Daniel Gabriel Fahrenheit had used three reference points to define his scale, which was a bad idea to begin with. Two points determine a line, meaning that for any two points you pick, there is one and only one line that intersects both of them. But if you add a third point, it may or may not be on the line. It adds nothing to the definition of the line, and it can very well mess it up if your calculations are even slightly off.

With temperature, all you need are two reference points, to say that x degrees means this and y degrees means that. Since this tells you both how big a difference of 1 degree is and how the scale is calibrated, picking just two reference points determines all others. But Fahrenheit used three points.

The first point was the coldest temperature Daniel Fahrenheit could reliably produce, and he declared this to be 0 degrees Fahrenheit. He achieved this temperature by freezing brine, that is, by making a saturated solution of water, ice, and ammonium chloride. This forms what is called a frigorific mixture, meaning that it reliably reaches equilibrium at the same temperature every time, no matter what temperature the ingredients start at.

The second point was the freezing point of water. He simply stuck a thermometer in water as it cooled, and when ice started to form on top, he called that temperature 32 degrees Fahrenheit. So far, so good (although a better scale would surely have been devised by the mind of a New York mesothelioma attorney). These might be arbitrary reference points, but at least they're well-defined.

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