_v_ = the velocity at which a solid column of water, whose section equals in area that of the bed of sand, moves downward through the sand in meters per day; this is practically the number of million gallons passing through the sand per acre per day. _c_ = a constant, having the value of 1000 for clean sand, and 800 for filter-sand after having been some time in use. _d_ = the effective size of the sand-grain in millimeters. _h_ = the head lost by the water in passing through the sand at the rate v; this is the effective head of water producing motion through the sand. _l_ = the thickness of the sand bed. _t_ = the temperature of the water in degrees Fahr. The velocity _v_, as determined by experiment, takes the following form: _h_ (_t_ + 10) _v_ = _cd²_ --- (--------). _l_ ( 60 ) This formula cannot be used for the flow of water through all sands of all thicknesses and under all circumstances. It is limited to effective diameters of sand between .1 and 3 mm., having a uniformity coefficient not greater than 5. _h_ and _l_ may be taken in any unit as long as both are expressed in the same unit, since the ratio of the two quantities will then not be affected. If the effective head of water on the filter or the head lost is equal to the thickness of the bed of sand, the ratio of _h_ divided by _l_ will be 1. In case the formula is used to express the quantity of water flowing through the sand per acre per day, it must be remembered that _v_ will be the number of million gallons and not the total number of gallons. The formula can only be used when the sand is well compacted and where the voids of the sand are entirely filled with water.