We analyze methanol excitation in the absence of external radiation andconsider LTE methods for probing interstellar gas. We show that rotationdiagrams correctly estimate the gas kinetic temperature only if they are builtfrom lines with the upper levels located in the same K-ladders, such as theJ_0-J_{-1}E lines at 157~GHz, the J_1-J_0E lines at 165~GHz or the J_2-J_1Elines at 25~GHz. The gas density should be no less than 10^7~cm^{-3}. Rotationdiagrams built from lines with different K values of the upper levels (2_K-1_Kat 96~GHz, 3_K-2_K at 145~GHz, or 5_K-4_K at 241~GHz) significantlyunderestimate the temperature but allow a density estimation. In addition, thediagrams based on the 2_K-1_K lines make possible methanol column densityestimates within a factor of about 2--5. We suggest that rotation diagramsshould be used in the following manner. First, one should build two rotationdiagrams, one from the lines at 96, 145, or 241~GHz, and another from the linesat 157, 165, or 25~GHz. The former diagram is used to estimate the gas density.If the density is about 10^7~cm^{-3} or higher, the latter diagram reproducesthe temperature fairly well. If the density is around 10^6~cm^{-3}, thetemperature obtained from the latter diagram should be multiplied by a factorof 1.5--2. If the density is about 10^5~cm^{-3} or lower, then the latterdiagram yields a temperature that is lower than the kinetic temperature by afactor of three or larger and should be used only as a lower limit on thekinetic temperature. Errors of methanol column density determined from theintegrated intensity of a single line may be larger than an order of magnitudeeven when the gas temperature is well-known. However, if the J_0-(J-1)_0Elines, as well as the J_1-(J-1)_1A^{+} or A^{-} lines are used, the relativeerror of the column density proves to be no larger than several units.
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