In distribution networks, the power generated or consumed at the various busbars is usually known, together with the voltage of one busbar and a specification of how the system losses are supplied; the information most useful to the power engineer is a list of the corresponding current flows and voltages throughout the network.The paper sets out a technique for carrying out this work with an automatic digital computer, with special reference to programming devices which have been found useful. The work was done on the Manchester Universal Digital Computer, and information about speeds of computation of a typical example is given. The example chosen is a “closed loop” system—i.e. the product of the vector transformation ratios around any loop taken in a common direction is unity.