Whatever method is adopted it would be advantageous that the losses of pressure in the pipes connecting the compressors with the motors should be reduced as much as possible, for in this case that loss would represent a loss of efficiency. If, on the other hand, owing to defective means of reheating, it is necessary to remain satisfied with a small amount of expansion, the loss of pressure in the pipe is unimportant, and has only the effect of transferring the limited expansion to a point a little lower on the scale of pressures. If W is the net disposable force on the shaft of the engine which works the compressor, v1 the volume of air at the compressor, p1. given by the compressor, and at the temperature of the surrounding air, and p0 the atmospheric pressure, the efficiency of the compressor, assuming the air to expand according to Boyle's law, is given by the well-known formula-- p1 v1 log (p1 / p0) -------------------. W [TEX: \frac{p_1 v_1 \log \frac{p_1}{p_0}}{W}] Let p2 be the value to which the pressure is reduced by the loss of pressure at the end of the conduit, and v2 the volume which the air occupies at this pressure and at the same temperature; the force stored up in the air at the end of its course through the conduit is p2 v2 log(p2/p0); consequently, the efficiency of the conduit is p2 v2 log(p2/p0) ---------------- p1 v1 log(p1/p0) [TEX: \frac{p_2 v_2 \log\frac{p_2}{p_0}}{p_2 v_2 \log\frac{p_2}{p_0}}] a fraction that may be reduced to the simple form log(p2/p0) ----------, log(p1/p0) [TEX: \frac{\log\frac{p_2}{p_0}}{\log\frac{p_2}{p_0}}] if there is no leakage during the passage of the air, because in that cause p2 v2 = p1 v1. Lastly, if W1 is the net disposable force on the shaft of the compressed air motor, the efficiency of this engine will be, W1 ---------------- p2 v2 log(p2/p0) [TEX: \frac{W_1}{p_2 v_2 \log \frac{p_2}{p_0}}] and the product of these three partial efficiencies is equal to W1/W, the general efficiency of the transmission. III. _Transmission by Pressure Water_.--As transmission of power by compressed air has been specially applied to the driving of tunnels, so transmission by pressure water has been specially resorted to for lifting heavy loads, or for work of a similar nature, such as the operations connected with the manufacture of Bessemer steel or of cast-iron pipes. The author does not propose to treat of transmissions established for this special purpose, and depending on the use of accumulators at high pressure, as he has no fresh matter to impart on this subject, and as he believes that the remarkable invention of Sir William Armstrong was described for the first time, in the "Proceedings of the Institution of Mechanical Engineers." His object is to refer to transmissions applicable to general purposes.