The sawtoothlike emission current (STEC) method and its theory are described, and this method is shown to make possible the simultaneous measurement of the time variation of the work function phi(t) and its derivative dphi/dt. Application of the STEC method to the field emission (FE) current from a tungsten emitter tip in an ultra-high vacuum of 2 X 10(-8) Pa shows that the time variation of phi(t) and dphi/dt can be divided into four stages. In addition, it gives the effective tip radius alphar(0) = 1.1 mum, resulting in alpha = 6.9 for the observed tip radius r(0) = 0.16 mum. The observed time variation of phi(t) and dphi/dt is analyzed from the viewpoint of the development of the adsorption of residual gas molecules on the emitter tip surface, and each stage is successfully identified as follows: The first stage is the formation stage of adsorption nuclei and clusters, the second stage is the free growth stage of adsorption islands, the third stage is their coalescence growth stage, and the fourth stage is their Langmuir growth stage. The mode of adsorption development is similar to the mode of crystal growth taking place in three-dimensional space and on surface.