This efficiency is dependent upon a large number of conditions many of which have already been discussed in connection with grain-size of filter sand, underdrains, rate of filtration, loss of head, etc., and a mere reference to them here will suffice. Perhaps the most important single condition is the rate, the numbers of bacteria passing increase rapidly with it. Next, fine sand and in moderately deep layers tends to give high efficiency. The influence of the loss of head, often mentioned, is not shown to be important by the Lawrence results, nor can I find satisfactory European results in support of it. Uniformity in the rate of filtration on all parts of the filtering area and a constant rate throughout the twenty-four hours are regarded as essential conditions for the best results. Severe winter weather has indirectly, by disturbing the regular action of open filters, an injurious influence, and has been the cause of most of the cases where filtered waters have been known to injure the health of those who have drunk them. This action is excluded in filters covered with masonry arches and soil, and such construction is apparently necessary for the best results in places subject to cold winters. The efficiency of filtration under various conditions has been studied by a most elaborate series of experiments at Lawrence with small filters to which water has been applied containing a bacterium (_B. prodigiosus_) which does not occur naturally in this country and is not capable of growing in the filter, so that the results should represent only the bacteria coming through the filter and not include any additions from the underdrains. These results, which have been published in full in the reports of the Massachusetts State Board of Health, especially for the years 1892 and 1893, show that the number of bacteria passing increases rapidly with increasing rate, and slowly with decreasing sand thickness and increased size of sand-grain. Assuming that the number of bacteria passing is expressed by the formula 1 [(rate)^2 × effective size of sand] Per cent bacteria passing = — ———————————————————————————————————————— 2 ([sqrt](thickness of the sand in inches)) where the rate is expressed in million gallons per acre daily, and calculating by it the numbers of bacteria for the seventy-three months for which satisfactory data are available from 11 filters in 1892 and 1893, we find that In 14 cases the numbers observed were 4 to 9 times as great as the calculated numbers; In 6 cases they were 2 to 3 times as great; In 35 cases they were between 1/2 and 2 times the calculated numbers. In 17 cases they were 1/2 to 1/3 of them. In 11 cases they were less than 1/3 the calculated numbers.