Least Squares, Method of. In making measurements, or using instruments of any kind, different observations of the same thing do not agree. Besides errors of the instrument which can be corrected in different ways, other errors, not reducible to any law, and often depending on the observer himself, still remain. From the number of observations taken, that value has to be found which is nearest to the truth. In direct observations on a single quantity the arithmetical mean gives the best result, but this is not the case with Observations on several quantities. The method of least squares is then employed. It is based on the theory of probability, and is much used in physical research.