CONTENTS. XV PAGE II.Determination of corresponding points and corresponding Elements of Surface in three planes cut by the rays. 301 5.Equations between the co-ordinates of the points in which a ray cuts three given planes. 801 §6. The relation of corresponding elements of surface 304 7.Various fractions formed out of six quantities to express the Relations between Corresponding Elements 3C9 III.Determination of the mutual radiation when there is no concentration of rays 310 $8.Magnitude of the element of surface corresponding to ds,on a plane in a particular position. 310 9.Expressions for the quantities of heat which da and ds,radiate to each other . 319 $10.Radiation as dependent on the surrounding medium 314 IV.Determination of the mutual radiation of two Elements of Surface in the case when one is the Optical Image of the other· $11.Relations between B.D.F,and 316 310 12.Application of A and C to determine the relation between the elements of surface 318 $13.Relation between the quantities of Heat which ds.and ds radiate to each other 319 V.Relation between the Increment of Area and the Ratio of the two solid angles of an Elementary Pencil of Rays.321 $14.Statement of the proportions for this case. 321 VI.General determination of the mutual radiation of two sur. faces in the case where any concentration whatever may take place. 824 $15.General view of the concentration of rays .324 16.Mutual radiation of an element of surface and of a finite surface through an element of an intermediate plane··· ·35 17.Matnal radiation of entire surfaces 8:8 $18.Consideration of various collateral circumstances. 329 s19.Summary of re8ults,·· 330 CHAPTER XIII. DISCUSSIONS ON THE MECHANICAL THEORY OF HEAT AS HERE DEVELOPED AND ON ITS FOUNDATIONS, $1.Different views of the relation between Heat and Work 332 $2.Papers on the subject by Thomson and the author ,8E3 $8. On Rankine's Paper and Thomson's Second Paper. 3e4 s4. Holtzmann'g Objections 837 55. Decher's Objections 339 $6.Fundamental principle on which the author's proof of the second main principle rests 840 $7.Zeuner's first treatment of the subject 341 s8. Zeuner's second treatment of the subject. 842CONTENTS. xv PAGB II. Determination of corresponding pointe and corresponding Elements of Surface in three planes cut by the rays • 301 § 5. Equations between the co.ordinates of the points in which a ray cuts three given planes. • . • • 301 § 6. The relation of corresponding elements of surface • • . 304 § 7. Various fractions formed out of six quantities to express the Relations between Corresponding Elements. • • • lIC9 m. Determination of the mutual radiation when there is 110 eoncentration of rays • • • • • • • 310 § 8. Magnitude of the element of surface corresponding to dI. on a plane in a particular position • • • • • • • 310 § 9. Expressions for the quantities of heat which dI. and dB. radiate to each other. • . • • • •• 312 § 10. Radiation as dependent on the surrounding medium. • • 314 IV. Determination of -the mutual radiation of two Elements of Surface in the case when one is the Optical Image of the other • • • • 316 § 11. Relations between B, D, F, and E • • • • • • 316 § 12. Application of .A and 0 to determine the relation between the elements of surface • . . • . . . • 818 § 13. Relation between the quantities of Heat which dI. and ds. radiate to each other • • • • . . • • 819 V. Relation between the Increment of Area and the Ratio of the two solid angles of an Elementary Pencil of Rays 821 § 14. Statement of the proportions for this case. • • . • 321 VI. General determination of the mutual radiation of two sur· faces in the case where any concentration whatever may take place. . . • . • 824 § 15. General view of the concentration of rays. . . • • 824 § 16. Mutual radiation of an element of surface and of a finite surface through an element of an intermediate plane • 3~ /) § 17. Mutual radiation of entire surfaces • • 3~8 § 18. Consideration of various collateral circumstances 32!J § 19. Summary of results 330 CHAPTER XIII. DISCUSSIONS ON THE MECHANICAL THEORY OF HEAT AS HERE DEVELOPED AND ON ITS FOUNDATIONS. § 1. § 2. § S. § 4. § 5. § 6. § 7. § 8. Different views of the relation between Heat and Work Papers on the subject by Thomson and the author On Rankine'S Paper and Thomson's Second Paper Holtzmann's Objections Decher's Objections • • • • • • • • • Fundamental principle on which the author's proof of the second main principle rests • • Zeuner's first treatment of the subjeet Zeuner's Beeond treatment of the subject 832 8[3 81:4 B37 339 340 8U 342 Digitized by Coogle ~