1. Formulæ are given in a convenient form for calculating the numbers of animals likely to be required in a controlled experiment for testing the effect of a treatment, when a rough knowledge of the possible maximum efficiency of the treatment is available, and the level of mortality amongst the controls is approximately known. For most purposes formula (8) is sufficiently accurate.

2. A formula (11) is deduced for calculating the limits between which the real advantage of the treated over the control is likely to lie.

3. The method has been extended to the case where various treatments are compared amongst themselves. A formula (15) is deduced for the calculation of the limits within which the real superiority (or inferiority) of any one treatment over the aggregate of all the treatments is likely to lie.