CONTENTS. xiii PAGE $3.Introduction of the Temperature as one of the Independent Variables 200 s4.Special case of the differential equations on the assumption that the only External Force is a uniform surface pressure 203 $5.Application of the foregoing equstions to Homogeneous Bodies and in particnlar to perfect Gases. 205 $6.Application of the equations to a body composed of matter in two States of Aggregation 207 $7.Relation of the expreasions Dzy and Ary CHAPTER X. ON NON-REVERSIBLE PROCESSES. $1.Completion of the Mathematical Expression for the Second Main Principle 。 213 $2.Magnitude of the Uncompensated Tran*formation 214 $3.Expansion of a Gas unaccompanied by Work 215 $4.Expansion of a Gas doing partial work .218 85.Methods of experiment used by Thomson and Joule. ·220 $6.Development of the equations relating to the above method 221 $7.Results of the experiments,and the equations of Elasticity for the gases,as deduced therefrom 221 $8.On the Behaviour of Vapour during expansion and under various circumstance8 223 CHAPTER XI. APPLICATION OF THE THEORY OF HEAT TO THE STEAM-ENGINE. $1.Necessity of a new investigation into the thoory of the Steam- Engine· 234 52.On the Action of the Steam-Engine. 236 $3.Assumptions for the purpose of Simplification. 233 §4. Determination of the Work done during a single stroke 239 85. Special forms of the expression found in the last section ,241 s6. Imperfections in the construction of the Steam-Engine ·241 $7.Pambour's Formula for the relation between Volume and Pres- gure 242 $8.Pambour's Determination of the Work done during a single 8troke. 244 $9.Pambour's Value for the Work done per unit-weight of steam 247 10.Changes in the Steam during its passage from the Boiler into the Cylinder,··· 249§4. § o. § 6. § 7. Introduction of the one of the Independent Variables. _..... _ . Special CBBe of the di1ferential equations on the assumption that the only Enemal Force is a uniform surface pressure. • Application of the foregoing equations to Homogeneous Bodies and in particular to perfect Gases. . . • • • Application of the equations to a body composed of matter in two States of Aggregation • • Relation of the expressions Dzy and t.zll x ON PROCESSES. 203 205 207 209 § 1. Completion of the Mathematical Expression for the Second Main Principle • . • • • • 212 § 2. Magnitude of the Uncompensated TramCnrma.tion 214 § 3. Expansion of a Gas unaccompanied by Work 215 § 4. Expansion of a GBB doing partial work . • 218 § 5. Methods of experiment used by Thomson and Joule • 220 § 6. Development of the equations relating to the above method 221 § Results of the experiments, equations of EI&I!ticity the gases, as deduced •.•. On the Behaviour of expansion and under circumstances CHAPTER XI. APPLICATION OF THE THEORY 01' HEAT TO THE STEAM-ENGINE. § 1. Necessity of a new investigation into the theory of the Steam￾Engine. • 234 On the Action of the Dttlanl-L,ngme Assumptions for the I)etermination of the a single stroke Special forms of the the last section Imperfections in the the StelWl-Engine Pambour's Formulllll between Volume sure • • • PlWlbour's Determination stroke • • • • • . • • '.' 244 § 9. Pambour's Value for the Work done per unit-weight of stelWl • 247 § 10. Changes in the Steam during its passage from the Boiler into the Cylinder . 24'3