Published (Thomson, 1855): a cable with resistance R and capacitance C per mile carries its voltage like heat along a bar, ∂V/∂t = (1/RC)·∂²V/∂x², with the time scale τ = RCℓ². With the far end earthed through the receiving instrument, the current there after the key goes down is I/I∞ = 1 + 2Σ(−1)ⁿe^(−n²π²t/τ). The equation is linear: the battery scales every current and changes no time.
Ours: the cable constants, derived from the published construction (the 1858 cable: 12.0 ohms and 0.21 µF per nautical mile, 2,174 miles; the 1866 cable: 4.27 ohms and 0.26 µF, 1,858 miles), and the reading rule: sampled once in the middle of every unit of the code, at the best delay, every mark must read higher than every gap (for the cable code, every dot positive, every dash negative and every gap nearer zero). Real clerks read better than this rule.