A quantity of such size that the probability that an error larger than that quantity will occur is the same as the probability that an error smaller than that quantity will occur. Probable error p½ is related to standard deviation ó by the formula p½ = 0.6745 σ if the errors have a Gaussian distribution. If the errors in a series of measurements be arranged in order of magnitude without regard to sign, and if the series be indefinitely large, the probable error will fit the middle place in that list of errors. Expressed in another way, the probable error of a result is a quantity such that a second determination obtained under the same conditions as the first has an equal chance of being less than or greater than the probable error. The probable error of the result of a series of measurements is a function of the random error attending the individual measurements of the series. A systematic error may often remain in the series with little effect on the size of the probable error. Probable errors are useful in comparing the precision or accuracy of similar measure-ments and may be used as criteria for prescribing degrees of precision and accuracy to be obtained. Probable error is currently little used in the sciences; standard deviation is used instead. It should therefore be used only if a definite advantage results. In such a case, the error should be identified specifically as probable error.