The fifth and last lesson deals with the measurement of Correlation, that is, with the closeness of the relation between any two systems whose variations are due partly to causes common to both, and partly to causes special to each. It applies to nearly every social relation, as to environment and health, social position and fertility, the kinship of parent to child, of uncle to nephew, &c. It may be mechanically illustrated by the movements of two pulleys with weights attached, 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-bone 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 them sufficient guidance for elaborating details.
Influence of Collective Truths upon Individual Conduct.
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 human action takes place is a superstructure into which emotion enters, we are guided on it less by Certainties and by Probabilities than by Assurance to a greater or lesser degree. The word Assurance is derived from sure, which itself is an abbreviation of secure, that is of se- cura, or without misgiving. It is a contented attitude of mind largely dependent on custom, prejudice, or other unreasonable influences which reformers have to overcome, and some of which they are apt to utilize on their own behalf. Human nature is such that we rarely find our way by the pure light of reason, but while peering through spectacles furnished with coloured and distorting glasses.
Locke seems to confound certainty with assurance in his forcible description of the way in which men are guided in their daily affairs (Human Understanding, iv. 14, par. 1):
Man would be at a great loss if he had nothing to direct him but what has the certainty of true knowledge. For that being very short and scanty, he would be often utterly in the dark, and in most of the actions of his life, perfectly at a stand, had he nothing to guide him in the absence of clear and certain knowledge. He that will not eat till he has demonstration that it will nourish him, he that will not stir till he infallibly knows the business he goes about will succeed, will have little else to do than to sit still and perish.
A society may be considered as a highly complex organism, with a consciousness of its own, caring only for itself, establishing regulations and customs for its collective advantage, and creating a code of opinions to subserve that end. It is hard to over-rate its power over the individual in regard to any obvious particular on which it emphatically insists. I trust in some future time that one of those particulars will be the practice of Eugenics. Otherwise the influence of collective truths on individual conduct is deplorably weak, as expressed by the lines:—
For others’ follies teach us not,