The aim of the paper is to obtain as accurate a solution as possible to problems arising in the transmission of superheated steam over long distances for ( a) industrial heating and ( b) power generation. After a general survey, with a description of two typical installations, the problem is discussed under headings ( a) and ( b), and the usual practice in fixing steam velocities is given. The present state of knowledge of radiation losses is reviewed; first, the standard English practice of using a coefficient based on the pipe surface and varying with the thickness of the insulating material; and second, the method, used mainly in America, which involves conductivity coefficients. The effect of air currents on heat loss is investigated and a new equation is deduced for the equivalent velocity past the pipe, due to natural convection. Standard formulæ for the coefficient of friction and the viscosity of steam are discussed; for the former a new formula of the rectangular hyperbola type is derived from Carnegie's results and corrected for roughness. Steam viscosity is considered in the light of Speyerer's and Sigwart's investigations; curves of Sigwart's results are plotted on a convenient base of logarithms of pressures. Conditions during flow in a horizontal straight pipe with perfect insulation are considered and new equations, simplifying the problem, are derived from the fundamental equations. The author treats from a new viewpoint the problem of power transmission by steam over long distances, based on the loss of available Rankine heat drop. Numerical examples are worked out, as also is the effect of air currents on the coefficient of heat loss. Finally the limiting factors, including the effect of radiation losses, in the long-distance transmission of steam are analysed and their practical importance is discussed.