reduces to 



TWO EQUAL MASSES OF OPPOSITE SIGNS. 135 



r r cos (o x 



\ m = 2am = 2am , 



r 2 R2 R3 



<o being the angle of the direction OP with the axis A' A. 



Let cr be a surface, a circle, for instance, traced by the point O 

 perpendicularly to AA', and let 6 be the solid angle under which this 

 surface is seen from the point P ; we have 



= T COS to, 



and therefore 



CT 



taking CT = 2ma, we get 



(16) V = 0. 



Thus, the value of the potential at a point, is the solid angle under 

 which we see from this point, a surface equal to the electrical moment 

 2ma of the two masses and perpendicular to the middle of the straight 

 line joining them. 



The equation of the equipotential surfaces, 



GT cos <o T3x 



~~ = 



shows that all these surfaces are similar, and that for the same direction 

 a>, the values of R are inversely as the square roots of the potentials. 

 152. In the equation of the lines of force, 



N 



COS to - COS to = 



the first member may be transformed in the following manner, de- 

 noting by 8 the infinitely small difference o> - to' : 



, . za . 



cos to - cos to = a. cos w = sin <o . 6 = sin o> . - = sin' 5 w. 



R R 



we have then 



sin 2 w i N N N 



R 



All these curves are similar, and for the same direction, R is 

 inversely as N. They are tangential to the axis at the origin the 



