Historically, the impedance analogy was in use long before the mobility analogy. Mechanical admittance and the associated mobility analogy were introduced by F. A. Firestone in 1932 to overcome the issue of preserving topologies.[32] W. Hähnle independently had the same idea in Germany. Horace M. Trent developed a treatment for analogies in general from a mathematical graph theory perspective and introduced a new analogy of his own.[33]