Boltzmann's Minimum Function

Abstract

I GATHER from Mr. Culverwell's last letter (NATURE, April 18), and Mr. Bryan's (May 9), that we may regard the following conclusion as established, namely, the proof of the H theorem, for any system depends on a certain condition (A) being fulfilled among the coordinates and momenta of the molecules forming the system. Considering these as elastic spheres, and using Dr. Watson's notation, fdp₁ … dq₃ is the chance that a sphere shall have for coordinates and momenta p₁ … p₁+ap₁, &c., and FdP₁…dQ₃ the chance that another sphere shall have P₁ … P₁+dP₁, &c. The condition required is that f and F are independent, even for two spheres on the point of collision.