Langelier tells you which side of saturation a water sits on. Operators wanted something that also graded how far, on a scale that never went negative and that could be indexed straight into a dosing table. John Ryznar's rewrite does exactly that, from the identical two inputs.

$\mathrm{RSI} = 2\,\mathrm{pH_s} - \mathrm{pH}$ — R-S-I equals two p-H-s, minus p-H. $\mathrm{RSI}$ is the Ryznar stability index, a bare number; $\mathrm{pH_s}$ is the same saturation pH as before and $\mathrm{pH}$ the same measured pH. Note which one carries the factor of two: the saturation pH. Swapping them is the single commonest slip on this index.

The scale runs backwards from Langelier, and that is the named trap of this lesson. Low numbers scale; high numbers corrode. Below about 5.5 heavy scale; 5.5 to 6.2 scale forming; 6.2 to 6.8 the quiet middle; 6.8 to 8.5 corrosion significant; above 8.5 heavy corrosion. A rising LSI and a rising RSI mean opposite things about the same water, and a report that mixes the two is worse than no report at all.

Then Puckorius, for a water that will not hold a pH between samples. $\mathrm{PSI} = 2\,\mathrm{pH_s} - \mathrm{pH_{eq}}$, with $\mathrm{pH_{eq}} = 1.465\log_{10}\mathrm{Alk} + 4.54$ — P-S-I equals two p-H-s minus p-H-e-q; and p-H-e-q equals one point four six five, log Alk, plus four point five four. $\mathrm{PSI}$ is the Puckorius, or practical, scaling index. $\mathrm{pH_{eq}}$ — p-H-e-q, the equilibrium pH — is the pH the water would settle at given its buffer alone, and $\mathrm{Alk}$ is total alkalinity as CaCO₃ in mg/L. The 1.465 and the 4.54 are the slope and intercept of the empirical fit; neither will do the other's job.

What Puckorius is FOR is the nugget. A poorly buffered cooling water shows a pH that swings on the smallest upset — a slug of acid, an hour of high load — and Ryznar then scores the same water differently every morning. Replacing the measured pH with one derived from alkalinity removes the swing and scores the water's actual buffering capacity, which is what governs whether a deposit can form and persist. On a well-buffered water the two indices agree closely; where they diverge, the alkalinity is usually telling the truer story.

The standing caution applies to both. These are saturation indices. Ryznar above 8.5 says a water will not build a protective carbonate film and is likely to be hard on steel. It does not say a rate, in mils per year or anything else, and there is no coefficient anywhere in the literature that converts one to the other.