Here is an interesting recap of the Newcomb and Benford findings on the distribution of the first digit in data records.

A century ago, Simon Newcomb observed an unexpected pattern in the first digits of logarithm tables: The digit 1 is significantly more likely to occur than 2, 2 than 3, and so on. More than a half-century later, Frank Benford rediscovered the first-digit phenomenon and found that it applied to many tables of numerical data, including the stock market, census statistics and accounting figures. New mathematical insights establish the empirical law developed by Newcomb and Benford as part of modern probability theory, and recent applications include testing of mathematical models, design of computers and detection of fraud in accounting.

Here is another interesting finding on temperature data and the final digits.  A proof and formal review of the original work is available, presented by Hall.

Here is an intuitive description of the Benford’s law.