TWO EQUAL MASSES OF THE SAME SIGN. 



123 



When the masses are all of "the same sign all the lines of force 

 are unlimited. If there are masses of contrary signs, the region 

 which includes the finite lines of force emitted by positive masses, 

 and absorbed by negative masses, is separated from the region which 

 contains the unlimited lines of force by a bounding surface, the 

 meridian section of which is determined by the value of the angle 

 given by the preceding equation, in which a is made = TT. 



142. Two EQUAL MASSES OF THE SAME SIGN. If the system is 

 made up of two equal masses of the same sign situate at A and A', at 

 the distance 20, (Fig. 33), the equipotential surfaces are given by the 

 equation 



= + = m ( - + - 

 r r 



The meridian curves are lemniscates. The meridian curve 

 for the surface corresponding to V = , has two lobes which 



intersect at O. The point O is one of unstable equilibrium ; the 

 force there is equal to zero. At this point the potential has a 

 minimum relative to the axis AA', and a maximum in reference to 

 the plane of symmetry PP'. 



For all values of V higher than , the equipotential surface 



consists of two separate lobes the section of which has the form of an 

 oval, and which surround each of the two centres. These ovals tend 

 more and more to merge into circles as we approach the centre. 



For lower values of V than , the surface consists of a single 



a 



sheet the narrowing of which tends to disappear as V diminishes, 



