Proceedings of the Edinburgh Mathematical Society

Table of Contents - Volume 38 - 1919  

Research Article

A Version of Hagen's Proof of the “Law of Error.”

Dr R. F. Muirhead

Hagen's proof (1837), as described in the 8th edition of Mansfield Merriman's “Method of Least Squares,” is based on the assumption that the error may be supposed to consist of the algebraic sum of an infinite number of infinitesimal errors of equal amount ε, each one of which is equally likely to be positive or negative. Thus if 2m is the number of the infinitesimal errors, the probability of the error x ≡ 2p ε occurring is

S0013091500035550_eqnU1

and the maximum value of P occurs when p = 0, and is

S0013091500035550_eqnU2

.

(Received January 05 1919)

(Revised December 12 1919)