George 1. Jones, Jr.
and Gilbert V. Shelden Clarkson College of Technology Potsdam, N e w York 13676
Concerning the Fundamental Distribution Law
The presentation of the fundamental distribution law, the most elementary exercise in statistical mechanics, can be simplified by defining the "derivative" of the natural logarithm of a large factorial numher and using an easily derivable logarithmic series found in standard mathematical tables. Proof of Stirling's factorial approximations, desirable in the usual derivation for the sake of rigor, is not needed since none of the forms of these approximations appear .. .. as such. According to the elementary laws of probability there are
By regarding each N , as independent and numerically large, the function In N t ! can be regarded as essentially continuous and its derivative determined by use of the elementary calculus
a C In Ni! ==
