  We use Hubble Space Telescope (HST) and ground-based imaging to study the
multiple populations of 47 Tuc, combining high-precision photometry with
calculations of synthetic spectra. Using filters covering a wide range of
wavelengths, our HST photometry splits the main sequence (MS) into two
branches, and we find that this duality is repeated in the subgiant and
red-giant regions (SGB, RGB), and on the horizontal branch (HB). We calculate
theoretical stellar atmospheres for MS stars, assuming different chemical
composition mixtures, and we compare their predicted colors through the HST
filters with our observed colors. We find that we can match the complex of
observed colors with a pair of populations, one with primeval abundance and
another with enhanced nitrogen and a small helium enhancement, but with
depleted C and O. We confirm that models of RGB and red HB stars with that pair
of compositions also give colors that fit our observations. We suggest that the
different strengths of molecular bands of OH, CN, CH and NH, falling in
different photometric bands, are responsible for the color splits of the two
populations. Near the cluster center, in each portion of the color-magnitude
diagram (CMD) the population with primeval abundances makes up only ~20% of the
stars, a fraction that increases outwards, approachng equality in the outskirts
of the cluster, with a fraction ~30% averaged over the whole cluster. Thus the
second, He/N-enriched population is more concentrated and contributes the
majority of the present-day stellar content of the cluster. We present evidence
that the CMD of 47 Tuc consists of intertwined sequences of the two
populations, whose separate identities can be followed continuously from the MS
up to the RGB, and thence to the HB. A third population is visible only in the
SGB, where it includes ~8% of the stars.
