galton.org 249
Test Weights
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that he can just distinguish between those hearing the register-marks 1 and 3, or 3 and 5, or
4 and 6, etc.; the difference being 2 in each case.
There can be but one interpretation of the phrase that the dulness of muscular sense in
any person, B, is twice as great as in that of another person, A. It is that B is only capable
of perceiving one grade of difference where A can perceive two. We may, of course, state
the same fact inversely, and say that the delicacy of muscular sense is in that case twice as
great in A as in B. Similarly in all other cases of the kind. Conversely, if having known
nothing previously about either A or B, we discover on trial that A can just distinguish
between two weights such as those bearing the register-marks and 7, and that B can just
distinguish between another pair, say, bearing the register-marks 2 and 6; then since the
difference between the marks in the latter case is twice as great as in the former, we know
that the dulness of the muscular sense of B is exactly twice that of A. Their relative
dulness, or if we prefer to speak in inverse terms, and say their relative sensitivity, is
determined quite independently of the particular pair of weights used in testing them.
It will be noted that the conversion of results obtained by the use of one series of test-
weights into what would have been given by another series, is a piece of simple arithmetic,
the fact ultimately obtained by any apparatus of this kind being the “just distinguishable”
fraction of real weight. In my own apparatus the unit of weight is 2 per cent.; that is, the
register-mark 1
means 2 per cent.; but I introduce weights in the earlier part of the scale
that deal with half units; that is, with differences of 1
per cent. In another apparatus the
unit of weight might be 3 per cent., then three grades of mine would be equal to two of the
other, and mine would be converted to that scale by multiplying them by 2/3. Thus the
results obtained by different apparatus are strictly comparable.
A sufficient number of test-weights must be used, or trials made, to eliminate the
influence of chance. It might perhaps be thought that by using a series of only five
weights, and requiring them to be sorted into their proper order by the sense of touch
alone, the chance of accidental success would be too small to be worth consideration. It
might be said that there are 5 x 4 x 3 x 2, or 120 different ways in which five weights can
be arranged, and as only one is right, it must be 120 to 1 against a lucky hit. But this is
many fold too high an estimate, because the 119 possible mistakes are by no means
equally probable. When a person is tested, an approximate value for his grade of
sensitivity is rapidly found, and the inquiry becomes narrowed to finding out whether he
can surely pass a particular level. At this stage of the inquiry there is little fear of a gross
