chronology (tree-ring history) whose dates are known. A fully anchored and cross-matched chronology for oak and pine in central Europe extends back 12,460 years, and an oak chronology goes back 7,429 years in Ireland and 6,939 years in England. Comparison of radiocarbon and dendrochronological ages supports the consistency of these two independent dendrochronological sequences. Another fully anchored chronology that extends back 8,500 years exists for the bristlecone pine in the Southwest US (White Mountains of California). Dendrochronological equation The dendrochronological equation defines the law of growth of tree rings. The equation was proposed by Russian biophysicist Alexandr N. Tetearing in his work "Theory of populations" in the form: where ΔL is width of annual ring, t is time (in years), ρ is density of wood, kv is some coefficient, M(t) is function of mass growth of the tree. Ignoring the natural sinusoidal oscillations in tree mass, the formula for the changes in the annual ring width is: where c1, c2, and c4 are some coefficients, a1 and a2 are positive constants. The formula is useful for correct approximation of samples data before data normalization procedure. The typical forms of the function ΔL(t) of annual growth of wood ring are shown in the figures. Sampling and dating Dendrochronology allows specimens of once-living material to be accurately dated to a specific year. Dates are often represented as estimated calendar years B.P., for before present, where "present" refers to 1 January 1950. Timber core samples are sampled and used to measure the width of annual growth rings; by taking samples from different sites within a particular region, researchers can build a comprehensive historical sequence. The techniques of dendrochronology are more consistent in areas where trees grew in marginal conditions such as aridity or semi-aridity where the ring growth is more sensitive to the environment, rather than in humid areas where tree-ring growth is more uniform (complacent). In addition, some genera of trees are more suitable than others for this type of analysis. For instance, the bristlecone pine is exceptionally long-lived and slow growing, and has been used extensively for chronologies; still-living and dead specimens of this species provide tree-ring patterns going back thousands of years, in some regions more than 10,000 years. Currently, the maximum span for fully anchored chronology is a little over 11,000 years B.P. IntCal20 is the 2020 "Radiocarbon Age Calibration Curve", which provides a calibrated carbon 14 dated sequence