Moreover, these results would appear to indicate a different law from that which is expressed by the formula b1 u², as is easy to see by representing them graphically. It would be very desirable that fresh experiments should be made on water pipes at high pressure, and of various diameters. Of machines worked by water pressure the author proposes to refer only to two which appear to him in every respect the most practical and advantageous. One is the piston machine of M. Albert Schmid, engineer at Zurich. The cylinder is oscillating, and the distribution is effected, without an eccentric, by the relative motion of two spherical surfaces fitted one against the other, and having the axis of oscillation for a common axis. The convex surface, which is movable and forms part of the cylinder, serves as a port face, and has two ports in it communicating with the two ends of the cylinder. The concave surface, which is fixed and plays the part of a slide valve, contains three openings, the two outer ones serving to admit the pressure water, and the middle one to discharge the water after it has exerted its pressure. The piston has no packing. Its surface of contact has two circumferential grooves, which produce a sort of water packing acting by adhesion. A small air chamber is connected with the inlet pipe, and serves to deaden the shocks. This engine is often made with two cylinders, having their cranks at right angles. The other engine, which is much less used, is a turbine on Girard's system, with a horizontal axis and partial admission, exactly resembling in miniature those which work in the hydraulic factory of St. Maur, near Paris. The water is introduced by means of a distributer, which is fitted in the interior of the turbine chamber, and occupies a certain portion of its circumference. This turbine has a lower efficiency than Schmid's machine, and is less suitable for high pressures; but it possesses this advantage over it, that by regulating the amount of opening of the distributer, and consequently the quantity of water admitted, the force can be altered without altering the velocity of rotation. As it admits of great speeds, it could be usefully employed direct, without the interposition of spur wheels or belts for driving magneto-electric machines employed for the production of light, for electrotyping, etc.