Given the nature of the soil, the line of least resistance, and the charge, to find the diameter of the excavation.
Rules.
1. Find the solidity of the earth to be raised, by a proportion from the nature of the soil, and multiply it by 1.27.—Divide the product by the line of least resistance, and to the quotient add the square of the line of least resistance: reserve the sum.
2. Multiply the square root of the sum reserved by twice the line of least resistance, and add the product to the said sum, and from the result subtract 3 times the square of the line of least resistance; so will the square root of the remainder be the diameter of the required excavation.
Example I.
Let a mine be charged with 100 pounds of powder in a soil which requires 11 pounds of powder to raise 216 cubic feet, and let its line of least resistance be 10 feet: what will be the diameter of the excavation?
By the nature of the soil 11lb. : 216 feet ∷ 100lb. : 1964 feet, which is the solidity of the earth to be raised.
| 1. Therefore multiply | 1964 |
| By | 1.27 |
| The product is | 2494.28 |
| Which divided by the line of least resistance, 10, is | 249.428 |
| To which add the square of the line of least resistance | 100.000 |
| And the sum to be reserved is | 349.428 |
| 2. The square root of 349.428 is 18.7, which multiplied by twice the line of least resistance, 20, gives | 374. |
| This added to the sum reserved gives | 723.428 |
| From which subtract 3 times the square of least resistance | 300. |
| And there will remain | 423.428 |
The square root of which is, 20.5 feet, being the required diameter of the excavation.
By Logarithms.