Let I = {i₁, …, i_n} denote different locations served by Postal Telegraph-Commercial Cable (Postal) and Western Union. Receipts used are listed in Appendices 1 and 2. Western Union estimated 68.9% of its receipts in cities served by Postal were to locations also served by Western Union is used in Eq. (2) (Western Union 1901–1908).

Let S_i denote the share of the total receipts earned by Western Union where S_i is 0 ≤ S_i ≤ 1. Let 1-S_i denote the share of the receipts earned by Postal.