A comparison of the X-ray properties and the Sunyaev-Zel'dovich effect for a cluster of galaxies may be used to measure the distance of the cluster, and hence the Hubble constant. We have applied this method to the rich cluster Abell 665 using IPC, HRI, and MPC data from the Einstein Observatory, LAC data from the Ginga satellite, and Sunyaev-Zel'dovich data from the OVRO 40 m telescope. The X-ray and Sunyaev-Zel'dovich effect data are consistent in their description of the cluster gas and may be fitted by a simple isothermal beta-model with beta almost-equal-to 0.66, cluster core radius almost-equal-to 1.6, and gas temperature almost-equal-to 8.2 keV. The relative normalizations of the X-ray and Sunyaev-Zel'dovich effect data then lead to an estimated Hubble constant H0 = 40 +/- 9 km s-1 Mpc-1 if only the random errors are included. When the possible systematic errors (which are most important if they are present in the Sunyaev-Zel'dovich data) are added in quadrature, the range of possible values of the Hubble constants expands to (40 to 50) +/- 12 km s-1 Mpc-1. The most immediate improvements in the error in this estimate for the Hubble constant would be produced by setting better limits on the zero level of the Sunyaev-Zel'dovich effect data (involving extensive observation), and by improved X-ray observations of the cluster, possibly with ROSAT, Astro-D, and AXAF. However, systematic errors associated with the unknown detailed thermal and density structures of the gas (clumping and low-surface brightness structures) provide limits to the accuracy of the method in principle.
