Formula for total Mechanical Effect per Minute of Steam when cut off at any proposed Part of the Stroke 514 Formulæ exhibiting the Relation between the Resistance of the Load, the Resistances of the Engine, the Evaporation, the Speed of the Piston, and the Magnitude of the Cylinder 515 Formulæ showing the Relation between the Power of the Engine, the Evaporation, and the useful Load 516 Formulæ for the _useful Effect_ and the _Duty_ 517 Estimates of the several Sources of Resistances 518 Tables to facilitate the Computation of the Effects of Expansive Engines 519 Table of the Areas of Pistons 520 EXAMPLES of the Application of these Formulæ 521 INDEX. 523 [Illustration: VIADUCT, NEAR WATFORD, BIRMINGHAM RAIL-ROAD.] [Pg001] THE STEAM ENGINE. [Pg003] [Illustration: HERO OF ALEXANDRIA.] CHAPTER I. THE STEAM ENGINE, A SUBJECT OF POPULAR INTEREST. — THE OBJECT OF THIS WORK. — DISPUTES RESPECTING THE INVENTION. — HERO. — DE GARAY. — DE CAUS. — BRANCA. — MARQUIS OF WORCESTER. — PHYSICAL PRINCIPLES. — ELASTIC AND INELASTIC FLUIDS. — THEIR PROPERTIES. — APPLICATION OF THESE PRINCIPLES TO THE ENGINES OF HERO, DE CAUS, AND LORD WORCESTER. — SIR SAMUEL MORLAND. — PAPIN. — ATMOSPHERIC PRESSURE. — THE WEIGHT OF AIR. — LESS AT GREATER HEIGHTS. — BAROMETER. — PRESSURE OF AIR. — ELASTIC FORCE OF AIR AND GASES. — FORCE PRODUCED BY A VACUUM. — COMMON PUMP. — RAREFACTION BY HEAT. — PAPIN'S METHODS OF PRODUCING A VACUUM. — HIS DISCOVERY OF THE CONDENSATION OF STEAM. — SAVERY. (1.) That the history of the invention of a piece of mechanism, and the description of its structure, operation, and [Pg004] uses, should be capable of being rendered the subject matter of a volume, destined not alone for the instruction of engineers or machinists, but for the information and amusement of the public in general, is a statement which at no very remote period would have been deemed extravagant and incredible.