Example I.
It is required to make a mine in the second sort of soil, mentioned in the foregoing experiments, which shall have a line of least resistance of 10 feet, and the diameter of its excavation 20 feet; what will be the proper charge?
The nature of this soil, by the table, requires 10 pounds of powder to 216 cubic feet.
Calculation.
| 1. The diameter of the excavation is 20, and its square | 400 |
| Double the line of least resistance is 20, and its square | 400 |
| Therefore the sum to be reserved is | 800 |
| 2. The square root of 800 is 28.3 Double the line of least resistance is 20 | 566 |
| Which leaves the remainder | 234 |
| 3. Half the remainder is | 117 |
| Which multiplied by the line of least resistance, | 10 |
| Gives the product | 1170 |
| Which multiplied by | 1.57 |
| Gives the solidity of the excavation feet | 1836.9 |
4. If feet.216 : lb.10 ∷ feet.1836.9 : lb.85 which is the charge required.
By Logarithms.
| 1. Diam. of excavation is = 20 | 1.301030 | |
| Diameter squared is | 2.602060 | 400 |
| Double the line of least resistance is = 20 and its square | 400 | |
| The sum to be reserved is | 2.903090 | 800 |
| 2. Square root of sum is 28.3 | 1.451545 | |
| Double the line of least resistance is = 20 | 1.301030 | |
| Product to be subtracted is | 2.752575 | 566 |
| Remainder is | 2.369216 | 234 |
| Line of least resist. = 10 | 1.000000 | |
| 10 pounds of powder | 1.000000 | |
| To 216 cubic feet, compl. arith. | 7.665546 | |
| To which add the const. log. | 9.894870 | |
And the sum is the logarithm charge required 1.929632 = 85 lb.
Problem II.