The spectra of two quasi-stellar radio sources, 3C 48 and 3C 273, have been studied in detall. We present as full conclusions as we can derive from the redshift, luminosity, emission-line, and continuous spectra. Together with the radio-frequency data and the light variability, these indicate the presence of very large total energies in a relatively small volume of space. We deliberately have not attempted to discuss the origin of these large energies, nor do we discuss the numerous other physical problems concerned with suggested mechanisms in the quasi-stellar objects. We first consider other explanations for the large redshifts, in particular the possibility of gravitational redshift. The presence of relatively narrow emission lines excludes objects near 1 M0 which are stable because of the small emitting volume. The presence of forbidden lines sets an upper limit to the gas density. Together with a limit to gravitational perturbations on our Galaxy, this leads to a lower limit of 10 M0, condensed to a 1017-cm radius. Whether such large masses can be even quasi-stable has not yet been demonstrated. We then adopt the interpretation that the redshifts are cosmological in origin. The absolute visual magnitudes are about - 26 for 3C 273 and - 25 for 3C 48. The forbidden lines of high ionixation potential are quite strong in 3C 48 relative to hydrogen. By analogy with planetary nebulae and assuming normal abundances, with astrophysical details given in the appendices, we derive the electron density, N , probably near to or less than 3 X 10 cm-3 the electron temperature is not very high, and the mass is about 5 X 106 M0 within a radius of 10 pc or more. The emitting volumes are obtained from N and the observed luminosity in H and Mg U. The forbidden lines and the Balmer lines are optically thin, but Mg ii is optically thick, leading to discussions in the appendices. For 3C 273, in which the forbidden lines are weaker, the surprising weakness of [0 ii] permits a closer estimate of N near 3 X 106 and a mass of 6 X 106 M0 within a radius of about 1 pc. The light variations observed in both, with cycles of 10 years or less, suggest the presence of a source of optical continuum with a diameter of 1 pc, possibly much less. We urgently need continued observations of the absolute intensities of lines and continuum and their variations. The thermal energy supply in the H ii region is small. The ionized gas must be of low density in the region in which the radio frequencies are generated, because of free-free absorption and Faraday rotation, i.e., N < 10 if R = 500 pc for the radio source. We explore models for synchrotron generation of radio and optical frequencies. If R = 500 pc, total energies required for radio emission are relatively low, about 10i erg at equipartition. The lifetimes for exhausting the total energy supply are about 106 years. If we wish to obtain optical synchrotron from the same volume as produces radio frequencies, the equipartition energy reaches 1058 erg. H optical synchrotron radiation is to arise within a volume 1 pc3, however, the total energy is small, 10i erg, the life about a year, and serious problems arise, such as cosmic-ray proton collisional loss, and inverse- Compton effect electron loss. Models for the jet radio source 3C 273A offer no particular difficulty. We review conditions under two possible age estimates of the inner components of the quasi-stellar objects. At 10 years, the object can be in expansion, with a velocity compatible with the emission- line width, about 1000 km/sec. The energy supply is sufficient for the radio spectrum, and the kinetic energy of the H II region is nearly enough to maintain the optical emission. On this hypothesis, the jet in 3C 273 and the nebular wisps in 3C 48, which are 150000 light-years in size, must have onginated in a separate event. If the age is 106 years, the H U region energy is much too small; in addition, its small radius and large internal motion would need to be stabilized by a gravitational mass near 10 M0, inside the H ii region. The radiated energy in 106 years is near 106 erg, so that nuclear-energy sources of 10 M0 are required. The simplest model of the quasi-stellar sources is one in which a small mass of 10 M0 is surrounded by shells of increasing radius in which the optical continuum, the emission lines, and the radio continuum, respectively, originate. The relation of these objects to the most intense radio galaxies is unclear. The quasi-stellar sources have small optical size, a high ratio of optical to radio emission, and an optical luminosity so high that, if their age exceeds 1000 years, continued input of energy is required from some not directly observable source. Table 11 gives a brief of numerical results.