1. The volume varies as the speed of the fan (resistance constant) (Figs. 3, 4 and 5.) 2. The water gauge varies as the square of the speed (resistance constant) (Figs. 3, 4 and 5.) 3. The mechanical efficiency is nearly proportional to the speed up to about 1700 r.p.m. The mechanical efficiency is not materially affected by changes of speed between 2000 and 2700 r.p.m. (Figs. 6, 7, 8 and 9.) 4. The volumetric ratio is affected by the equivalent orifice of the drift, the pitch and the number of air -screws. It increases with the equivalent orifice and number of air - screws but decreases as the pitch is increased. This would seem to be one of the reasons for the smaller pitches giving the higher efficiencies. 5. The water -gauge increases with the number of air - screws and the volume is approximately proportional to the square root of the number of air- screws. (Fig. 12.) 6. Within the limits of the experiments carried out, the mechanical efficiency increased over a wide range of equivalent orifices as the pitch was reduced. (Speed constant) (Fig. 14.) 7. At constant speed and over a wide range of equivalent orifices, the mechanical efficiency increased with the number of air -screws. (Fig. 15.) 8. The maximum efficiency for each pitch and for each combination of air - screws was obtained at approximately the same equivalent orifice. This would seem to show that the diameter of the fan is vitally important, and that for a particular fan there is an equivalent orifice with which all pitches and all combinations of air - screws give their highest mechanical efficiency. 9. By greasing the fan casing and using confetti, I found that with even one impeller the air -flow is axial in an air-screw fan with a short évasée except when the resistance of the drift is very great. By means of an anemometer I found that re-entry then takes place at the inner two- thirds of the circular évasée. As regards Rateau's criterion it is very difficult to obtain data for the purpose of comparison. Mr. Steart's figures and those of Professor Hay and Mr. Lindley are available, but the difference between the pitches of their impellers and mine makes a direct comparison of dimensions impossible. Nevertheless, I have shown, I believe, that the small air - screw fan is capable of performing as efficiently as the larger diameter fans tested in South Africa and at Grange Colliery, and from an examination of Mr. Steart's results I axa of the opinion that Rateau's criterion, namely, R₂/R₁= √a₂/a₁, holds true for air-screw fans.