We present a comprehensive study of the physical and chemical conditio
ns along the TMC-1 ridge. Temperatures were estimated from observation
s of CH3CCH, NH3, and CO. Densities were obtained from a multitransiti
on study of HC3N. The values of the density and temperature allow colu
mn densities for 13 molecular species to be estimated from statistical
equilibrium calculations, using observations of rarer isotopomers whe
re 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 t
he 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 r
elative abundance peak. In contrast, the well-studied cyanopolyyne pea
k is most likely due to an enhancement in the abundance of long-chain
carbon species. Comparisons of the derived abundances to the results o
f time-dependent chemical models show good overall agreement for chemi
cal timescales around 10(5) yr. We find that the observed abundance gr
adients can be explained either by a small variation in the chemical t
imescale 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.