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.
The agreement is only moderately good, and in fact no such formula could be expected to give more than very rough approximations, because it does not take into consideration the numerous other elements, such as uniformity and regularity of filtration, the influence of scraping, the character of the sediment in the raw water, etc., which are known to affect the results. Perhaps the most marked general difference is the tendency of new or freshly-filled filters to give higher, and of old and well-compacted filters to give lower, results than those indicated by the formula.
Comparing this formula with Piefke’s results given in his “Neue Ermittelungen”[28] the formula gives in the first series (0.34 mm. sand, 0.50 m. thick, and rate 100 mm. per hour), 0.25 per cent passing, while the average number of B. violacious reported, excluding the first day of decreased efficiency after scraping, was 0.26 per cent. In the second series, with half as high a rate the numbers checked exactly the calculated 0.06 per cent.
In other experiments,[29] however, in 1893, when the calculated per cent was also 0.25, only 0.03, 0.04, and 0.07 per cent were observed in the effluents.
Comparing the results from the actual filters, (which numbers also include the bacteria from the underdrains and should therefore be somewhat higher) with the numbers calculated as passing through, I find that for the 46 days, Aug. 20 to Oct. 4, 1893, for which detailed results of the Stralau works are given by Piefke, the average calculated number passing is 0.20 per cent, while twice as many were observed in the effluents; although three of the filters gave better effluents than the other eight, and the numbers from them approximated closely the calculated numbers. If we calculate the percentages of bacteria passing a number of filters, using the maximum rate of filtration allowed for the German filters where this is accurately determined, and for the English filters taking the maximum rate at one and one-half times the rate obtained by dividing the daily quantity by the area of filters actually in use, we obtain:
| Average Depth of Sand, Inches. | Effective Size of Sand- grain. | Maximum Rate of Filtration. | Per cent Bacteria passing 1 r2d = — ——— 2 √sand | |
|---|---|---|---|---|
| Hamburg | 32 | 0.31 | 1.60 | 0.07 |
| Altona | 28 | 0.34 | 2.57 | 0.21 |
| Berlin, Stralau | 20 | 0.34 | 2.57 | 0.25 |
| Berlin, Müggel | 20 | 0.34 | 2.57 | 0.25 |
| Berlin, Tegel | 20 | 0.37 | 2.57 | 0.27 |
| London, Southwark & Vauxhall | 36 | 0.34 | 2.81 | 0.22 |
| London, West Middlesex | 39 | 0.37 | 2.81 | 0.23 |
| London, Chelsea | 54 | 0.36 | 3.27 | 0.26 |
| London, Grand Junction | 30 | 0.40 | 3.27 | 0.39 |
| London, Lambeth | 36 | 0.36 | 3.75 | 0.42 |
| Middlesborough | 20 | 0.42 | 5.85 | 1.58 |
| Zürich | 26 | 0.35 | 7.50 | 1.90 |
The numbers actually observed are in every case higher than the calculated per cents passing, as indeed they should be on account of those coming from the underdrains, accidental contamination of the samples, etc.