105, 106] 



NEWTONIAN POTENTIAL FUNCTION. 



201 



which give a new conformal representation of the sphere on the 

 plane, the meridians corresponding to radial lines yjx = tan (, 

 and the parallels to concentric circles. This is the stereographic 

 projection, obtained by projecting points on the sphere upon a 

 plane tangent at one pole from the other pole as a center of 

 projection. Figure 23 projected upon the sphere by this 

 transformation is shown in perspective in Fig. 47. 



FIG. 47. 



106. Diagrams. If we have a diagram representing a plane 

 section of a set of equipotential surfaces, corresponding to equal 

 increments of potential, and we superpose upon this a second 

 diagram representing a second set of equipotential surfaces, drawn 

 for the same differences of potential, we may draw the curves 

 representing the equipotentials due to a distribution which is the 

 sum or difference of the other two by simply drawing lines con- 

 necting opposite corners of the curvilinear quadrilaterals into 

 which the diagram is divided by the two equipotential systems. 

 For as we go from vertex to vertex, the increase of potential due 

 to one system is just counterbalanced by the decrease due to 

 the other. Fig. 49 represents a combination of Fig. 23 with a 

 straight field in this manner. 



