36 



DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



fig. 37, we get bands of equal transport and can leave out the curvesof equal intensity. 

 If this field represents a field of motion, it gives the picture of two currents flowing 

 against each other, bending off against each other, and canceling at the neutral point. 

 Neutral points of a more complex nature, where three or more currents cancel 

 simultaneously, may also be conceived (fig. 38). 



121. Graphical Addition of Two-Dimensional Solenoidal Fields. The investi- 

 gation of the two-dimensional solenoidal vectors is much assisted by a construction 

 allowing us to pass from the representations of the fields of two such vectors to that 

 of their vector-sum. 



Let the two given fields be represented by the two sets of thin lines of fig. 39. 

 These lines divide the plane into a set of parallelograms. Every diagonal in any 

 one of the parallelograms represents a section simultaneously of two unit bands, viz, 

 of one belonging to the first and of one belonging to the second of the given fields. 

 It is further seen that through one diagonal in a parallelogram goes the sum of the 

 transports in two unit bands, i. e., the transport 2, while through the other goes the 

 difference, i. e., the transport zero. Drawing the diagonal curves formed by the 



Fig. 39. Graphical addition of two-dimensional 

 solenoidal fields. 



Fig. 40. Addition of oppositely directed divergent 

 fields. 



latter set of diagonals, we evidently get lines of flow of the field due to the coexist- 

 ence of the two given fields. These lines are drawn heavy in fig. 39. Further, it is 

 seen that the bands separating these lines are unit bands. For two of them corre- 

 spond to each diagonal through which we found the transport to be equal to 2. 



As an application of the construction, fig. 40 shows how a deformation-field 

 with neutral point and hyperbolic vector-lines is produced by the coexistence of 

 two oppositely directed fields with straight, slightly divergent vector-lines. 



Figure 41 shows the effect of adding the field with parallel and equidistant 

 straight vector-lines to that with the hyperbolic vector-lines. As is seen, the result 

 is simply a displacement of the latter field, the neutral point turning up where the 

 two^fields cancel. 



