Weber's law in illusions. 
63 
illusion involved. As has been proven (pages 5—9 in my investigation 
cited above) the illusion of weight persists, but is not so strong when the 
fact of the illusion is known ; therefore, observers who are aware of the 
illusion and those who are not aware of it fall into two distinct classes. 
In the present experiments even the details of the illusions of weight and 
of this illusion in particular were demonstrated before the observers until 
all were conversant with the facts in question. Therefore, the illusion 
here measured is not the maximum. The preparatory demonstration 
was, however, made by a different set of cylinders in which the diameters 
varied so that none of the observers knew the exact extent of the illusion 
in the present apparatus. 
The aim was to determine two classes of facts: (1) the threshold, or 
least perceptible difference, for each pair of cylinders, and (2) the 
amount and kind of illusion in A and B respectively when measured by 
C as a standard. The first was determined by the following method : 
The weights in the continuous series rising by one gram each step were 
tried until three successive increments had been correctly perceived. 
The lowest of these was considered a threshold value. The observers 
were allowed to answer “equal ” or “different” and, in the latter case, 
they were required to point out the heavier. The amount of the illusion 
was found by determining how much the weight in the C cylinder had to 
be varied from the standard in order to make it equal to the A cylinder. 
The same procedure was repeated for the B cylinder. The series of 
weights which differed by five-gram steps were used in the measurement 
of the illusion. 
The results are given in the Table. One determination was made in 
the order J A, AB, A C, K, K’ of which the results are recorded in the 
«-columns. Then the series was repeated in the reverse order with 
another complete determination on each point. These results are re¬ 
corded in the ^-columns. For the threshold a and b have the same value, 
but in the illusion-measurements a represents the lowest difference which 
made these two cylinders apparently equal, and b the highest ; i. e., in a 
I started from the point of physical equality and continued to the first 
point of subjective or apparent equality, while in b I started with an ex¬ 
cessive difference and decreased this until the upper limit of apparent 
equality was reached. 
The experimenter handed the cylinders from behind a screen by pairs, 
placing them on end side by side in a convenient position upon a baize- 
covered table. The observer was required to grasp them as nearly as 
possible in the same manner and lift them always to the same height 
with the same speed. He was also required to keep them as near to-