=21.= When, in the close attack of the work, the besiegers are subject to vertical fire from small mortars, better overhead cover must be obtained by bomb-proofs, constructed by deepening the trench, using stronger beams, and a greater thickness of earth. Twelve-inch timbers laid touching each other, with spans of 5 feet and 5 feet of earth cover, have been considered sufficient; but with the improvement of high-angle fire and the use of high-explosive shells greater protection will be needed in the future. Experimental data for fixing the amount is not now available; an approximate thickness of earth cover may be computed as indicated below. The mining effect of dynamite in common earth is something less than twice that of an equal weight of gunpowder. (See Military Mining, Arts. 13 and 14.) An explosive enclosed in a strong case, however, expends a part of the energy due to explosion in rupturing this case. The stronger the explosive the less will be the percentage of the total energy required for breaking the case, and the greater the percentage remaining for performing other work. For this reason equal weights of high explosives and of gunpowder enclosed in strong shells will not produce the same relative effects in forming craters, &c., that they would if contained in paper cases. The effect of the high explosive is relatively much greater when contained in a strong shell. Experiments made at Fort Hamilton, 1890-91, with 8-inch shells loaded with explosive gelatine, showed this explosive to have between 4 and 5 times the effect of gunpowder, while in paper cases the relative effects were as 1.7 to 1.0. (See Report of Board of Ordnance and Fortification, Ex. Doc. No. 12, 52d Congress, 1st Session, January 5th, 1892.) Since the mining effects of the charges contained in shells are, however, less than when packed in thin cases, the thickness of cover determined by the use of the usual mining formulas should err on the side of safety. Knowing the charge contained in shells to be fired against a bomb-proof, and their probable penetration, the formulas given in Arts. 7 to 12, Military Mining, may be used for finding equivalent common mines and radii of rupture for dynamite and explosive gelatine by substituting in them 1/17 for 1/10. The values given in Art. 11 will probably be sufficiently accurate for the radii of rupture. The cover given in the direction of the fire must be greater than the sum of the penetration and the radius of rupture. When the penetration is equal to or greater than twice the L. L. R. of an equivalent common mine a camouflet will probably be formed, whose radius of rupture, from the formulas, will be equal in all directions and may be assumed as ⅕ of the L. L. R. of the equivalent common mine. In this connection, see par. 61, p. 58. SAPPING. =22.= When the trenches have been carried so near the work that the simple or flying trench cannot be used without undue loss, recourse must be had to the _sap_.