Page:Popular Science Monthly Volume 71.djvu/178

172 persons was determined by simple methods, the individual variations being left out of account as too difficult to deal with. A population was treated by the old methods as a structureless atom, but the newer methods treat it as a compound unit. It will be a considerable intellectual gain to an otherwise educated person, to fully understand the way in which this can be done, and this and such like matters the proposed course of lessons is intended to make clear. It can not be expected that in the few available minutes more than an outline can be given here of what is intended to be conveyed in perhaps thirty-fold as much time with the aid of profuse illustrations by objects and diagrams. At the risk of being wearisome, it is, however, necessary to offer the following syllabus of what is proposed, for an outline of what teachers might fill in.

The object of the first lesson would be to explain and illustrate variability of size, weight, number, etc., by exhibiting samples of specimens that had been marshalled at random (Fig. 1), or arrayed in order of their magnitude (Fig. 2). Thus when variations of length were considered, objects of suitable size, such as chestnuts, acorns, hazelnuts, stones of wall fruit, might be arrayed as beads on a string. It will be shown that an "array" of variates of any kind falls into a continuous series. That each variate differs little from its neighbors about the middles of the arraj's, but that such differences increase rapidly towards their extremities. Abundant illustration would be required, and much handling of specimens.

Arrays of variates of the same class strung together, differing considerably in the number of the objects they each contain, would be laid side by side and their middle-most variates or "medians" (Fig. 3) would be compared. It would be shown that as a rule the medians become very similar to one another when the numbers in the arrays are large. It must then be dogmatically explained that double accuracy usually accompanies a four-fold number, a treble accuracy a nine-fold number, and so on.

(This concludes the first lesson, during which the words and significations of variability, variate array, and median will have been learned.)

The second lesson is intended to give more precision to the idea of an array. The variates in any one of these strung loosely on a cord, should be disposed at equal distances apart in front of an equal number of compartments, like horses in the front of a row of stalls (Fig. 4), and their tops joined. There will always be one more side to the row of stalls than there are objects, otherwise a side of one of the extreme stalls would be wanting. Thus there are two ways of indicating the portion of a particular variate, either by its serial number as "first," "second," "third," or so on, or by degrees like those of a thermometer.