Book Ii Chapter Iv De La Probabilité Des Erreurs Des Résultes Moyens D’un Grand Nombre D’observations Et Des Résultats Moyens Les plus Avantageux

An element being known quite nearly, to determine its correction by the collection of a great number of observations. Formation of the equations of condition. By disposing them in a manner that, in each of them, the coefficient of the correction of the element has the same sign, and adding them, we form a final equation which gives a mean correction. Expression of the probability that the error of this mean correction is comprehended within some given limits. The most general manner to form the final equation is to multiply each equation of condition by an indeterminate factor and to add all these products. Expression of the probability that the error of correction given by this final equation is comprehended within some given limits. Expression of the mean error that we are able to fear more or less. Determination of the system of factors which render this error a minimum. We are led then to the result that the method of least squares of the errors of observations gives. Mean error of its result. Its expression depends on the law of facility of the errors of the observations. Means to render it independent. N 20.