An error produced by irregular causes whose effects upon individual measurements are governed by no known law connecting them with circumstances and which therefore can never be subjected to computation a priori. Sometimes called an irregular error or, more commonly, an accidental error. The theory of elemental errors assumes that a random error is assumed to be composed of an infinite number of independent, infinitesimal errors, all of equal magnitude, each as likely to be positive as negative. In practice, a random error is composed of an indefinitely large number of finitely small errors, each as apt to be positive as negative. With these assumptions, probabilities can be associated with the results of the method of least squares, and it is to the elimination of random errors only that the method of least squares properly may be applied.