Energy exchange processes occurring at microprojections on a cathode surface are analysed, and expressions are obtained for the critical current necessary to produce thermal instability in projections of different geometries leading to a vacuum arc. The effect of energy transfer due to lattice electrons (Nottingham effect) is included in the analysis, and it is found that when this effect is included the critical current decreases by a factor of 2·8 in the case of a conical microprotrusion and by a factor of 1·2 in the case of a cylindrical microprotrusion.