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course would be to fix tho 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 lise 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:
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 points at which the grade changes, happen to be those found by the computation w hereafter described, ard they ore used here fir 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 described in the next chapter. From stake 7 to the mam 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 beat adjustment in less time than by computation. Ordinarily, however, the form of computation given in the following table, which refers to the same drain, ( C,) will be nore expeditious, and its results are mathematically more torrect.* ,
* The figures in this table, as well as in the next preceding one, an adopted for the published profl le of drain G, Fig. 21, to avoid confusion. In ordinary cases, the points which are fixed as the basis of the computation are given in round numbers;—for instance, the depth at OS would be assumed to be 4.10 or 4.20, instead of 4.13. The fraction! given in the table, and in Fig. 21, arise from the fact that the decimals are not abae> lutolv correct, being carried out only for two figure*.
Note.—The method of making the foregoing computation 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 wI>pm- stake t'. 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 ptneU, 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, l?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
""" " " Stake No. 3 16.88"
Difference 8.47 H
Distance between tha two 186.—"
1 8 6) 3.4 7 (1.8 6 5 or 1.8 7
— - - 186 •,>,- , . 1610
8th. Multiply the numbers of the second column by those of the third and divide the product by 100. The result will be the amount of fall between the stakes, (fourth column.)—Example: 1.8? x82=153+100=1.68.
9th. Subtract the first number of the fourth column from the first number of the fifth column, (on the line above It,) and place the remainder on the next line of the fifth column.—Example: 20.70—1.643 19.06. .
Then, from this new amount, subtract the second number of the fourth column, for the next number of the fifth, and so on, until, in place of the entry in pencil, (Stake 8,) we place the exact result of the computation.
Proceed in like manner with the next interval,—8 to 7.
10th. Subtract the numbers in the sixth column from those in the fifth, and the remainders will be the depths to be entered in the last.
Under the head of "Remarks," note any peculiarity of the drain which may require attention in the field.
The main lines A, J), and E, and the drain JB, should next be graded on the plan set forth for C, and their laterals, all of which have considerable fall, and being all so steep as not to require silt-basins at any point,—can, by a very simple application of the foregoing principles, be adjusted at the proper depths. In grading the stone and tile ch ain, (IT, I,) it is only necessary to adopt the depth of the last stakes of the laterals, with which it is connected, as it is immaterial in which direction the water flows. The ends of this drain,—from 2Ttothe head of the drain C10, and; from I to the head of C17,—should, of course, have a decided fall toward the drains.
The laterals which are placed at intervals of 20 feet, over-the underground rock on the east side of the field, should be continued at a depth of about 3 feet for nearly their whole length, dropping in a distance of 8 or 10 feet at their lower ends to the top of the tile of the main. The intervals between the lower ends of C7e, C7d, and C7e, being considerably more than 20 feet, the drains may be gradually deepened, throughout their whole length from 3 feet at the upper ends to the depth of the top of the main at the lower ends.
The main drains Funi G, being laid in flat land, theii outlets being fixed at a depth of 3.50, (the floor of the main outlet,) and it being necessary to have them as deep as possible throughout their entire length, should be graded with great care on the least admissible fall. This, in ordinary agricultural drainage, may be fixed at .25, or 3 inches, per 100 feet. Their laterals should commence with the top of their $ tile even with the top of the 2£ collar of the main,—or .15 higher than the grade of the main, —and rise, at a uniform inclination of .25, to the upper end.
Having now computed the depth at which the tile is to lie, at each stake, and entered it on the map, we are ready to mark these depths on their respective stakes in the field, when the preliminary engineering of the work will be completed.
It has been deemed advisable in this chapter to consider the smallest details of the work of the draining engineer. Those who intend to drain in the best manner will find such details important. Those who propose to do their work less thoroughly, may still be guided by the principles on which they are based. Any person who will take the pains to mature the plans of his work as closely as has been here recommended, will as a consequence sommence his operations in the field much more understandingly. The advantage of having everything decided beforehand,—so that the workmen need not be delayed for want of sufficient directions, and of making, on the map, such alterations as would have appeared necessary in the field, thus saving the cost of cutting ditches in the wrong places, will well repay the work of the evenings of a whole winter.