DODECAHEDRON, is one of the platonic bodies, or five regular solids, and is contained under 12 equal and regular pentagons. The solidity of a _dodecahedron_, is found by multiplying the area of one of the pentagonal faces of it by 12; and this latter product by ¹⁄₃d of the distance of the face from the centre of the _dodecahedron_, which is the same as the centre of the circumscribing sphere. The side of a _dodecahedron_ inscribed in a sphere, is the greater part of the side of a cube inscribed in that sphere, cut into extreme and mean proportion. If the diameter of the sphere be 1,0000, the side of a _dodecahedron_ inscribed in it will be .35682 nearly. All _dodecahedrons_ are similar, and are to one another as the cubes of the sides; and their surfaces are also similar, and therefore they are as the squares of their sides; whence as .509282 is to 10.51462, so is the square of the side of any _dodecahedron_ to the superficies thereof; and as .3637 is to 2.78516, so is the cube of the side of any _dodecahedron_ to the solidity of it. DOG-_Nails_. See NAILS. DOLPHINS. See CANNON. DOMMAGE, _Fr._ in a general acceptation of the term, signified in the old French service, the compensation which every captain of a troop, or company was obliged to make in consequence of any damage that their men might have done in a town, or on a march. If any disagreement occurred between the officers and the inhabitants, with respect to the indemnification, a statement of losses sustained was sworn to by the latter, before the mayor or magistrates of the place, who determined the same. But if the officers should refuse to abide by their decision, a remonstrance was drawn up and transmitted to the secretary at war, with a copy of the same to the intendant of the province. Officers have frequently been displaced or degraded on this account. Hence the term dommage is supposed to have been derived from the latin words _damnum jactura_, and signifies the loss or privation of a step. DONJON. See DUNGEON. DOSSER, in military matters, is a sort of basket, carried on the shoulders of men, used in carrying the earth from one part of a fortification to another, where it is wanted. DOUBLING, in the military art, is the placing two or more ranks, or files into one. DOUBLE _your ranks_, is for the 2d, 4th, and 6th ranks (when so drawn up) to march into the 1st, 3d, and 5th; so that of 6 ranks they are made but 3; which is not so when they double by half files, because then 3 ranks stand together, and the 3 other come up to double them; that is, the 1st, 2d, and 3d, are doubled by the 4th, 5th, and 6th, or the contrary. DOUBLE _your files_, is for every other file to march into that which is next to it, on the right or left, as the word of command directs; and then the 6 ranks are doubled into 12, the men standing 12 deep; and the distance between the files is double what it was before. By this method 3 files may be doubled into 6, &c.