[Footnote 4:  Gould’s Military and Anthropological Statistics, p. 530.  New York, 1869.]

We inherit our language from barbarous ancestors, and it shows traces of its origin in the imperfect ways by which grades of difference admit of being expressed.  Suppose a pedestrian is asked whether the knapsack on his back feels heavy.  He cannot find a reply in two words that cover more varieties than (1) very heavy, (2) rather heavy, (3) moderate, (4) rather light, (5) very light.  I once took considerable pains in the attempt to draw up verbal scales of more than five orders of magnitude, using those expressions only that every cultivated person would understand in the same sense; but I did not succeed.  A series that satisfied one person was not interpreted in the same sense by another.

The general intention of this chapter has been to show that a delicate power of sense discrimination is an attribute of a high race, and that it has not the drawback of being necessarily associated with nervous irritability.

SEQUENCE OF TEST WEIGHTS.

I will now describe an apparatus I have constructed to test the delicacy with which weights may be discriminated by handling them.  I do so because the principle on which it is based may be adopted in apparatus for testing other senses, and its description and the conditions of its use will illustrate the desiderata and difficulties of all such investigations.

A series of test weights is a simple enough idea—­the difficulty lies in determining the particular sequence of weights that should be employed.  Mine form a geometric series, for the reason that when stimuli of all kinds increase by geometric grades the sensations they give rise to will increase by arithmetic grades, so long as the stimulus is neither so weak as to be barely felt, nor so strong as to excite fatigue.  My apparatus, which is explained more fully in the Appendix, consists of a number of common gun cartridge cases filled with alternate layers of shot, wool, and wadding, and then closed in the usual way.  They are all identical in appearance, and may be said to differ only in their specific gravities.  They are marked in numerical sequence with the register numbers, 1, 2, 3, etc., but their weights are proportioned to the numbers of which 1, 2, 3, etc., are the logarithms, and consequently run in a geometric series.  Hence the numbers of the weights form a scale of equal degrees of sensitivity.  If a person can just distinguish between the weights numbered 1 and 3, he can also just distinguish between 2 and 4, 3 and 5, and any other pair of weights of which the register number of the one exceeds that of the other by 2.  Again, his coarseness of discrimination is exactly double of that of another person who can just distinguish pairs of weights differing only by 1, such as 1 and 2, 2 and 3, 3 and 4, and so on.  The testing is performed by handing pairs of weights