Equation of _vis viva_, and transmission of work in machines, account being taken of the different causes of power and resistance. Physical constitution of machines; _receiver_, _communicators_, and _operator_. Influence of the weights, of frictions, of shocks, and any changes in the _vis viva_. Parts with continuous or uniform motion, with alternating or oscillating motion. Laws of the motion on starting from rest, and when the stationary condition is established. The positions to which the maximum and minimum of the _vis viva_ correspond are those in which there is equilibrium between all the forces, exclusive of the forces of inertia. Advantage of uniform or periodic motion. General methods for regulating the motion; symmetrical distribution of the masses and strains; flys and various regulators. Brakes and moderators; their inconveniences. Object and real advantages of machines. LESSONS 27-35. _Hydraulic Wheels._ Vertical wheels with float-boards, with curved ladles, and with spouts. Figure of the surface of the fluid in these latter. Horizontal wheels working by float-boards, buckets, and reaction. Turbines. Description, play, and useful effects compared according to the results of experiment. Vertical wheels of windmills and steamboats. Screw propeller. _Windmills._ Description. Result of Coulomb’s observations. _On the principal kinds of Pumps._ Special organs of pumps. Valves and pistons, force pump, sucking pump; limit to the rise of the water. Sucking and force pump. Dynamical effects. Indication as to the losses of _vis viva_ and the waste in different pumps. Explanation of the hydraulic ram. Air vessel. Fire pumps. Double action pumps. _Various Hydraulic Machines._ Hydraulic press. Water engine. Exhausting machines; _norias_; under and overshot wheels; Archimedes’ screw, construction and experimental data. LESSONS 36-39. _Steam Engines._ Succinct description of the principal kinds of steam-engine with or without detent. Effects and advantages of the detent. Condenser. Air Pump. Furnace and feeding-pump. Variable detent. Formulæ and experimental results. LESSONS 40-42. _Revision._ Reflections on the totality of the subjects of the course. IV. PHYSICS.--_FIRST YEAR._ GENERAL PROPERTIES OF BODIES.--HYDROSTATICS.--HYDRODYNAMICS. LESSONS 1-5. _Preliminary Notions._ Definitions of physics. Phenomena. Physical laws. Experiments are designed to make them spring out of the phenomena. Method of induction. Physical theories; different character of the experimental and mathematical methods. _General Properties of Bodies._ Extension. Measure of lengths. Vernier. Cathetometer. Micrometer screw. Spherometer. Dividing engine. Divisibility. Porosity. Ideas generally received on the molecular constitution of bodies. These conceptions, which are purely hypothetical, must not be confounded with physical laws. Elasticity. Mobility. Inertia. Forces; their equilibrium, their effects, their numerical estimation. _Weight or Gravity._