The electrochemical double layer is an important practical and theoretical problem. Generally speaking, experiment gives valuable information about quantities, such as potential differences, that involve integrals of density and charge profiles but does not provide direct information about the profiles themselves. Computer simulations have given numerical information about these profiles. However, explicit expressions are useful in understanding these data. For some years an exact expression has been known for the contact value of total density profile of the ions in the double layer but, until recently, an expression for the contact value of the more important charge profile has been lacking. A few years ago, a semi-empirical local result for the charge profile, valid at low electrode charge, was proposed and, very recently, extended to higher electrode charge. This expression contains a parameter; the effect of variations in this parameter is explored in this paper and the result is compared with a large set of simulation data for the contact values of various profiles that we have accumulated in the past few years. The agreement of the semi-empirical expression with our simulation results is excellent. The best values for this parameter are fairly close to the value suggested by theory.