! the old one, and the new observations should be computed to the original plane. It is not necessary that these levels should be noted on the map, they are needed only for computing the depth of cutting, and if entered on the map, might be mistaken for the figures indicating the depth, which it is more im pcrtant to have recorded in their proper positions, for con. venience of reference during the work. The Depth and Grade of the Drains. Having now staked out the lines upon the land, and ascertained and recorded the elevations at the different stakes, it becomes necessary to determine at what depth the tile shall be placed at each point, so as to give the proper fall to each line, and to bring all of the lines of the system into accord. As the simplest means of illustrating the principle on which this work should be done, it will be convenient to go through with the process with reference to the main drain C, of the plan under consideration. A profile of this line is shown in Fig. 21, where the line is broken at stake 'No. 7, and continued in the lower section of the diagram. The topmost line, from "Silt Basin " to " 17," is the hori zontal datum-line. The numbers above the vertical lines indicate the stakes; the figures in brackets between these, the number of feet between the stakes; and the heavy figures at the left of the vertical lines, the recorded measurements of depth from the datum-line to the surface of the ground, which is indicated by the irregular line next below the datum-line. The vertical measurements are, of course, very much exaggerated, to make the profile more marked, but they are in the proper relation to each other. The depth at the silt-basin is fixed at 24 feet (2.50.) The rise is rapid to stake 3, very slight from there to stake 7, very rapid from there to stake 10, a little less rapid from there to stake 11, and still less rapid from there to stake 17. To establish the grade by the profile alone, the proper course would be to fix the depth at the stakes at which the inclination is to be changed, to draw straight lines between the points thus found, and then to measure the vertical distance from these lines to the line indicating the surface of the ground at the different stakes; thus, fixing the depth at stake 3, at 4 feet and 13 hundredths,* the line drawn from that point to the depth of 2.50, at the siltbasin, will be 3 feet and 62 hundredths (3.62) below stake 1, and 3 feet and 92 hundredths (3.92) below stake 2. At stake 7 it is necessary to go sufficiently deep to pass from 7 to 10, without coming too near the surface at 9, which is at the foot of a steep ascent. A line drawn straight from 4.59 feet below stake 10 to 4.17 feet at stake 17, would be unnecessarily deep at 11, 12, 13, and 14; and, consequently it is better to rise to 4.19 feet at 11. So far as this part of the drain is concerned, it would be well to continue the same rise to 12, but, in doing so, we would come too near the surface at 13, 14, and 15; or must considerably depress the line at 16, which would either make a bad break in the fall at that point, or carry the drain too deep at 17. By the arrangement adopted, the grade is broken at 3, 7, 10, and 11. Between these points, it is a straight line, with the rate of fall indicated in the following table, which commences at the upper end of the drain and proceeds toward its outlet: RATE OF FALL To DEPTH. DISTANCE. TOTAL FALL. PER 100 FEET. STAKE, It will be seen that the fall becomes more rapid as we "ascend from stake 7, but below this point it is very much *The depth of 4.13, in Fig. 21, as well as the other depths at the pointe at which the grade changes, happen to be those found by the computation as hereafter described, ard they are used here for illustration. reduced, so much as to make it very likely that silt will be deposited, (see page 91), and the drain, thereby, obstructed. To provide against this, a silt-basin must be placed at this point which will collect the silt and prevent its entrance into the more nearly level tile below. The construction of this silt-basin is more particularly des cribed in the next chapter. From stake 7 to the main sil.basin the fall is such that the drain will clear itself. The drawing of regular profiles, for the more imporant drains, will be useful for the purpose of making the beginner familiar with the method of grading, and with the principles on which the grade and depth are computed; and sometimes, in passing over very irregular surfaces, this method will enable even a skilled drainer to hit upon the best adjustment in less time than by computation. Ordinarily, however, the form of computation given in the folowing table, which refers to the same drain, (C) will be nore expeditious, and its results are mathematically more correct.* No. of * Silt Basin. C. 1. C. 2. C. 3. 82 ft. 89 ** 65" 12 ft. do. .56 28" 43" do. 24" 47" do. .26" do. .18" 16.02 11.69" 4.51" 14.86 11.37" 3.49" do. .34" 14.52" 11.06" 3.46" .99" 13 53" .82" 12.61" .44 12.27" do. .41" 8.94" 4.59 ** Silt-Basin here. Made deep at Nos, 7 and 10 to pass a depression of the sur face at No. 9. 11.83. 7.70" 4.13 " do. ,44" 11.39" 7.39" 4.00" do. do. .44" 7.06" 8.89 "* do. 44" 10.95" * The figures in this table, as well as in the next preceding one, are adopted for the published profile of drain C, Fig. 21, to avoid confusion. In ordinary cases, the points which are fixed as the basis of the compu. tation are given in round numbers;-for instance, the depth at C3 would be assumed to be 4.10 or 4.20, instead of 4.13. The fractions given in the table, and in Fig. 21, arise from the fact that the decimals are not abso lutely correct, being carried out only for two figures. NOTE. The method of making the foregoing computa tion is this: 1st. Enter the lettering of the stakes in the first column, commencing at the lower end of the drain. 2d. Enter the distances between each two stakes in the second column, placing the measurement on the line with the number of the per stake the two. 3d. In the next to the last column enter, on the line with each stake, Its depth below the datum-line, as recorded in the field book of levels, (See page 105.) 4th. On the first line of the last column, place the depth of the lower end of the drain, (this is established by the grade of the main or other outlet at which it discharges.) 5th. Add this depth to the first number of the line next preceding it, and enter the sum obtained on the first line of the fifth column, as the depth of the drain below the datum-line. 6th. Having reference to the grade of the surface, (as shown by the figures in the sixth column,) as well as to any necessity for placing the drain at certain depths at certain places, enter the desired depth, in pencil, in the last column, opposite the stakes marking those places. Then add together this depth and the corresponding surface measurement in the column next preceding, and enter the sum, in pencil, in the fifth column, as the depth from the datum-line to the desired position of the drain. (In the example in hand, these points are at Nos. 8, 7, 10, 11, and 17.) 7th. Subtract the second amount in the fifth column from the first amount for the total fall between the two points-in the example, “3” from "Silt-Basin." Divide this total fall, (in feet and hundredths,) by one hundredth of the total number of feet between them. The result will be the rate of fall per 100 feet, and this should be entered, in the third column, opposite each of the intermediate distances between the points. Example: Depth of the Drain at the Silt-Basin..........20.45 feet. 66 66 66 66 .....16.98 |