This thesis is concerned with the determination of the ratio of transition probabilities of two nearby but different upper energy levels in neon. A theory is developed from consideration of the processes, especially collisional transfer of energy between levels, occurring in a neon gas discharge. This gives an expression for the ratio of the two transition probabilities as a function of the pressure of the gas. A helium-neon gas laser oscillating at 3.39 μ is then used to influence the population densities of two adjacent upper levels in an isolated neon gas discharge. The resulting population perturbations are observed as changes in intensity of the light emitted by a downward transition from each of these levels, specifically the 3s₅→2P₉, 6182Å transition and the 3s₄→2P₈, 6213Å transition. This confirms the existence of collisional energy transfer, and allows the ratio of the two transition probabilities to be measured. The value obtained is A₆₁₈₂ Å/A₆₂₁₃ Å = 2.18 ± .24, where A represents the transition probability and the subscript is the wavelength.