The long range charge density (Friedel) oscillations around an adsorbed atom give rise to an adatom-adatom interaction. It is argued, that this indirect electronic interaction is the most important one in many cases for determining the structure of an adsorbed layer at less than full coverage and not too large temperatures. For this reason, the Friedel oscillations around an adatom are investigated. A new analytical asymptotic expression for these oscillations, which reduces to the one for the bulk when the adatom is far inside the surface, is compared with an earlier one without this property as well as with the results of a self-consistent purely numerical calculation. It is found that the new expression, but not the earlier one, is in good agreement with the numerical calculation as shown by results for H on several jellium surfaces. As an illustration, the new expression is used to discuss the LEED pattern from H on some transition metal surfaces. © 1979.