The variation of electrical resistivity of thin rectangular, single crystal films of 99.9999% gallium has been investigated from 1.1° to 20°K, as a function of crystalline orientation, for thicknesses between 40 and 250 µ. As long as the ratio of the thickness to the average bulk mean free path ≪1, the ideal resistivity is proportional to a power which depends on the orientation of the film and which varies betweenT 3 andT 1.5 . It is argued that the strongT 2 term, found in the bulk resistivity at low temperatures, is not a consequence of electron-electron collisions, but is caused by an averaging, over the entire Fermi surface, of temperature dependences which are different for different regions because of Umklapp scattering. For the thinnest specimens size effects are appreciable up to 15°K, but there is both quantitative and qualitative disagreement between our results and the theoretical calculations of Fuchs, which are for an idealized metal. Attempts are made to show that a change in the nature of the bulk scattering mechanisms can be deduced by comparing our data with Fuch's predictions.