DIRECT DRAWING OP THE LINES OP FLOW, ETC. 5 1 



together. It will therefore be important to consider the conditions for the formation 

 of some such complexes of singularities. 



Let us for this purpose consider two coexistent fields, a simple field of trans- 

 lation represented by the parallel straight lines of flow, and a field containing a 

 point of divergence, having the straight radial lines of flow of fig. 49 a. For the sake 

 of simplicity we may consider also the last field as solenoidal except at the center 

 itself, the normal supply being localized to this point instead of being spread over 

 a finite area. Under these conditions we can add the solenoidal fields graphically 

 (section 121). We then get the resultant field represented by the heavy lines of 

 fig. 49 A, containing the constellation of two singular points, a point of divergence 

 and a neutral point. Fig. 49 b shows the result of the same construction when the 

 field of translation is retained, while the second field is changed into one containing 

 a center of convergence. The field has the same character as the preceding one, 

 only reversed. 



This constellation of a point of convergence or divergence and a hyperbolic 

 point will often occur on the charts of air-motion along the earth's surface. It 

 appears as the result of a main horizontal wind and a vertical descending, respec- 

 tively ascending, current. The discrimination of this constellation will cause no 

 difficulty when the phenomenon is on a sufficiently large scale, and the two singular 

 points are thus at sufficiently great distances from each other; but they may also 

 get so near to each other that no observations of the air-motion is obtained between 

 them. The direct drawing of the lines of flow from the observations will then give 

 points or places where a line of flow branches out into several branches (fig. 49 c), 

 or several lines of flow join into one (fig. 49 d). At the point of ramification the 

 different branches may touch each other or cut each other under finite angles. The 

 first case presumes a minimum and the second zero numerical value of the vector 

 at this point. 



130. Complex Phenomena in Connection with Lines of Convergence and of 

 Divergence. The theoretical possibility of certain complex singularities is seen at 

 once. A line of convergence or of divergence can contain a neutral point in which 

 the direction of the motion tangential to the line changes its sign (fig. 50 a, b). 

 A line of divergence can come out from a point of divergence, and a line of converg- 

 ence can end in a point of convergence (fig. 50 c, d) . The latter seems to be no rare 

 phenomenon in well-developed cyclones. Several lines of convergence are also often 

 seen to join into one (fig. 50 E). 



A specially interesting feature is the closed line of convergence containing 

 within the inclosed area a point of divergence (fig. 50 p) . This gives the kinematic 

 aspect of the phenomenon called eye of cyclone, which seems to be common in strong 

 cyclones. Corresponding eyes of anticyclone are also kinematically possible, 

 though for dynamic reasons less probable. 



A remarkable feature sometimes found on synoptical maps representing the 

 air-motion along the ground is lines alternately of convergence and of divergence 

 running more or less parallel to each other. 



