124 PARTICULAR CASES OF EQUILIBRIUM. 



and which ultimately would be confounded at a great distance with 

 a sphere the centre of which is the point O. 

 The equation of the lines of force is 



cos o> + cos G>' = i + cos 0, 

 and that of the asymptote 



2 cos a = i+ cos 0, 

 or 



cos a = cos 2 -0. 



2 



The expression for the force at a point on the transverse 

 axis OP is 



2m . 2my v 



F = sin to = - - = 2 m 



f T 7 //j2 



it is a maximum at points D and D' for which 



y-* tt -r- 



It is only a maximum in reference to the transverse axis, and on 

 the contrary is a minimum for the direction parallel to AA'. 



The lines of force proceeding from m and m' are separated by 

 the plane perpendicular to the axis AA', passing through the point O. 



143, TWO UNEQUAL MASSES OF THE SAME SlGN. If two maSSCS 



of the same sign are unequal, the general form of the equipotential 

 surfaces is the same as in the preceding case excepting the symmetry. 

 The point of equilibrium corresponding to the point of intersection 

 of the surface with two sheets is defined by the ratio 



m m 1 r 



^ = ^2' or ->'- 



Putting r + r' = 20, we get from this 

 Jm 



m 



