Now let us compute the average turbidity of the water taken from the stream for water-works purposes. The water-works require, let us say, one volume each day, and we have for the first day water with a turbidity of 1.00, and then for nine days water with a turbidity of 0.10. The average turbidity of the water taken by the water-works for the period is thus only 0.19 in place of 0.57, the average turbidity of the whole run-off. The average turbidity of all the water flowing in the stream is thus three times as great as that of the water taken from the stream for water-works purposes. It is often noted that with long streams the water becomes muddier farther down, and it may naturally be thought that it is because of the added erosion of the stream upon its bed in its longer course. This, of course, may be a cause, or the lower tributaries may be muddier than the upper ones, but the fact that the water taken at the lower point is more muddy than farther up is not an indication of this. Let us take, for example, a watershed of twice the size of that assumed above, that is, so long that 48 hours will be required for the water from the most remote feeders to reach the water-works intake. Let us divide this shed into two parts, which we will assume to be equal, one of which furnishes water reaching the intake within 24 hours, and the other water reaching the intake between 24 and 48 hours. Now suppose a storm upon the watershed producing turbidities equal to those just assumed for the smaller stream. On the first day the water from the lower half of the shed, namely, 100 volumes having a turbidity of 1.00, passes the intake, but this is mixed with 10 volumes of water from the upper half of the watershed, having a turbidity of 0.10, and the total flow is thus 110 volumes of water having a turbidity of 0.92. On the second day the water from the lower half of the watershed has returned to its normal condition, and the flood-flow of the upper half of the watershed, 100 volumes with a turbidity of 1.00, is passing, and mingles with the 10 volumes from the lower half with a turbidity of 0.10, and the total flow is again 110 volumes having a turbidity of 0.92. The following eight days, until the next rain, will have flows of 20 volumes each, with turbidities of 0.10. The average turbidity of all of the water flowing off is 0.57 as before, but the water taken for water-works purposes will consist of 2 volumes of water with turbidities of 0.92, and 8 volumes with turbidities of 0.10 making 10 volumes with an average turbidity of 0.26. By doubling the length of the watershed we have thus doubled the length of time during which the water is turbid, and have increased the average turbidity of the water taken for water-works purposes from 0.19 to 0.26, although the average turbidity of all the water running off remains exactly the same.