Abstract: In order to quantify the results of geochemical effect of lanthanides discovered previously,the geochemical behaviors of lanthanides of five different types coal ( including gas coal,fat coal,coking coal,lean coal and meagre coal) from No. 8 coal seam,Shanxi Province,China,were investigated by the regression analysis between the trivalent ionic radii of lanthanides and their geochemical behaviors. Then the regression equation of geochemical effect of lan- thanides was put forward. According to the preliminary results deducted by the author,this equation can reflect the mathematical relationship among any quantified geochemical or other chemical behaviors of lanthanides,the trivalent ionic of lanthanides radii,and the mathematical relationship between ∑REE and LREE / HREE in any geological body. Among these studies, the slop of liner regression equation is always positive correlation with the concentration of ∑REE and the power exponent of power function is significant positive with the differentiation extent of LREE and HREE. The goodness of fit of the regression equation may be associated with the degree of some thermodynamic equi- librium during the natural evolution and metamorphism of the geological body,and with the existing state and chemical properties of the lanthanides. However,how the evolution or metamorphism direction affects the goodness of fit is un- clear. Usually,the degree of thermodynamic equilibrium of LREE is always higher than that of HREE in the same evo- lution or metamorphism process, but sometimes on the contrary, and the scientific significance is not clear. If the process is artificially-intervened and rapid (e. g. ,the acid removal rate of lanthanide elements in coal),the thermody- namic equilibrium is hard to reach because it is far away from sufficient natural evolution. At this moment,the good- ness of fit is relatively low although the regression equation is available.