Heat does not kill a population all at once. Hold a spore suspension at a fixed temperature and plot the survivors on semi-log paper, and what you get is a straight line going down. Bigelow found that in 1921, and every thermal process written since rests on it.

The slope of that line has a name and a symbol: $D$, the decimal reduction time — read aloud: D is the time for one decimal reduction. It is the time at a fixed temperature that cuts the population by a factor of ten, which is the same as saying it kills 90% of whatever is there when it starts.

$D = \dfrac{t}{\mathrm{LR}}$ — D equals t over L-R. The letters: $t$ is the holding time, the minutes spent at that temperature; $\mathrm{LR}$ is the log reduction, a bare count of the powers of ten the population fell by; and $D$ is the answer, in minutes. Divide the hold by the logs it bought and you have the price of one log. Turn it around and $t = D \times \mathrm{LR}$ is the design direction: pick the reduction you need, and pay a whole $D$ for each log of it.

Where does the log reduction itself come from? From plates, either side of the process: $\mathrm{LR} = \log_{10}\!\left(\dfrac{N_0}{N}\right)$ — L-R equals log of N-nought over N. Here $N_0$ — N-nought — is the count BEFORE, and $N$ the count after; the subscript zero always means the start, in this chapter and everywhere else in process work. Both counts are per the same volume or the same can, so only their ratio survives into the logarithm and the units cancel themselves.

Two things to carry out of this card. First, a D-value is meaningless without its temperature. The literature writes $D_{121}$ for the decimal reduction time at 121 °C, and the same organism ten degrees either side has a completely different one. Write the temperature down beside the number or you have recorded nothing.

Second, the straight line is an approximation and an honest one. Real survival curves shoulder at the start, while the population is still warming and the injured are not yet dead, and they tail at the end, where a stubborn subpopulation hangs on. Fit $D$ on the log-linear stretch between them. And the D you use must be YOUR organism in YOUR product: fat, sugar and low water activity all protect microorganisms, so a D measured in clean buffer badly understates what the same spore survives in a fatty sauce.