time which will elapse while the run-off from the furthest point of the drainage-area is reaching the sewer. This time is an uncertain quantity and will to a certain extent vary. with R. Some engineers assume a velocity of about 2 feet per second over the surface. The formula v = 2000 VS is offered as an empirical one for calculating the velocity of run-off over the surface in feet per minute, S being the sine of the slope. While I does not directly affect this velocity, it is observed that the most impervious surfaces usually offer the least obstruction to the flow of water, and vice versa. The time for which is assumed is obtained by dividing vinto, the length of the furthest corner of the drainage-area from the sewer.

The same method is also applied to determining the time of run-off from each smaller area to its inlet, in such cases being taken as the distance by gutter of the furthest point from its inlet.

The amount of run-off to each point of interception thus found must be provided for by inlets of sufficient size and number (see Art. 41) and by ample sewer capacity. The following tabulation of a calculation by the above method for the district shown in Plate V is given as an illustration. a is the size of each sub-area, I its imperviousness; AI is in each case the sum of all the preceding al's. s is the surface-slope of the sub-area, is the greatest distance traversed by the run-off in crossing each sub-area, t is the time occupied by the run-off in travelling the distance 1, r is the rate of rainfall for the time t, qaIr. S is the slope of the sewer removing the run-off from the point in question, L its length to the point next considered (usually the next inlet or sewer-junction), Tis the time occupied by the run-off in flowing from the extreme limit of the entire drainage-area A over the surface and through the sewers to the point under consideration, R is the rate of rainfall for the time T, Q is the total

.006 26.9 1.7 40.8 36" 432 360 Ave. B, 1st St. to 2d St. .006 27.7 1.7 44.2 36" 436 310 2d St., Ave. B to Ave C.

.005 28.4 1.751.0 42" 424 510 Ave. C, 2d St. to 3d St.

.008 12.4 2.6 15.0 22" 419 830 3d St., Ave. B to Ave. C.

6 (one half) 1.8.80 1.44 42.96.005 63011.12.7 3.9

9 (one half) 1.8.80 1.44 44.40.007 630 9.42.9 4.2

.004 29.6 1.6 71.048" 432

3d St., Ave. C to Ave. D.

* and R taken from the rainfall-curve (Plate IV, page 125) for the New England States.

amount of run-off from all the drainage-areas above = AIR. q(= aIr) as well as Q should be calculated for each sub-area, and if the Q for any stretch of sewer is at any place less than the immediately tributary to the same the latter should determine the size.

Plate IV will be found convenient for determining a, and also R when the rates of rainfall of the place in question can be represented by any of the curves there given, these being for rains of the second class. To find a in acres from the diagram, use one dimension (in feet) of the area (or of an equivalent rectangle if it is not rectangular) as an ordinate and find the corresponding abscissa of the acre-curve in the diagram; divide this into the other dimension of the area and the quotient will be a in acres.

By the table the run-off from the undeveloped territory is placed at 40.8 cubic feet per second, which is carried by a 36-inch sewer on a .6% grade for 360 feet, where it receives still more sewage; the maximum amount to be received there, both over the surface and through the sewer, being 44.2 cubic feet, although q for the block No. I alone is 6.2 cubic feet. But is not equal to 40.8 +6.2, because the latter quantity was due to a rainfall of 6.25 minutes' duration, or rather to the maximum rate for that time, during which only such water would have arrived from the upper end of the drainagearea as was due to a lower rate of rainfall; but the time of 27.7 minutes is that for which the run-off is calculated from both the undeveloped territory and block No. 1. Blocks No. 2 and No. 3 both reach the sewer at the same point, and, taking the rate of rainfall for 28.4 minutes, we have a total run-off from all the territory above of 51.0 cubic feet per second and, the grade being .5%, a 42-inch sewer is found to be necessary.

Blocks No. 4 and No. 7 discharge first into a branch sewer, which it is found should be 22 inches in diameter.

Where this joins the main the run-off from blocks No. 5 and No. 8 and from half of No. 6 and No. 9 also reaches it, and it must consequently be increased in size. The time T at this point is 26.09+0.8 (in the Ave. B sewer) +0.7 (in the Second Street sewer)+1.2 (in the Ave. C sewer), or 29.6 minutes, and the rate of rainfall for this time is used for the run-off from the entire area.

It will be seen that the method here employed is but a practical application of the principles stated in Art. 18. More, and more accurate, data for determining t and I, as well as R, are needed before this or any method can be relied upon to give more than general approximations to the run-off. Fortunately with the method here given the approximation becomes more close as the area becomes more urban, and is most so in the most densely populated districts, where the danger from gorged sewers would be greatest.

ART. 37. GRADE, SIZE, AND DEPTH OF SEWERS.

For both determining and recording the grades of the proposed sewers use is usually made of the profiles of the streets, plotted from the level notes. Upon these Upon these a vertical longitudinal section of the proposed sewer through its centre line is placed, thus showing the size, grade, and depth of the sewer. While designing, however, it will be found convenient to pencil in the line of the invert only, since then changes in its vertical location can more readily be made.

A short experience in sewer-designing will demonstrate how mutually involved are Q, S, the diameter and the depth of the sewer. In many cases it will be necessary to alter and realter the grade and diameter before obtaining for each reach of sewer the best obtainable depth and velocity. is a fixed quantity for any given case, S may vary between fixed limits, the size also has its limits in some cases, but the depth of the