CONTENTS. XV 



PAGE 



Dimensions of these quantities 60 



Index and coefficient of probability of configuration 61 



Index and coefficient of probability of velocity 62 



Dimensions of these coefficients 63 



Relation between extension-in-configuration and extension-in-velocity 64 

 Definitions of extension-in-phase, extension-in-configuration, and ex- 

 tension-in- velocity, without explicit mention of coordinates . . 65-67 



CHAPTER VII. 



FARTHER DISCUSSION OF AVERAGES IN A CANONICAL 

 ENSEMBLE OF SYSTEMS. 



Second and third differential equations relating to average values 



in a canonical ensemble 68, 69 



These are identical in form with thermodynamic equations enun- 

 ciated by Clausius 69 



Average square of the anomaly of the energy of the kinetic en- 

 ergy of the potential energy 70-72 



These anomalies are insensible to human observation and experi- 

 ence when the number of degrees of freedom of the system is very 



great 73, 74 



Average values of powers of the energies 75-77 



Average values of powers of the anomalies of the energies . . 77-80 

 Average values relating to forces exerted on external bodies . . 80-83 

 General formulae relating to averages in a canonical ensemble . 83-86 



CHAPTER VIII. 



ON CERTAIN IMPORTANT FUNCTIONS OF THE ENERGIES 

 OF A SYSTEM. 



Definitions. V = extension-in-phase below a limiting energy (e). 



$ = \odVldc 87,88 



V q = extension-in-configuration below a limiting value of the poten- 

 tial energy (e ? ). fa = \o^dV q jd fq 89,90 



V p = extension-in-velocity below a limiting value of the kinetic energy 



(*). ^ p = lo S dV p jd p 90,91 



Evaluation of V p and $ p 91-93 



Average values of functions of the kinetic energy 94, 95 



Calculation of FfromF^ 95,96 



Approximate formulae for large values of n 97,98 



Calculation of V or < for whole system when given for parts ... 98 

 Geometrical illustration . 99 



