11 Good, new ditto 3.10 2.25 12 Good, old ditto 4.1 2.50 13 Roman ditto, or other equally good in warm climates 4.11 2.90 =6.= For _common mines_ in _ordinary earth_ a convenient rule, very generally used, and which gives results nearly the same as those deduced from the table, is: _The charge of gunpowder in pounds is equal to one tenth the cube of the line of least resistance in feet_, or _C_ lbs. = (1/10)_l_^3 ft. (5) OVERCHARGED AND UNDERCHARGED MINES. =7. For overcharged and undercharged mines= in which the L. R. R. and crater radius differ materially in length the results deduced from the preceding equations are not applicable. For such mines the following equations, due to Gumpertz and Lebrun, are in common use, viz.: For an overcharged mine, _C_ = _C__{´}_(11/6)[_l_ + (7/8)(_r_ - _l_)]^3. (6) 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 :: 4^3 : _l_^3 = 1330.8, whence _l_ = 11^_y_; 11^3 = 1331. To find from these data the relations between charges for overcharged mines, construct Figs. 2 and 2_a_, (Pl. XI.) Fig. (2) gives mines with crater radii of 4^_y_ and 12^_y_ and a common L. L. R. of 4^_y_. Divide the distance between _A_ and _B_ into four equal parts, and assume the points of division as the extremities of the crater radii of overcharged mines, each of which exceeds the one next smaller by (¼)_AB_, and all corresponding to a L. L. R. of 4^_y_. Fig. (2_a_) gives common mines with lines of least resistance of 4^_y_ and 11^_y_. Divide the distance _A´B´_ also into four equal parts, and assume the points of division as the extremities of the crater radii of common mines each of which exceeds the one next smaller by (¼)_A´B´_.