The linear dependence of Computed Tomography (CT) numbers on linear attenuation coefficients was investigated. CT numbers were fit to linear attenuation coefficients using the least squares method for energies from 55 to 80 keV. The variance was recorded. The energy representing the lowest variance was assumed to be the effective energy of the scanner. Six points were insufficient to unambiguously define the effective energy. Nine materials were used in all subsequent studies; unambiguous values were obtained. Linearity was determined as a function of field of view, phantom size from 10 cm to 30 cm diameter, and energy. Two plastics (polysulfone and acetal) are described which extend the linearity curve to 215 and 360 Houndsfield numbers respectively (scale is 1000). Practical applications were investigated.