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we denote by 0 and 0' the points on bodies 1 and 2 for which the separation distance is least and let H be this distance of closest approach.An axis system is erected on 0 with the z axis along the inward normal to body 1 and the(x,y)plane as shown in Fig.4.The orientation of the xy axis system in this plane we will specify shortly.The bodies are assumed smooth and quadratically curved in the neighbourhood of 0 and 0'.

when dealing with interactions between macrobodies,it is often the case that the range of the interaction is such that the two bodies do not interact significantly until the distance of closest approach is small compared to the radii of cuvarture of the bodies.Under these circumtances,a very useful approximate expression for theinteraction energy per unit area of plane parallel half-spaces.The approximation is due,originally,to Deryaguin(1934)

Consider an element of area dS at the point P(x,y,z)on the surface of body 1.Provided the radii of curvature of bodies 1 and 2 are large compared to the separation distance H,then the area element can be approximately regarded as a surface element of a plane half-space with the properties of body 1 parallel to and separated a distance D(see fig.4)from another planar half-space with the properties of body 2.If E(D) the energy per unit area of half-space 1 interacting with the half-space 2,then,in this approximation,dV=E(D)dS is the interaction energy of the area element dS of body 1 with body 2.