Hard armour, such as chilled cast iron, cannot be perforated but must be destroyed by fracture, and its destruction is apparently dependent solely upon the striking energy of the projectile and independent of its diameter. The punching of hard-faced armour by uncapped projectiles is intermediate in character between perforation and cracking, but approaches the former more nearly than the latter. The formula most used in England in this case is Krupp's formula for K.C., viz. t^2 = wv^2/dA^1, where t, w, v and d are the same as before, and log A^1 = 6.3532. This, if we assume the sectional density (w/d^3) of projectiles to be constant and equal to 0.46, reduces to the very handy rule of thumb t/d = v/2200, which, within the limits of striking velocity obtainable under service conditions, is sufficiently accurate for practical purposes. For oblique attack up to an angle of 30 deg. to the normal, the same formula may be employed, t sec [theta] being substituted for t, where [theta] is the angle of incidence and t the normal thickness of the plate attacked. More exact results would be obtained, however, by the use of Tresidder's W.I. formula, given above, in conjunction with a suitable figure of merit, according to the nature and thickness of the plate. It should be remembered in this connexion that the figure of merit of a plate against a punching attack falls off very much when the thickness of the plate is considerably less than the calibre of the attacking projectile. For example, the F.M. of a 6-in. plate may be 2.6 against 6-in. uncapped A.P. projectiles, but only 2.2 against 9.2-in. projectiles of the same character. In the case of the perforating action of capped projectiles, on the other hand, the ratio of d and t does not appear to affect the F.M. to any great extent, though according to Tresidder, the latter is inclined to fall when d is considerably less than t, which is the exact opposite of what happens with punching. Another method of measuring the quality of armour, which is largely employed upon the continent of Europe, is by the ratio, r, between the velocity requisite to perforate any given plate and that needed to pierce a plate of mild steel of the same thickness, according to the formula of Commandant Jacob de Marre, viz. v = Ae^(0.7).a^(0.75)/p^(0.5) where e = the thickness of the plate in centimetres, a = the calibre of the projectile in centimetres, p = the weight of the projectile in kilogrammes, v = the striking velocity of the projectile in metres per second, and log A = 1.7347. Converted into the usual English units and notation, this formula becomes v = A^1t^(0.7).d^(0.75)/w^(0.5), in which log A^1 = 3.0094; in this form it constitutes the basis of the ballistic tests for the acceptance of armour plates for the U.S. navy.