Photometry and spectroscopy of a sample of the brightest cluster galaxies (BCGs) are presented, and the relationships between scale length, surface brightness, velocity dispersion, and line strength are determined and compared with the relations determined for lower luminosity ellipticals (LLEs). It is found that the relation between log r(e), log sigma, and mean surface brightness reported by Dressler et al. for LLEs also describes the relation for BCGs fairly well. Fundamental plane solutions for BCGs are derived which can be used as distance indicators with a predicted error of about 21 percent per galaxy. Only a weak correlation is found between the Na D 5893 line strength and velocity dispersion for BCGs, in contrast to the significant correlation between these quantities reported for LLEs. It is found that the mean mass-to-light ratio for BCGs is a factor of about two greater than for the LLEs in the Virgo and Coma sample of Dressler et al.