Abstract: The Fuel characteristic coefficient is for the first time found to be representing a group of dehydration lines focusing in H2O on zero carbon line in the C-H-O triaxial diagram of carbohydrates. Through the application of the Fuel characteristic coefficientβ' in the C-H-O triaxial diagram, a group of decarboxylation lines focusing in CO2 on zero- hydrogen: line and a group of demethanation lines focusing in CH4 on zero oxyger line are also found out on the diagram. There exists very important definite relationship between the Iso-β dehydration lines and the decarboxylation lines and also between the lso-β' dehydration lines and the demethanation lines. Examples to show the relationship are given in this paper. Through the application of the Fuel Characteristic coefficient in the C-H-O triaxia jdiagram, The molecular structure of any carbohydrate on any Iso-β' line can be estimated from any known carbohydrate compound on the same Iso-β' line. As the Fuel characteriatic coefficient V represent the quality index of any combustible, minerels including coal as proved in the two previous papers, it can be used as one of the coordinates with Vr or Cr to classify all the combustibe Minerals as shown in graph-3.