Ultrathin films of Sn have been grown incrementally on substrates held at 15 K and then studied in situ at low temperatures. This process of repeatedly increasing the thickness of a film facilitates the investigation of thickness-dependent physical properties. The superconducting transition temperature has been found to oscillate with a period which was nominally about 4. The latter is approximately a factor of 2 larger than the prediction of simple theoretical models. Oscillations of the normal-state resistance with thickness have not been observed.