If a column, A B C D, receive a shock or be suddenly moved in the direction of the arrow, the centre of gravity, G, of this column will revolve round the edge, and tend to describe the path G O. If it passes O, the column will fall. The work done in such a case as this is equal to lifting the column through the height _o_ _h_. If G A = _a_, the angle G A _h_ = φ, and the weight of the body = W, then the above work equals W_a_ (1 - cos φ). This must equal the work acquired—that is to say, the kinetic energy of rotation of the body, or W _w_^2 K^2 W_a_ (1 - cos φ) = ———————————. 2 _g_ Where _w_ is the angular velocity of the body at starting, K the radius of gyration round A, and _g_ the velocity acquired by a falling body in one second. Whence _w_^2 K^2 = 2 _ga_ (1 - cos φ), but _w_, the angular velocity, is equal to the statical couple applied, divided by the moment of inertia, or, V_a_ cos φ _w_ = ——————————, K^2 squaring and substituting K^2 1 - cos φ V^2 = 2_g_ × ——— × —————————, _a_ cos^2 φ K^2 and since the length of the corresponding pendulum is _l_ = ———, _a_ 1 - cos φ V^2 = 2_gl_ × —————————. cos^2 φ To apply this to any given case we must find the value of _l_ or of K^2 ———. _a_ Mallet finds these values for the cube, solid and hollow rectangular parallelopipeds, solid and hollow cylinders, &c. In these formulæ we have a direct connection between the dimensions and form of a body and the velocity with which the ground must move beneath it to cause its overthrow. [Illustration: FIG. 15.] Not only is the case discussed for horizontal forces, but also for forces acting obliquely. Similar reasonings are applied to the productions of fractures in walls, but as there is uncertainty in our knowledge of the co-efficient of force necessary to produce fracture _through joints across_ beds of masonry, the deductions ought not to be applied as the measures of velocity. Where the fractures occur at the base or in horizontal planes, or in those of the continuous beds of the masonry, or through homogeneous bodies, the uncertainty is not so great, and for cases like these Mallet gives several illustrations. The distance to which bodies had been projected, as, for example, ornaments from the tops of pedestals, coping-stones from the edges of roofs, were also used as means of determining the angle at which the shock had emerged, or, if this be known, for determining the velocity.