_C´_ = _C_ (_V´_/_V_) = _C_[(11/6)(_l´r_´^2)/(11/6)(_lr_^2)] = _C_[(_l´r´_^2)/(_lr_^2)] ... (1) Equation (1) is applicable to _mines in which r does not differ materially from l or r´ from l´_. From an experimental mine giving a crater of this general type the relations between _C_, _l_, and _r_ may be determined, and assuming any two of the quantities _C´_, _l´_, and _r´_ for a mine with a crater nearly similar in form, the other may be found from eq. (1). When _l_ = _r_ and _l´_ = _r´_, we have _C_ : _C´_ : :(11/6)_l_ : (11/6)_l_´^3, and _C´_ = _C_[(11/6)(_l_´^3)/(11/6)(_l_^3)] = _C_[(_l_´^3)/(_l_^3)] (2) Equation (2) is applicable to common mines, and shows that _in common mines the charge varies as the cube of the line of least resistance_. Assuming _C__{´}_ as the charge which will produce a crater with a volume of unity, equations (1) and (2) become, by omitting the primes from _l_ and _r_, _C_ = _C__{´}_(11/6)_lr_^2, (3) and _C_ = _C__{´}_(11/6)_l_^3 (4) Equation (4) gives the rule for determining the charge for common mines whose L. L. R. is given, viz.: _Multiply 11/6, the cube of the line of least resistance in yards, by the quantity of explosive required to throw out one cubic yard_. The latter quantity is determined by experiment. A similar rule may be written out from eq. (3) for mines differing but little from common mines. =5.= The quantity of gunpowder required to throw out a cubic yard of material has been calculated from a great number of mines fired in different kinds of soil. The following table gives the quantities required according to Lebrun and Macaulay, respectively the French and English authorities on the subject:[8] TABLE A. Number. Description of Earth, Rock, or Weight per Charge, Charge, Proportional Masonry. cubic foot. Gumpertz Macaulay. value and Lebrun. of charge. lbs. lb. oz. lb. oz. 1 Light sandy earth (_common earth, 85 1.8 1.13 1.12 Lebrun_) 2 Hard sand 111 1.10¾ 2.0 1.25 3 Fat earth mixed with sand and gravel (_common earth, Macaulay_) 116 1.5⅓ 1.10 1.00 4 Wet sand 118 1.12 2.2 1.30 5 Earth mixed with stones 118 1.14 2.4 1.40 6 Clay mixed with tufa 124 2.1 2.8 1.55 7 Fat earth mixed with pebbles 143 2.4 2.12 1.69 8 Rock 143 3.0 3.10 2.25 9 New or old moist brickwork or masonry 2.2 1.30 10 Inferior brickwork or masonry 2.11 1.66