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General asymptotic formulas are given for the coefficient $C_\ell$ of theterm of multipole number $\ell$ in the temperature correlation function of thecosmic microwave background, in terms of scalar and dipole form factorsintroduced in a companion paper. The formulas apply in two overlapping limits:for $\ell\gg 1$ and for $\ell d/d_A\ll 1$ (where $d_A$ is the angular diameterdistance of the surface of last scattering, and $d$ is a length, of the orderof the acoustic horizon at the time of last scattering, that characterizesacoustic oscillations before this time.) The frequently used approximation that$C_\ell$ receives its main contribution from wave numbers of order $\ell/d_A$is found to be less accurate for the contribution of the Doppler effect thanfor the Sachs--Wolfe effect and intrinsic temperature fluctuations. For $\elld/d_A\ll 1$ and $\ell\geq 2$, the growth of $C_\ell$ with $\ell$ is shown to beaffected by acoustic oscillation wave numbers of all scales. The asymptoticformulas are applied to a model of acoustic oscillations before the time oflast scattering, with results in reasonable agreement with more elaboratecomputer calculations.Comment: 16 pages, one inessential figure. Improved treatment of damping in  companion paper used here in calculations, reference added, minor corrections  and changes made. Accepted for publication in Phys. Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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