Theory of Errors

Abstract

The function $y = \frac{1} {{\sigma \surd \left( {2\pi } \right)}}{e^{ - {{\left( {x - \bar x} \right)}^2}/2{\sigma ^2}}}$ which defines a normal frequency distribution is often called the Gaussian law of error. This “law” states that measurements of a given quantity which are subject to accidental errors are distributed normally about the mean of the observations. More precisely, the law infers that any set of measurements of a given quantity may be regarded as a sample taken from a very large population—the aggregate of all the observations that could be made if the instruments and time allowed—and that this population is normal.

“Everybody believes in the exponential law of errors; the experimenters because they think it can be proved by mathematics; and the mathematicians because they believe it has been established by observation.”(7)