DEVELOPPER, _Fr._ to unfold, to unravel; as _Se développer sur la tête d’une colonne_, to form line on the head of a column. DEVICE, the emblems on a shield or standard. DEUIL _militaire_, _Fr._ military mourning. DEVUIDER, in the _manege_, is applied to a horse that, upon working upon volts, makes his shoulders go too fast for the croupe to follow. DIABLE. _Fr._ See CHAT. DIAGONAL, reaching from one angle to another; so as to divide a parallelogram into equal parts. DIAGONAL MOVEMENTS. See ECHELLON. DIAMETER, in both a military and geometrical sense, implies a right line passing through the centre of a circle, and terminated at each side by the circumference thereof. See CIRCLE. The impossibility of expressing the exact proportion of the diameter of a circle to its circumference, by any received way of notation, and the absolute necessity of having it as near the truth as possible, has put some of the most celebrated men in all ages upon endeavoring to approximate it. The first who attempted it with success, was the celebrated Van Culen, a Dutchman, who by the ancient method, though so very laborious, carried it to 36 decimal places: these he ordered to be engraven on his tomb-stone, thinking he had set bounds to improvements. However, the indefatigable Mr. Abraham Sharp carried it to 75 places in decimals; and since that, the learned Mr. John Machin has carried it to 100 places, which are as follows: If the diameter of a circle be 1, the circumference will be 3.1415926535,​8979323846,​2643383279,​5028841971,​6939937510,​ 5820974944,​5923078164,​0528620899,​8628034825,​3421170679,​+ of the same parts; which is a degree of exactness far surpassing all imagination. But the ratios generally used in the practice of military mathematics are these following. The diameter of the circle is to its circumference as 113 is to 355 nearly.--The square of the diameter is to the area of the circle, as 452 to 355. The cube of the diameter is, to the solid content of a sphere, as 678 to 355.--The cubes of the axes are, to the solid contents of equi-altitude cylinders, as 452 to 355.--The solid content of a sphere is, to the circumscribed cylinder, as 2 to 3. _How to find the_ DIAMETER _of shot or shells_. For an iron ball, whose diameter is given, supposing a 9-pounder, which is nearly 4 inches, say, the cube root of 2.08 of 9 pounds is, to 4 inches, as the cube root of the given weight is to the diameter sought. Or, if 4 be divided by 2.08, the cube root of 9, the quotient 1.923 will be the diameter of a 1-pound shot; which being continually multiplied by the cube root of the given weight, gives the diameter required.