Of the large number of experiments recorded by Penfold (1914) in connexion with the question of lag in bacterial growth, a certain proportion have been carried out in such detail as to render them eminently suitable for mathematical analysis. In all work of this kind, which is intended to throw light on the numerical aspect of bacterial growth, it is desirable to take observations at frequent and, if possible, regular intervals, during the period of lag, and to count a sufficiently large number of colonies on the plates. To secure this last and most important desideratum, orientating experiments must be performed, from the results of which one is enabled to calculate what dilution of the culture at any given period of growth will yield a tolerably large and accurately countable plate population.