CONTENTS. 



Introduction 1 



Chapter I. The fundamental differentia! equation in statistical mechanics. 



§ 1. Continuous changes of the velocities 3 



§ 2. Discontinuous changes of the velocities 6 



Chapter II. Passages. 



§ 3. Definitions 8 



§ 4. Number of stars thrown out 9 



§ 5. Number of stars thrown in 10 



§ 6. Increase in the number of stars 11 



§§ 7 — 10. Relations between the velocities before and after a passage 12 



§§ 11 — 17. The integral invariant in statistical mechanics 17 



§ 18. Final form of the passagefunction \/{f) 24 



Chapter III. Collisions. 



§ 19. Relation between the velocities before and after a collision 26 



§ 20. The integrals of areas 27 



§ 21. The energy integral 27 



§ 22. Number of stars thrown out 28 



§ 23. Number of stars thrown in 29 



§ 24. The collision function 30 



§ 25. Total number of collisions 31 



Chapter IV. The iï-theorem. 



§§ 26 — 27. An auxiliary theorem 34 



§§ 28—29. The W-theorem 37 



§ 30. The paradox of Loschmidt 39 



§ 31. General remarks on the //-theorem 40 



Chapter V. Integration of the fundamental equation in statistical mechanics. 



§ 32—33. Some theorems on the development of a frequency function in a series of 



type A 42 



§ 34. ^ series with several variables 44 



§ 35. Integration of the fundamental equation 45 



§ 36. Remarks 48 



