Grain-size scale, phi scale কী?

The grain-size scale of sedimentology divides the diameters of grains into classes whose limits double from one class to the next, starting from $1\,\mathrm{mm}$; each class is named (sand, silt…). The phi scale expresses a diameter $d$ by

so that $d = 2^{-\varphi}$ mm: $1\,\mathrm{mm}$ is $\varphi = 0$, $2\,\mathrm{mm}$ is $\varphi = -1$, $0.25\,\mathrm{mm}$ is $\varphi = 2$, and finer grains have larger values of $\varphi$.