The Science behind the Index

Back when Jock Hamilton serviced pools, he began to notice something; pools that were supposedly balanced still managed to stain, scale, and get algae. He then asked the important question “Why?” Thus began his journey to develop the first index for pools, called the Hamilton Index™. So what makes it better, and why? Here we retrace the steps and science behind Jock’s big breakthrough.

The Langelier Index (LSI)

Wilfred Langelier developed his breakthrough index in the 1930’s as a means of predicting calcium solubility in water pipes. The challenge at the time was scaling in municipal pipes which would impede water flow. Wilfred’s index not only predicted when a pipe was likely to scale, but also gave a means for prevention. Focusing on pH as the primary parameter, municipalities could simply adjust the pH to prevent pipes from scaling.

The pool industry quickly adopted the index since it provided a means of balancing to predict chemical behavior in the pool.

Over the years, modifications were made to take into account the sanitation factors in the pool, determining a preferred pH range of 7.2 to 7.4, then later 7.2 to 7.6.

Limitation of the LSI

While a major breakthrough at the time, the LSI was never intended for application outside that of pipes. When applied to a very different system, such as pools, there are certain additional factors that the LSI doesn’t take into account.

Open vs Closed

First, a pool is an open system while a pipe is a closed system. In pools, when an acids are neutralized by Alkalinity, the net resulting reactions yield water and CO2. The CO2 is then gassed off, leading to a rise in pH and drop in Total Alkalinity.

However, in a closed system like a pipe, CO2 can’t be gassed off and is forced back into solution. This is a major difference that affects the solubility of compounds.

Also, the number of compounds that can be introduced into an open system is much greater than a closed system. In a closed system – such as pipes – the source water is the major factor. However, in an open system like pools, there are many more factors; rain, wind, surrounding soil, swimmer contaminants, etc.


Sanitation wasn’t a factor either of the LSI – at least not in the context of a pool. A pool is a much more stagnant body of water versus water flowing through a pipe. In addition, the water in a pipe is shielded from sunlight while water in a pool is not.

This is why the LSI was needed to be modified for pool use; the pH range was limited to ensure adequate sanitation while keeping the index below saturation levels. And since pH was the determining factor in the LSI, the limitation of an acceptable pH range reduced the the flexibility of the index.

Starting from Scratch

Jock Hamilton recognized these challenges of using the LSI as a service technician. Taking it upon himself, he began studying chemistry and analyzed the conditions pools operate within. He used his Service Tech background to develop a practical system for balancing tailored to the factors of pools. Thus was born the Hamilton Index™.

Focusing on Total Alkalinity

Rather than focus on pH, Jock found direct correlation between Total Alkalinity and Staining. Total Alkalinity measures carbonates. And carbonates turn metal compounds insoluble (see Alkalinity is the Problem and Solution on page…) Using empirical data from his service pools, he developed an algorithm to predict staining based on Total Hardness. He chose Total Hardness since it includes hardness beyond simply calcium hardness.

For Plaster: f(TH)=-20ln(TH)+195, for Non-Plaster: f(TH)=-20ln(TH)+185
Where f(TH) is the Total Alkalinity staining threshold.

Note: the difference in surface is that plaster contains carbonates that are released into water.
This gave a way to predict staining in a much linear fashion. Simply put, when the actual Total Alkalinity exceeds the threshold Total Alkalinity, probability of staining increases dramatically. When these values are equal, staining may occur. However, as long as the actual Total Alkalinity stays below the threshold, staining is avoided. We can use a similar format to the LSI to express this.

f(TH) = TAthreshold,

  • If TAactual – TAthreshold > 0, water will be supersaturated; staining likely to occur
  • If TAactual – TAthreshold = 0, water will be saturated; staining may occur
  • If TAactual – TAthreshold < 0, water will be undersaturated; staining unlikely to occur

With insight into the correlation between Total Alkalinity, Total Hardness, and Staining, we then need to address pH.

The Role of pH

Jock believed that a high pH improved sanitizer efficiency for maintenance by reducing chlorine loss from UV light.

In addition, Jock understood that if we were to maintain both a low pH and low Total Alkalinity, we increase the corrosivity of the water and likelihood of etching a plaster surface (by dissolving calcium carbonate).

It’s also worth noting that pH will naturally increase in a pool overtime: a pool will natural trend to a high pH as Total Alkalinity continues to neutralize acids in water. As this happens, Total Alkalinity itself is lowered. This is due to a pool being an “open system”, allowing CO2 to be gassed out of solution.

This makes maintaining a high pH sensible – especially if we are to focus on Total Alkalinity.

However, Jock limited the upper pH range to 8.2, since at 8.3 Calcium becomes very insoluble and can lead to scaling.

Making it practical

Jock went one step further with his findings. He understood that usability of the index is also important factor. He knew few people would carry with them the graphing calculator needed to make all these complex calculations to find threshold values.

Instead he made it as simple as possible, expressing the Index as a chart. By finding the Total Hardness value, you could see what the Total Alkalinity threshold is, and where to maintain Alkalinity below.

We have included Calcium Hardness estimates to increase usability. Although Total Hardness is preferred, Calcium Hardness tests are more common. The value of Calcium Hardness is estimated as approximately 70% of the value of Total Hardness.


The beauty of this approach is that it focuses on the unique factors of the pool environment.

Rather than “forcing a square peg into a round hole”, the Hamilton Index™ embraces the natural tendencies of a pool with small adjustments to get the best results. The results are a stain-free, algae-free pool that requires dramatically less chemical to maintain.