Suppose there are two type of particles, A and B, and that like particles repel and unlike particles attract. It is very convenient to explain such a situation in terms of charges, say q_A and q_B, where q_A and q_B are of opposite signs. The force between two particles, i and j, would be of the form

F = Hq_iq_jf(s_i,j)

where H is a constant and s_i,j is their separation distance. If i and j are of the same type then q_iq_j is positive for the force is a repelling one. On the other hand, if i and j are of different types then q_iq_j is negative and the force is an attraction.

The potential energy involved for the two particles is then

V_i,j(s) = Hq_iq_j∫_s^∞f(z)dz

The values of potential energy for the three possible interactions at the same distance; i.e., V_A,A(s₀), V_A,B(s₀) and V_B,B(s₀). What conditions do these three quantities have to satisfy in order that their values can be explained by a pair of charges q_A and q_B?

If such a pair of value do exist then

V_A,A/V_A,B = q_A/q_B = V_A,B/V_B,B
which reduces to
V_A,AV_B,B = V²_A,B
or, equivalently
V_A,AV_B,B − V²_A,B = 0

This is the relation that has to be satisfied in order that the values of V_A,A, V_A,B and V_B,B can be explained by two charges q_A and q_B. The same relation would have to prevail for the forces F_A,A, F_A,B and F_B,B.

If the effects are arrayed as a matrix; i.e.,

| VA,A	VA,B |
|VB,A	VB,B |

then the condition to be satisfied is that the determinant of this matrix be zero.