DIRECT DRAWING OF THE LINES OF FLOW, ETC. 55 



each other along a set of singular lines, each produced by the coincidence of a line 

 of convergence and a line of divergence. 



(4) To the velocities of fig. 5 1 a we shall finally add a constant velocity of 

 direction normal to the wave-ridges and now of greater intensity than the greatest 

 velocity due to pure wave-motion. We then get velocities which are periodically 

 increasing and decreasing, but without any change of direction (fig. 51 g). If we add 

 to these velocities the same constant velocity parallel to the direction of the wave- 

 ridges as above, we shall get the system of asymmetric wave-formed lines of fig. 5 1 H, 

 containing no singularity. 



(5) If we increase still further the velocity normal to the wave-ridges, and then 

 add the same velocity parallel to the wave-ridges as before, we shall get fig. 51 

 1 and k respectively. The lines of flow of the latter figure are very nearly sinus- 

 lines, but of very small amplitude. 



In all of the figures B, d, f, h, k, the velocity parallel to the wave-ridges has the 

 same value, and a very small value. If we increase this velocity, the lines of flow 

 of the figures b, d, f will be stretched out in the direction of the singular lines, i.e., 

 in the direction of the wave-ridges, and the lines of flow of the figures h and k will 

 get higher waves. 



132. Practical Rules for the Direct Drawing of the Lines of Flow and the 

 Curves of Equal Intensity. When a chart is given containing arrows and numbers 

 representing the observations of the motion, the first thing to do in order to pass 

 on to the continuous representation of the motion will be this: by examination 

 of the distribution of arrows and of the corresponding intensities to find out the 

 nature and the approximate situation of the singularities. 



This being done, it will generally be best first to draw certain of the lines of 

 flow issuing from the singularities. Some lines of flow will generally be found whose 

 course can be drawn with great certainty. A set of such lines being drawn, the 

 general character of the whole field will practically be determined, for they will 

 divide the chart into areas within which the other lines must have their course, as 

 intersections are excluded except in the singularities. 



The lines of flow and those of equal intensity should be drawn with continuous 

 attention to each other. The closed intensity-curves surrounding the singular points 

 are first drawn, then other closed curves surrounding other places of maximum or of 

 minimum values of the vector, and then by and by the curves which have a more 

 complicated course. 



In this way, it will generally not be found too difficult to draw the lines of flow 

 and curves of equal intensity, representing the air-motions along the ground over 

 the areas where we have a satisfactory network of meteorological stations. Cases 

 of doubt as to the character of the singularities as well as to the detailed course of the 

 curves may arise. But making the experiment of letting different workers draw 

 the curves of flow from the same observations independently, we have always 

 found that the result has been very nearly the same as soon as the observations 

 have the completeness of those from Europe or from the United States. 



