Since the charges for the common mines whose lines of least resistance are respectively 4^_y_ and 11^_y_ are identical with those of the overcharged mines whose crater radii are 4^_y_ and 12^_y_ respectively, it is assumed that the charges for the intermediate common mines are the same as would be required to produce the corresponding intermediate overcharged mines. The increment of the crater radius and line of least resistance of any one of these common mines is equal to 7/8 the increment of the crater radius of the corresponding overcharged mine; consequently the charge which gives an overcharged mine whose L. L. R. and crater radius are _l_´ and _r_´, respectively, will produce a common mine whose L. L. R. _l_ will be given by the equation _l_ = _l_´ + (7/8)(_r_´ - _l_´). (_a_) Since the charge for a common mine is obtained from equation (4), _C_ = _C__{1}(11/6)_l_^3, the charge for the overcharged mine will be _C_ = _C_{1}(11/6)[_l_´ + (7/8)(_r_´ - _l_´]^3, as above. For ordinary earth and gunpowder, when L. L. R. is measured in feet, eqs. (6) and (7) become, respectively: For an overcharged mine, _C_ = (1/10)[_l_ + (7/8)(_r_ - _l_)]^3 (6´) For an undercharged mine, _C_ = (1/10)[_l_ - (7/8)(_l_ - _r_)]^3 (7´) =8.= Giving to _l_ the same value in equations (4), (6), and (7), we have _C_´ = _C_((7/8)[_r_/_l_] + (1/8))^3, (8) In which _C_ = charge for _common mine_ with L. L. R. and crater radius = _l_. _C_´ = charge for _over_ or _undercharged mine_ with L. L. R. = _l_ and crater radius _r_. Equations (6), (7), and (8) having been deduced from the relations existing between _C_, _l_, and _r_ for mines varying from common mines up to those in which _r_ = 3_l_ may safely be used for _overcharged_ mines up to this limit.[9] In their applications to _undercharged_ mines they become uncertain when _r_ = (½)_l_; and when _r_ = (⅜)_l_ the computed charge generally produces a camouflet. These computed charges are: for _r_ = (½)_l_, _C_´ = 0.1779_C_; for _r_ = (⅜)_l_, _C_´ = O.1636_C_. A rule of the French engineers states that a charge which will produce a common mine with L. L. R. = _l_ will produce a camouflet if the L. L. R. is increased to (7/4)_l_. At this depth _C_´ = 0.187_C_, and the formula gives a crater radius of 25/49. As a safe “rule of thumb,” we may assume that _a charge which will give a common mine with L. L. R. = l_ will give a camouflet with L. L. R. = 2_l_ (_r_´ from formula = (3/7)_l_). Conversely, _a camouflet will be produced by ⅛ of the charge which will produce a common mine_. =9. Radius of Rupture.=--The determination of the _radius of rupture_ is an important consideration in underground warfare, since, when it is known, miners may so place their chambers as to break in the galleries of the enemy without injuring their own.