Spectroscopic measurements of Mira variable stars, as a function of phase, probe the stellar atmospheres and underlying pulsation mechanisms. Modeling the atmospheres is difficult due to the hydrodynamic nature of the gas as deduced from the large light variations and velocity measurements of various spectral lines. Many questions still need to be resolved concerning the atmospheres of these stars. Are the depths of formation of the molecular species such as TiO, VO, and ZrO produced in an extended region above the layers where Balmer line emission occurs or below this shocked region? What is the explanation for the Balmer-line increment, where the strongest Balmer line at phase zero is Hδ and not Hα? Furthermore, why is the H∊ line virtually absent in the spectra of Miras when the other Balmer lines are strong? A new program of low resolution (1.08 Å/pixel) spectroscopy from about 6000Å to 8750Å is presented in this paper. The spectra are taken in a region which includes Hα, TiO, VO, ZrO, and the Ca II infrared (IR) triplet. Spectra of nine Mira variables are presented. Seven Mira variable stars (o Cet [Mira], U Ori, R Leo, V CVn, R CVn, V Boo, and χ Cyg) were observed at more than one phase. Two other Mira variables (R Tri and R Gem) were observed at a single phase, but both show strong Hα emission. In this paper, we investigate the final question listed above by noting variations in the Ca II IR triplet in relationship with Hα variations as a function of phase. These preliminary observations suggest that H∊'s observational characteristics result from an interaction of H∊ photons with the Ca II H line.