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of each series is derived from the series itself. There is more than one kind of them, but they are all mutually convertible, just as measures recorded in feet are convertible into inches. The most convenient unit for purpose of explanation, though not for calculation, is the half difference between the marks or measures corresponding to the lower or to the upper quantities respectively.'

Deviations expressed in statistical units are usually found to conform with much closeness to the results of a certain theoretical law, discovered by Gauss, the great mathematician, and properly called by his name, though more familiarly known as the Normal Law. It supposes all variability to be due to different and equally probable combinations of a multitude of small independent causes. The relative frequency of different amounts of these, reckoned in statistical units, can thence be computed. It is done by refined methods based on the same general principles as those by which sequences of different lengths, in successive throws of dice, are determined.

Results of the computation are shown in the bottom line of the following small table :

Centiles and Corresponding Deviation from the Median.


Centiles   .










Deviations .








+ 1.25

+ 1.90


1 This unit is known by the uncouth and not easily justified name of " Probable Error," which I suppose is intended to express the fact that the number of deviations or " Errors " in the two outer fourths of the series is the same as those in the two middle fourths ; and therefore the probability is equal that an unknown error will fall into either of these two great halves, the outer or the inner.