Theoretical sequences of horizontal branch models, constructed using a new algorithm for the treatment of semiconvection, are described. The adopted composition parameters were chosen to bracket the ranges in metallicity and helium abundance appropriate to the globular cluster NGC 104 (47 Tucanae). By fitting the theoretical models to recent CCD photometry of the cluster, it is found that, on standard assumptions, its initial helium content must have been close to 24 percent by mass. In addition, best fits show that models for Fe/H = -0.65 provide an excellent match to the horizontal branch, if (m - M)v of about 13.44, and thereby yield consistency over the entire color-magnitude diagram of the cluster. This result reinforces the present age determination of about 13.5 Gyr for 47 Tuc. 44 refs.