The equipotential curves will thus have the general character of those shown in Figure 220, 

 where the axes are so placed that c„ = - c^. The broken lines show the equipotentials that 

 meet at Q. 



Figure 220 — For a uniform line of transverse point dipoles in a stream flowing 

 perpendicularly to the line, traces of the equipotential surfaces are shown on a 

 plane drawn through the line of dipoles and parallel to the stream. 

 The equipotential surfaces may be those of the transverse flow 

 past a certain solid of revolution which is represented, in a 

 section through its axis of symmetry, by the heavy closed 

 curve. See Section 133. (Copied from Reference 7.) 



The streamlines will be three-dimensional, in general, but in the xy-pla.ne they will be 

 plane curves orthogonal to the equipotential curves. Clearly there will be one streamline 

 which, approaching with y decreasing, divides at Q and passes around the line of dipoles 

 along a closed dividing curve C, then re-unites at the other stagnation point and proceeds to 

 y = - tx). The same geometrical curve C can be drawn on any plane through the a;-axis; and on 

 all planes it will have the property that at any point the component of the velocity lying in 

 the plane will be tangent to the curve, since both this component and the curve C must be 

 perpendicular to the equipotential curve through the point. The surface of revolution generated 

 by rotation of the curve C about the a;-axis is thus a dividing surface and may be taken as the 

 surface of a solid body. The formulas then represent the transverse flow past this body, or, 

 also, the flow caused by the line of dipoles inside of a similar shell. 



333 



