Page:Popular Science Monthly Volume 71.djvu/181

Rh suspended from a cord held by one of the hands of three different persons, 1, 2, and 3. No. 2 holds the middle of the cord, one half of which then passes round one of the pulleys up to the hand of No. 1; the other half similarly round the other pulley up to the hand of No. 3. The hands of Nos. 1, 2 and 3 move up and down quite independently, but as the movements of both weights are simultaneously controlled in part by No. 2, they become "correlated."

The formation of a table of correlations on paper ruled in squares, is easily explained on the blackboard (Fig. 9). The pairs of correlated values A and B have to be expressed in units of their respective variabilities. They are then sorted into the squares of the paper,—vertically according to the magnitudes of A, horizontally according to those of B, and the mean of each partial array of B values, corresponding to each grade of A, has to be determined. It is found theoretically that where variability is normal, the means of B lie practically in a straight line on the face of the table, and observation shows they do so in most other cases. It follows that the average deviation of a B value bears a constant ratio to the deviation of the corresponding A value. This ratio is called the "index of correlation," and is expressed by a single figure. For example: if the thigh-bones of many persons deviate "very much" from the usual length of the thigh-bones of their race, the average of the lengths of the corresponding arm-bones will differ "much," but not "very much," from the usual length of arm-bones, and the ratio between this "very much" and "much" is constant and in the same direction, whatever be the numerical value attached to the word "very much." Lastly, the trustworthiness of the index of correlation, when applied to individual cases, is readily calculable. "When the closeness of correlation is absolute, it is expressed by the number 1·0, and by 0·0, when the correlation is nil.

(New words and ideas—correlation and index of correlation.)

This concludes what I have to say on these suggested object lessons. It will have been tedious to follow in its necessarily much compressed form but will serve, I trust, to convey its main purpose of showing that a very brief course of lessons, copiously illustrated by diagrams and objects to handle, would give an acceptable introduction to the newer methods employed in biometry and in eugenics. Further, that when read leisurely by experts in its printed form, it would give quite sufficient guidance for elaborating details.

We have thus far been concerned with probability, determined by methods that take cognizance of variations, and yield exact results, thereby affording a solid foundation for action. But the stage on which