As a result of experiments made at the Lawrence Experiment Station[4] we have a standard by which we can definitely compare various sands. The size of a sand-grain is uniformly taken as the diameter of a sphere of equal volume, regardless of its shape. As a result of numerous measurements of grains of Lawrence sands, it is found that when the diameter, as given above, is 1, the three axes of the grain, selecting the longest possible and taking the other two at right angles to it, are, on an average, 1.38, 1.05, and 0.69, respectively and the mean diameter is equal to the cube root of their product. It was also found that in mixed materials containing particles of various sizes the water is forced to go around the larger particles and through the finer portions which occupy the intervening spaces, so that it is the finest portion which mainly determines the character of the sand for filtration. As a provisional basis which best accounts for the known facts, the size of grain such that 10 per cent by weight of the particles are smaller and 90 per cent larger than itself, is considered to be the _effective size_. The size so calculated is uniformly referred to in speaking of the size of grain in this work. [Illustration: FIG. 3.—APPARATUS USED FOR MEASURING THE FRICTION OF WATER IN SANDS.] Another important point in regard to a material is its degree of uniformity—whether the particles are mainly of the same size or whether there is a great range in their diameters. This is shown by the _uniformity coefficient_, a term used to designate the ratio of the size of the grain which has 60 per cent of the sample finer than itself to the size which has 10 per cent finer than itself. The frictional resistance of sand to water when closely packed, with the pores completely filled with water and in the entire absence of clogging, was found to be expressed by the formula _v_ = _cd_^2(_h_/_l_)(_t_ Fah. + 10°)/60, where _v_ is the velocity of the water in meters daily in a solid column of the same area as that of the sand, or approximately in million gallons per acre daily; _c_ is an approximately constant factor; _d_ is the effective size of sand grain in millimeters; _h_ is the loss of head (Fig. 3); _l_ is the thickness of sand through which the water passes; _t_ is the temperature (Fahr.). TABLE SHOWING RATE AT WHICH WATER WILL PASS THROUGH EVEN-GRAINED AND CLEAN SANDS OF THE STATED GRAIN SIZES AND WITH VARIOUS HEADS AT A TEMPERATURE OF 50°.