This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
The fresh air inlet shown just above the running trap Fig. 74 is to cause a circulation of air through the soil pipe, as shown by the arrows. The connection should be made just inside of the trap, so that the entire length of the drain will be swept by the current of fresh air. It is sometimes advised to extend the fresh air pipe up to the roof, because foul air may at times be driven out by heavy flushing of the drain pipe, but where this is done there is much less chance for circulation, as the inlet and outlet are nearly on a level, and the columns of air in them are more likely to be balanced. By carrying the inlet six or eight feet above the ground both objections are overcome to some extent, unless this brings it near a window, which, of course, would not be safe. The main trap does not require a back vent, for should it be siphoned under ordinary conditions, it will always be filled again within a few minutes; and if the main soil pipe is open at the top and all fixtures are properly tapped, no harm would come from the slight leakage of gas into the drain under these conditions, and some engineers recommend the omission of the running trap.
Where a house drains into a cesspool instead of a sewer, it is far more necessary that the system should be trapped against it as it gives off a constant stream of the foulest gases. The usual form of running trap serves to protect the house, but the cesspool should have an independent vent pipe leading to some unobjectionable point and carried well up above the surface of the ground.