Method for measuring the density of a fluid medium to be investigated flowing through a tube or located in a tube, - wherein the fluid medium to be investigated is conducted into a tube section of a tube bent into a U-shape, the legs of which are clamped so as to be able to vibrate, wherein a natural frequency or resonant frequency of the tube is excited and determined in the region of the tube section, - wherein the density of the medium to be investigated is determined on the basis of the determined natural frequency or resonant frequency from the predetermined relationship between the density of fluid media and the period duration P of the natural frequency, and - wherein the density (pO) is determined and made available at a time point t 0 by a rule according to equation 1: ρ=AP 2 - B for determining the density in advance at least in a two-point adjustment method by determining the adjustment constants A, B, wherein - before performing the measurement at a time point t 1 a test measurement is carried out, in which - the tube is filled or flowed through with a reference medium of known density, - while the reference medium is in the tube or flows through it, the natural frequency or resonant frequency of the clamped, filled tube section is determined, - the density (ρ Ref) determined at time point t0 by the rule according to equation 1: equation ρ= AP 2 - B_for calculating the density of the reference medium is compared with the actual density (ρ' Ref) of the reference medium determined in the test measurement at time point t1 by the predetermined rule according to equation 3 p'= AP '2 - B, - in the event of a deviation of the determined density (ρ Ref) of the reference medium from the actual density (ρ Ref) of the reference medium a corrected period duration for obtaining a correct density value is determined and a correction factor (c') according to equation 8: c'= P'Med/ P'ref is derived therefrom for the actual period duration, - the correction factor (c') determined in this way is applied for correction to the further period durations determined for any medium to be investigated, and - the density of the medium to be investigated is determined by the originally determined adjustment constants A, B using these corrected period durations. - wherein the fluid medium to be investigated is conducted into a tube section of a tube bent into a U-shape, the legs of which are clamped so as to be able to vibrate, wherein a natural frequency or resonant frequency of the tube is excited and determined in the region of the tube section, - wherein the density of the medium to be investigated is determined on the basis of the determined natural frequency or resonant frequency from the predetermined relationship between the density of fluid media and the period duration P of the natural frequency, and - wherein the density (pO) is determined and made available at a time point t 0 by a rule according to equation 1: ρ=AP 2 - B for determining the density in advance at least in a two-point adjustment method by determining the adjustment constants A, B, wherein - before performing the measurement at a time point t 1 a test measurement is carried out, in which - the tube is filled or flowed through with a reference medium of known density, - while the reference medium is in the tube or flows through it, the natural frequency or resonant frequency of the clamped, filled tube section is determined, - the density (ρ Ref) determined at time point t0 by the rule according to equation 1: equation ρ= AP 2 - B_for calculating the density of the reference medium is compared with the actual density (ρ' Ref) of the reference medium determined in the test measurement at time point t1 by the predetermined rule according to equation 3 p'= AP '2 - B, - in the event of a deviation of the determined density (ρ Ref) of the reference medium from the actual density (ρ Ref) of the reference medium a corrected period duration for obtaining a correct density value is determined and a correction factor (c') according to equation 8: c'= P'Med/ P'ref is derived therefrom for the actual period duration, - the correction factor (c') determined in this way is applied for correction to the further period durations determined for any medium to be investigated, and - the density of the medium to be investigated is determined by the originally determined adjustment constants A, B using these corrected period durations.