$D$ answers one question at one temperature. Move the temperature and $D$ moves with it, hard — and $z$ is the number that says how hard.

$z = \dfrac{T_2 - T_1}{\log_{10}\!\left(D_1/D_2\right)}$ — z equals T-two minus T-one, over log of D-one over D-two. The letters, and the subscript convention, stated once: subscript 1 is the cooler trial and subscript 2 the hotter one, so $T_1$ and $T_2$ are the two temperatures in °C, and $D_1$ and $D_2$ are the decimal reduction times measured at each, in minutes. The hotter trial always carries the shorter $D$; if it does not, the pairing has been crossed and the arithmetic will hand back a negative $z$ to tell you so.

Read the result in plain English: z is the temperature change that moves the D-value by a factor of ten. Raise the process by one $z$ and the same lethality arrives in a tenth of the time. Raise it by two and a hundredth.

Now the unit, because this one bites. $z$ is a temperature difference, an interval, and the site writes it C° to keep it apart from a temperature written °C. A $z$ of 10 C° is 18 F°, not 50 °F — an interval converts by the ratio alone, with no offset. A z-value put through the temperature conversion instead of the interval one comes out wildly wrong, and it comes out wrong in a direction that looks plausible.

The two working forms. To carry a D up or down the line: $D_2 = D_1 \times 10^{-(T_2 - T_1)/z}$. To find the temperature that would deliver a D you want: $T_2 = T_1 + z\,\log_{10}\!\left(D_1/D_2\right)$. Both are the same straight line read from different ends.

The nugget that makes the next two lessons possible: z belongs to the thing, not to the heat. Bacterial spores run near 10 C°, which is why the F₀ convention was built on that figure. Vegetative cells run smaller. And quality attributes — colour, vitamin retention, texture, browning — run much larger, 25 to 45 C°. That gap between a small microbial z and a large quality z is the entire commercial argument for high-temperature short-time processing, and it is coming up in lesson five.

One caution. Bigelow's line is straight over the range it was measured on. Extrapolate a few degrees with confidence, twenty with suspicion, and beyond that go and get data — especially downward, from retort temperatures toward pasteurisation, where the arithmetic stays perfectly happy and the biology does not.