This thesis deals with electrical conductivity in thin films. Classical and quantum size effects in conductivity are discussed including some experimental evidence of quantum size effects. The component conductivity along the applied electric field of a thin film in a transverse magnetic field is developed in a density matrix method.

Electron densities and collision frequencies were obtained on a number of gases in a dc discharge at low pressures (0.70-2mm of Hg). These measurements were performed by microwave probing of a filament of the dc discharge placed coaxially in a resonant cavity operating in a TM₀₁₀ mode. The equipment and techniques for making the microwave measurements employing the resonant cavity are described. One of the main features of this investigation is the technique of differentiating the resonance signal of the loaded cavity in order to make accurate measurements of the resonant frequency and half-power point frequencies.