For an undercharged mine,
| C = C´(11/6)[l + (7/8)(l - r)]3. (7) |
In which C = charge of explosive in pounds, l = L. L. R. in yards, r = crater radius in yards, C´ = amount of explosive in pounds necessary to throw out one cubic yard of earth in a common mine in the same soil.
These formulæ are deduced as follows, viz.:
It was found by experiments made independently by Belidor and Marescot that 3660 lbs. of powder in a mine with L. L. R. equal to 4 yards gave a crater with a radius of 12 yards in earth requiring for a common mine 1½ lbs. of powder per cubic yard. The charge for a common mine in the same soil with L. L. R. equal 4 yards is
| (11/6)(4 yds.)3 × (1½) = 176 lbs. |
Representing by l the L. L. R. for a common mine requiring a charge of 3660 lbs., since the charges of common mines are proportional to the cubes of their lines of least resistance, we have
| 176 : 3660 :: 43 : l3 = 1330.8, |
whence
| l = 11y; 113 = 1331. |