106. The table thus made may be of the following form:—
| Cut (or fill), in feet. | Cubic yards Earth. Slopes 1½ to 1. | Cubic yards Rock. Slopes ¼ to 1. |
|---|---|---|
| 1 | 76 | 68 |
| 2 | 163 | 137 |
| 3 | 261 | 208 |
| 4 | 371 | 282 |
| 5 | 491 | 356 |
| 6 | 622 | 433 |
| 7 | 802 | 512 |
| 8 | 919 | 593 |
| 9 | 1083 | 675 |
| 10 | 1260 | 759 |
i. e., cut being eight feet, each one hundred feet length gives nine hundred and nineteen cubic yards; one thousand feet, 9190 yards, and ten feet of length 91.9 cubic yards.
107. The preceding system is intended only for approximate estimates. Let one person read off the cuts or fills from the profile, a second give the corresponding number of yards by the table made as above, while a third sets the figures down; being careful to separate the cuts from the fills.
For final measurements, none but the prismoidal formula should be used; the length of the prismoids being taken at each one hundred feet, and nearer when the ground is rough.
108. As an example of the comparative amounts given by the above formula, and by the common method of averaging end areas, take the following, the slopes being 1½ to 1.
| Base. | Distance. | Cut. | End Area. | Mean Area. | Middle Area. |
|---|---|---|---|---|---|
| 20 | 0 | 0 | 000 | 000 | 000 |
| 20 | 50 | 5 | 137 | 069 | 059 |
| 20 | 50 | 10 | 350 | 244 | 236 |
| 20 | 50 | 15 | 637 | 493 | 483 |
| 20 | 50 | 00 | 000 | 318 | 236 |
By averaging end areas we have
| 50 × | 69 = | 3,450 | |
| 50 × | 244 = | 12,200 | |
| 50 × | 493 = | 24,650 | |
| 50 × | 318 = | 15,900 | Sum, 56,200. |
And by the prismoidal formula,