The character and coarseness of the sand employed are both elements affecting its efficiency as a filtering material. It should not be calcareous, for then masses of it may be cemented together and injure or partially destroy the working capacity. Again, if it is too coarse and approaches the size of gravel, water may run freely through it without experiencing any purification. Much labor has been expended, especially by the State Board of Health of Massachusetts, in investigating the characteristics of sand and the sizes of grains best adapted to filter purposes. In that work it has become necessary to classify sands according to degrees of fineness or coarseness. The diameter of a grain of sand in the system of classification employed means the cube root of the product of the greatest and least diameters of a grain multiplied by a third diameter at right angles to the greatest and least. The “effective” size of any given mass of sand means the greatest diameter of the finest 10 per cent of the total mass. There is also a term called the “uniformity coefficient.” The uniformity coefficient is the quotient arising from dividing the greatest diameter of the finest 60 per cent of the mass by the greatest diameter of the finest 10 per cent of the same mass. These are arbitrary terms which have been reached by experience as convenient for use in classifying sands. Evidently absolute uniformity in size will be indicated by a uniformity coefficient of 1, and the greater the variety in size the greater will be the uniformity coefficient. Sands taken from different vicinities and sometimes even from the same bed will exhibit a great range in size of grain. [Illustration: FIG. 5.—Sizes of Grain or Fineness of Sand.] Fig. 5 represents the actual variety of size of grain as found in eight lots of sand among others examined in the laboratory of the Massachusetts State Board of Health. The vertical scale shows the per cent by weight of portions having the maximum grains less in diameter than shown on the horizontal line. The more slope, like No. 5 or 6, the greater is the variety in size of grain. Those lines more nearly vertical belong to sands more nearly uniform in size of grain.