where a is the per cent of bacteria actually passing the filter.
Both of these terms depend upon a whole series of complex and but imperfectly understood conditions. In general the bacteria from the underdrains are low in cold winter weather, often almost nil, while at Lawrence with water temperatures of 70 to 75 degrees, and over, in July and August, the numbers from this source may reach 200 or 300, but for the other ten months of the year rarely exceed 50 under normal conditions. In summer especially it seems to be greater at low than at high rates of filtration (although a high rate for a short time only increases it), and so varies in the opposite way from the numbers actually passing the filters. This subject is by no means clearly understood; it is difficult, almost impossible, to separate the numbers of bacteria into the two parts—those which come directly through and may be dangerous, and those which have other origins and are harmless. The sketch, Fig. 14, is drawn to represent my idea of the way they may be divided. It has no statistical basis whatever. The light unshaded section shows the percentage number of bacteria which I conceive to be coming through a filter under given conditions at various rates of filtration, while the shaded section above represents the bacteria from other sources, and the upper line represents the sum of the two, or the total number of bacteria in the effluent. The relative importance of the two parts would probably vary widely with various conditions. With the conditions indicated by the sketch the number of bacteria in the effluent is almost constant: for a variation of only from 1.4 to 2.5 per cent of the number applied for the whole range is not a wide fluctuation for bacterial results, but the number in the lower and dangerous section is always rapidly increasing with increasing rate.
This theory of filtration accounts for many otherwise perplexing facts. The conclusion reached at Zürich and elsewhere that the efficiency of filtration is independent of rate may be explained in this way. This is especially probable at Zürich, where the number of bacteria in the raw water was only about 200, and an extremely large proportion relatively would have to pass to make a well-marked impression upon the total number in the effluent.
These underdrain bacteria are, so far as we know, entirely harmless; we are only interested in them to determine how far they are capable of decreasing the apparent efficiency of filtration below the actual efficiency, or the per cent of bacteria really removed by the filter.
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 √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;