Volltext: Weber's Law in Illusions (4)

```Weber's law in illusions.
67
The error involved by substituting the empirical results is 5% in the
first equation and 10% in the second. Both these, it may be seen from
the table, are less than the respective mean variations. Disregarding the
illusion (K and K’ in the above formulas) as has always been done, the
error in substitution would be 15% in the first and 21% in the second
equation. Hence Weber’s law stands in a much closer relation to the
apparent weight than to the physical standard.
If we know the increment needed for an object of a given weight and
size, e. g., C, at any standard, and know the amount of the illusion for
all differences’in size in objects of this weight, we may be able to calcu¬
late the threshold of perceptible difference for all such cases. For
and
- ^ — 1’
C—K **
_ AB
C+ K’
AC
C
_ 1
— îï
_ 1
— ’
These give a constant fraction for all the equations, in this case approxi¬
mately -j-j-. This fraction may be supposed to hold as a constant for all
conditions, of which the above A, B and C are representative. Hence,
we may state the principle for the dependence of Weber’s law upon ap¬
parent weight, as
AE
S+K
= M
where AE is the threshold of perceptible difference, S the physical
standard weight, K the amount of the illusion (which must retain its
sign -f- or — according as it is underestimation or overestimation of the
standard), and Ma. constant.
A question may here be raised as to the reason for and effect of choos¬
ing C of this particular size. It was chosen, after some preliminary ex¬
periments, because it seemed to correspond fairly to the size that the
adopted standard weight might suggest. What would have been the ef¬
fect of making it larger or smaller than this ? It may be possible to detect
some law for the dependence of the illusion upon this, but at the present
stage of measurements in illusions this factor is negligible and the standard
may be chosen of any size which is not so extreme as to introduce other
sources of error, such as difficulty in grasping, provided the results are
stated in terms of that size.^ Such results may also be convertible into
```

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