The paper describes three unexpected phenomena which were observed dur
ing studies of the vapour adsorption onto solids. A quadratic variatio
n of the adsorption of water onto borosilicate glass is found at low p
ressures. Water films condensed onto mica start to conduct electricity
at a thickness of almost exactly one monolayer, with fluctuations in
the conductivity in the region of onset. Diffusion through a backgroun
d atmosphere slows the adsorption process and asymetrical fluctuations
in thickness are observed.