where N ˙ {\displaystyle {\dot {N}}\,\!} is one of two parameters in this simple model: the nucleation rate per unit volume, which is assumed to be constant. Since growth is isotropic, constant and unhindered by previously transformed material each nucleus will grow into a sphere of radius G ˙ ( t − τ ) {\displaystyle {\dot {G}}(t-\tau )} and so the extended volume of β {\displaystyle \beta } due to nuclei appearing in the time interval will be: