As different mining galleries, however, differ from each other so much in strength to resist crushing, and as the cost of an exhaustive series of experiments to determine their relative strength would be so great both in time and money, but little well-established data exist upon which to found a rule for determining the radius of rupture. =10.= The rule deduced by Gumpertz and Lebrun, however, from the material available at their time corresponds very nearly with the results of later experiments and observations, and is generally admitted as sufficiently near correct for practical use. This rule is based upon the theory that the surface of rupture is an oblate spheroid, (Pl. XI, Fig. 3), with its axis of revolution vertical and its centre at the centre of the charge; the intersection with the surface of the ground _AD_ coinciding with the edge of the crater. The ratio between the semi-transverse axis _CF_ and the semi-conjugate axis _CH_ of the generating ellipse of this assumed spheroid is the same as that between the radius of explosion _CD_ and L. L. R., _CK_. The rule is, that _the radius of rupture in any direction is equal the corresponding radius of this spheroid_. From the conditions assumed the following values of the semi-transverse and semi-conjugate axes _h_ and _v_ (which are the horizontal and vertical radii of rupture) are obtained, viz.:[10] _h_ = _l_√(1 + 2(_r_/_l_)^2); _v_ = _l_√[(1 + 2(_r_/_l_)^2)/(1 + (_r_/_l_)^2)]. For common mines these formulas give: _h_ = 1.732_l_ = (7/4)_l_ = (7/4)_r_; _v_ = 1.225_l_ = (5/4)_l_ = (5/4)_r_. For six-line craters, _h_ = 4.358_l_ = (35/8)_l_ = (3/2)_r_; _v_ = 1.378_l_ = (11/8)_l_ = (1/2)_r_. =11.= The English authorities adopt the value of (7/4)_l__{´} for the horizontal and _l__{´} √(2) = 1.41421 _l__{´} = (7/5)_l__{´} for the vertical radius of rupture of all classes of mines. In which _l__{´} = L. L. R. of an equivalent common mine = _l_ + (7/8)(_r_-_l_), etc. Some later experiments at Chatham have given _v_ = (5/3)_l_ for a 4-lined crater; _v_ = 2_l_ for a 5-lined crater; and _v_ = (5/2)_l_ for a 7½-lined crater. =12.= There are other good reasons for believing that Lebrun’s value for the vertical radius is too small; but as its use leads to increasing the charges designed to produce crushing effects, the error, if it exists, is in the right direction, and justifies the use of the formula until more exact data are available. EXPLOSIVES. =13.= No military mining operations of note have been carried on since the introduction of dynamite and other high explosives; consequently our knowledge of their value for work of this kind rests entirely upon the results obtained from experimental mines. Unfortunately but few experiments seem to have been made, and the published results of these are very meagre.