Chapter II: Appendix

_On the Relation between the Temperature, Pressure, and_
_Density of Common Steam._

Empirical Formula of Biot, showing the
Relation between the Pressure and Temperature 505

Empirical formula of Southern 506
Tredgold 506
Mellet 506
De Pambour 506
MM. Dulong and Arago 506

Law of the Expansion of elastic Fluids,
discovered by Dalton and Gay Lussac 506

Formula for the Relation between the Volumes
and Temperatures 507

Law of Mariotte 507

Table of Pressures, Temperatures, Volumes, and
Mechanical Effects of Steam 509

Empirical Formulæ for the Relation between the
Volume of Water and that of the Steam produced
by its Evaporation under given Pressures 511

Formula of Navier 511

Modified by De Pambour 511

_On the Expansive Action of Steam._

Mechanical Effect produced during a given
Extent of Expansion 511

Mechanical Effect produced during Evaporation
and subsequent Expansion 512

Application to double-acting Engines 513

Formula for Pressure of Steam in Cylinders 514

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

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THE STEAM ENGINE.

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