Langelier and Ryznar both ask one question: can this water lay down calcium carbonate. Larson and Skold asked a different one, out of a long study of Great Lakes distribution water: even where a film could form, are there enough aggressive ions present to keep breaking it open? Chloride and sulphate are the two that do that, and bicarbonate alkalinity is what repairs it.

$\mathrm{LS} = \dfrac{\frac{\mathrm{Cl}}{35.45} + \frac{\mathrm{SO_4}}{48.03}}{\frac{\mathrm{Alk}}{50.04}}$ — read aloud L-S equals: Cl over thirty-five point four five, plus S-O-four over forty-eight point oh three, all over Alk over fifty point oh four. $\mathrm{LS}$ is the Larson–Skold index, a bare ratio. $\mathrm{Cl}$ is chloride as Cl⁻ in mg/L and $\mathrm{SO_4}$ is sulphate as SO₄²⁻ in mg/L, each as the ion itself. $\mathrm{Alk}$ is total alkalinity as CaCO₃, in mg/L. The three divisors are those species' equivalent weights, so every term becomes equivalents per litre before anything is compared — chemistry reacts equivalent for equivalent, never milligram for milligram.

The bands, from the original work on mild steel: below about 0.8 the bicarbonate wins and a protective film establishes itself; 0.8 to 1.2 is the marginal ground where local breakdown starts; above 1.2 chloride and sulphate dominate and pitting of mild steel is expected. The practical lever is almost always the DENOMINATOR: you rarely control the chloride in a supply, and raising alkalinity moves the ratio directly.

Now the other half of corrosion, and the reason temperature belongs in this lesson. Steel in water corrodes because oxygen is reduced at the cathodic sites, and how much oxygen is available is set by the saturation curve. $\Delta \mathrm{O_2} = C_s(T_1) - C_s(T_2)$ — delta-O-two equals C-s at T-one, minus C-s at T-two. $C_s$ is the saturation concentration of dissolved oxygen in mg/L at a given temperature, read from the published table; $T_1$ is the colder state and $T_2$ the warmer one, so the difference is the oxygen a warming water must shed.

The table to carry in your head, fresh water at one atmosphere: 14.6 mg/L at 0 °C, 11.3 at 10 °C, 9.1 at 20 °C, 8.3 at 25 °C and 7.6 at 30 °C. Solubility falls steadily as water warms, which sets up the nugget worth taking away: hot systems hold less oxygen and yet corrode faster, because the reaction rate climbs with temperature far harder than the supply of oxygen falls. And an OPEN hot system is the worst of all worlds — it sheds oxygen at the surface and takes fresh oxygen straight back in.