In the case of a single lock, if two boats are to pass through, one descending and one ascending (cases 2 and 3), the descending boat would be passed through first if the lock were full, and the ascending boat first if empty; in either case, the total lockage is L, or L/2 for each boat. This also appears from case 5. Cases 6 to 10 show that if a long train of boats descends, even though the lock is full for the first boat or if a long train ascends even the lock is empty for the first boat, the total lockage is nearly L per boat. Thus in a single lock, boats should pass up and down alternately so far as this may be possible. In the case of a flight of _m_ locks, a single boat in descending uses no more water than if there were only one lock, the same water passing from lock to lock, but in ascending it uses more. In the case of a number (2_n_) of boats going up and down alternately (case 5), the lockage is _m_ _n_ L, the lockage per lock per boat being L/2, but in the case of a long train of boats descending followed by an equal train ascending (cases 7 and 8), the lockage is less. If _n_ is supposed to be equal to _m_, the average lockage per boat is as follows:-- _m_ = 1 2 3 4 5 6 Infinity Lockage = L/2 L 7L/6 5L/4 13L/10 4L/3 3L/2 per boat Thus in a case where _n_ and _m_ are very large, the average lockage per boat, when the boats pass up and down in trains, is to the lockage per boat, when the single boats pass up and down alternately through _m_ single locks all at different places, as 3 is to _m_. The reason for the difference, which may appear puzzling, is that when the locks are at different places they are worked independently of one another. Sometimes a lock is provided with intermediate gates which provide a short lock for short vessels. In the Manchester Ship Canal, alongside each lock there is another of smaller size to be used for small vessels and thus save lockage. At the Eastham lock, where the Manchester Ship Canal descends into the estuary of the Mersey, there is, below the tail gates, an extra pair of gates opening towards the estuary, so that the lock can be worked when the water of the estuary is higher than that in the canal. Water can be economised by means of a “side-pond,” into which the upper portion of the water from a lock can be discharged and utilised again when the lock has to be filled. If two locks are built side by side, each acts as a side-pond to the other. Two flights of locks can be built side by side. Sometimes instead of a lock there is an inclined plane, up or down which are drawn on rails caissons containing water in which the boats float. The rails extend below the water-levels of the two reaches, and the caissons can thus be run under the boats. “Lifts” have also been constructed by which the boats can be lifted bodily and swung over from one reach to the other.