With sand filters the frequency of scraping is nearly proportional to the turbidity; and as scraping represents most of the expenses, the costs of operation are proportional to the turbidity, except the general costs, and the cost of the amount of scraping, which is necessary with even the clearest waters. With mechanical filters the amount of sulphate of alumina required for clarification increases with the turbidity, and most of the costs of operation increase in the same ratio. The diagram shows the amount of sulphate of alumina in grains per gallon necessary for clarification with different degrees of turbidity. With the clearest waters the costs of operation on the two systems are substantially equal. With muddy waters, the expense of operating sand filters increases more rapidly than the expense of operating mechanical filters. [Illustration: TURBIDITY FIG. 26.—COST OF OPERATION OF FILTERS.] There is another element which often comes into the comparison, namely, the question of purification from the effects of sewage-pollution. Nearly all rivers used for public water-supplies receive more or less sewage, and in filtering such waters it is regarded as necessary to remove as completely as possible the bacteria. The quantities of sulphate of alumina required for the clarification of the least turbid waters are not sufficient to give even tolerably good bacterial efficiencies. To secure a reasonably complete removal of bacteria with mechanical filters, the use of a considerable quantity of sulphate of alumina is required. Let us assume that 98 per cent bacterial efficiency is required, and that to produce this efficiency it is necessary to use one grain of coagulant to the gallon. With water requiring less than this quantity of coagulant for clarification this quantity must nevertheless be used, and the costs will be controlled by it, and not by the lower quantities which would suffice for clarification, but would not give the required bacterial efficiency. I have added this line to the diagram, and this, combined with the upper portion of the line showing cost of clarification, represents the cost of treating waters with mechanical filters, where both bacterial efficiency and clarification are required. This line, considered as a whole, increases much less rapidly with increasing turbidity than does the corresponding line for sand filters, and the two lines cross each other. With the clearest waters sand filters are cheaper than mechanical filters, and for the muddiest waters they are more expensive. It does not appear from the diagram, but it is also true in each case, that the cheaper system is also the more efficient. Sand filters are more efficient in removing bacteria from clear waters than are mechanical filters, and mechanical filters are more efficient in clarifying very muddy waters than are sand filters. WHAT WATERS REQUIRE FILTRATION?