We note that the pressure inside the droplet exceeds the external pressure by an amount given by the Laplace equation, so that p 2 -p 1 = γ 12 /R, where R is the radius of the droplet. The above force balance then simplifies to γ s1 = γ s2 + γ 12 (1 -H/R). It follows from elementary Euclidean geometry that if the droplet profile is considered as an arc of a circle, the half-angle subtended by the 'footprint' of the droplet on the surface at the centre of this circle is equal to the contact angle as indicated in Fig. . This implies H = R(1 -cos θ), and so we recover the Young equation as given in Eq. (1) in the main text.