If these conditions are met, then a transformation of formula_1 into formula_2 will proceed by the nucleation of new particles at a rate formula_3 per unit volume, which grow at a rate formula_4 into spherical particles and only stop growing when they impinge upon each other. During a time interval formula_5, nucleation and growth can only take place in untransformed material. However, the problem is more easily solved by applying the concept of an "extended volume" – the volume of the new phase that would form if the entire sample was still untransformed. During the time interval τ to τ + dτ the number of nuclei "N" that appear in a sample of volume "V" will be given by