Consider the force F(h) between two identical spheres of radius R as an illustration. The surfaces of the two respective spheres are thought to be sliced into infinitesimal disks of width dr and radius r as shown in the figure. The force is given by the sum of the corresponding swelling pressures between the two disks 
where x is the distance between the disks and dA the area of one of these disks. This distance can be expressed as x=h+2y. By considering the Pythagorean theorem on the grey triangle shown in the figure one has
Expanding this expression and realizing that y ≪ R one finds that the area of the disk can be expressed as 
The force can now be written as 
where W(h) is the surface free energy per unit area introduced above. When introducing the equation above, the upper integration limit was replaced by infinity, which is approximately correct as long as h ≪ R.