Friedrich Kohlrausch in 1875–1879 established that to a high accuracy in dilute solutions, molar conductivity can be decomposed into contributions of the individual ions. This is known as Kohlrausch's law of independent ionic migration.
For any electrolyte AB, the limiting molar conductivity is expressed as x times the limiting molar conductivity of A and y times the limiting molar conductivity of B.
where:
: λ is the limiting molar ionic conductivity of ion i,
: ν is the number of ions i in the formula unit of the electrolyte (e.g. 2 and 1 for Na and sulfate| in NaSO).
Kohlrausch's evidence for this law was that the limiting molar conductivities of two electrolytes with two different cations and a common anion differ by an amount which is independent of the nature of the anion. For example,  =  for X = Cl, I and  . This difference is ascribed to a difference in ionic conductivities between K and Na. Similar regularities are found for two electrolytes with a common anion and two cations.