Drops at rest on a tilted plane

A liquid drop on a tilted plate can remain at rest, provided that an hysteresis for the contact angle exists. We examine in this paper the case of small contact angle hysteresis, for which the drops are found to be nearly spherical caps, despite the slope. We derive in particular the condition (both in angle and hysteresis) under which the drop remains stuck on the surface: a simple model is proposed and compared with experimental data.