The contact angle that a liquid drop makes on a soft substrate does not obey
the classical Young's relation, since the solid is deformed elastically by the
action of the capillary forces. The finite elasticity of the solid also renders
the contact angles different from that predicted by Neumann's law, which
applies when the drop is floating on another liquid. Here we derive an
elasto-capillary model for contact angles on a soft solid, by coupling a
mean-field model for the molecular interactions to elasticity. We demonstrate
that the limit of vanishing elastic modulus yields Neumann's law or a slight
variation thereof, depending on the force transmission in the solid surface
layer. The change in contact angle from the rigid limit (Young) to the soft
limit (Neumann) appears when the length scale defined by the ratio of surface
tension to elastic modulus γ/E reaches a few molecular sizes
