{449} and the other 200), you would never make an error except through
carelessness; but if one were 100 and the other 120 grams, you would
make an occasional error, and the number of errors would increase as
the difference was decreased; finally, comparing 100 and 101 grams,
you would get almost as many wrong as right, so that your perception
of that small difference would be extremely unreliable.

ERRORS IN PERCEIVING SMALL DIFFERENCES
OF WEIGHT (From Warner Brown)

Difference 20 16 12 8 4 8 2 1 grams

Errors 1 2 5 18 28 81 89 44 per hundred trials

The weights were in the neighborhood of 100 grams; each weight was
compared with the 100-gram weight, and each such pair was lifted and
judged 1400 times. Notice that the per cent of errors gradually
increases as the difference becomes smaller.

The smaller the difference between two stimuli, the more numerous the
errors in perceiving it, or, the less perceptible it is, and there is
no sharp line between a difference that can be perceived and one that
is too small to be perceived. That is the first great result from the
study of the perception of small differences.

The second great result is called _Weber's law_, which can be stated
as follows: In the same sort of perception, equal relative (not
absolute) differences are equally perceptible. For example, from the
preceding table we see that 28 per cent. of errors are made in
comparing weights of 100 and 104 grams; then, according to Weber's
law, 28 per cent, of errors would also be made in comparing 200 grams
with 208, or 500 with 520, or 1000 with 1040 grams, or any pair of
weights that stood to each other in the ratio of 100 to 104. Weber's
law is only approximately true for the perception of weights, since
actually fewer errors are committed in comparing 500 and 520 than in
comparing 100 and 104 grams; but the discrepancy is not extremely
great here, and in {450} some other kinds of perception, as especially
in comparing the brightness of lights or the length of seen lines, the
law holds good over a wide range of stimuli and only breaks down near
the upper and lower extremes. We are familiar, in ordinary life, with
the general truth of Weber's law, since we know that an inch would
make a much more perceptible addition to the length of a man's nose
than to his height, and we know that turning on a second light when
only one is already lit gives a much more noticeable