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We present a comprehensive study of the physical and chemical conditions along the TMC-1 ridge. Temperatures were estimated from observations of CH3CCH, NH3, and CO. Densities were obtained from a multitransition study of HC3N. The values of the density and temperature allow column densities for 13 molecular species to be estimated from statistical equilibrium calculations, using observations of rarer isotopomers where possible, to minimize opacity effects. The most striking abundance variations relative to HCO+ along the ridge were seen for HC3N, CH3CCH, and SO, while smaller variations were seen in CS, C2H, and HCN. On the other hand, the NH3, HNC, and N2H+ abundances relative to HCO+ were determined to be constant, indicating that the so-called NH3 peak in TMC-1 is probably a peak in the ammonia column density rather than a relative abundance peak. In contrast, the well-studied cyanopolyyne peak is most likely due to an enhancement in the abundance of long-chain carbon species. Comparisons of the derived abundances to the results of time-dependent chemical models show good overall agreement for chemical timescales around 10(5) yr. We find that the observed abundance gradients can be explained either by a small variation in the chemical timescale from 1.2 x 10(5) to 1.8 x 10(5) yr or by a factor of 2 change in the density along the ridge. Alternatively, a variation in the C/O ratio from 0.4 to 0.5 along the ridge produces an abundance gradient similar to that observed.