

 direction of the arrows in the figure, then it delineates a Lemnis- 

 coid which may resemble the course of an actual stream. This is 

 illustrated in Fig. 2. In it the sinuous curve falls into three 

 parts, each consisting of a double bow, corresponding to a com- 

 plete excursion of the tracing point round one of the figures of 

 eight. The horizontal line indicates the path of undisturbed 

 flow of the stream running from left to right in the direction 

 of the arrows. It is divided into 72 equal spaces, each of 

 which represents the distance \vhich would be covered by the 

 undisturbed stream in the interval of time in which the circle 

 which generates the transverse reciprocating motion describes 

 one twenty-fourth of a revolution, so that the undisturbed 

 stream passes over 24 spaces in the time that the tracing point 

 passes once round the figure of eight. The resultant path of 

 the tracing point is the sinuous curve, which cuts the horizontal 

 line at 12 and 24 when the symmetrical 8 is used, and in 36, 

 48, or 60, 72 when one of the other two figures is used. It is 

 an essential condition that the tracing point shall go round the 

 8 in the direction of the arrows, so that it shall be moving in 

 the same sense as the undisturbed water when it traverses the 

 outside parts of the figure which are approximately parallel to 

 the path of undisturbed flow. In describing the sinuous line 

 it i- convenient to draw the figure of eight on tracing paper. 

 Then, when the centre of the 8 is placed over any mark on the 

 horizontal line numbered, say, 9, the point on the periphery 

 of the 8 numbered 9 must be superposed on the point on the 

 sinuous curve also numbered 9. 



The description of the sinuous line is a simple case of 

 mechanical drawing, and presents no difficulty. By varying 

 the harmonic composition of the figure of eight and the rate of 

 undisturbed flow of the water, an infinite number of different 

 individual curves can be produced which an- all covered by 

 the same generic specification h i ,m interesting occupation, 

 in leisure moments, to compose curves of this kind and to 

 compare them with those traced by artual iivnx on tin 

 of the earth. 



