_Area of greatest Overturning Moment._—Although the rate of dissipation of the impulsive effects of an earthquake may follow a law like that just enumerated, it must be remembered that if the depth of the origin is comparable with the radius of the area which is shaken, the maximum impulsive effect as exhibited by the actual destruction on the surface may not be immediately above the origin where buildings have simply been lifted vertically up and down, but at some distance from this point, where the impulsive effort has been more oblique. At the _epicentrum_ we have the maximum of the true intensity as measured by the acceleration of a particle, or the height to which a body might be projected, but it will be at some distance from this where we shall have the maximum intensity as exhibited by an overturning effort. This will be rendered clear by the following diagram. In the accompanying diagram let O be the origin of a shock, and O C the seismic vertical equal to _r_. Let the direct or normal shock emerge at C, C_{1}, C_{2}, and at the angles θ_{1}, θ_{2}, &c. Assuming that the displacement of an earth particle at C equals C B, and at C_{1} equals _c__{1} _b__{1}, and at C_{2} equals _c__{2} _b__{2}, &c., and let these displacements C B, _c__{1} _b__{1}, _c__{2} _b__{2}, &c., for the sake of argument, vary inversely as _r_, _r__{1}, _r__{2}, &c. [Illustration: FIG. 9.] The question is to determine where the horizontal component C A of these normal motions is a maximum. First observe that the triangle O C _c_ is similar to _a_, _b_, _c_. _h_ Also _r_ = —————, and therefore the normal component _c__{1} sin θ sin θ _b__{1} at C_{1} is equal to C —————. _h_ Also _c__{1} _a__{1} = _c__{1} _b__{1}, cos θ. sin θ cos θ _c_ sin 2θ ∴ C_{1} _a_ = C ———————————— = ———— ∙ ———————, _h_ _h_ 2 and sin 2θ is greatest when 2θ = 90° or θ = 45°. That is to say, the horizontal component reaches a maximum where the angle of emergence equals 45°. This question has been discussed on the assumption that the amplitude of an earth particle varies inversely as its distance from the origin of the shock. Should we, however, assume that this amplitude varies inversely as the square of the distance from the origin, we are led to the result that the area of greatest disturbance is nearer to the point where the angle of emergence is 55° 44′ 9″. Both of these methods are referred to by Mallet, but the first is considered as probably the more correct.