Bauhaus-Universität Weimar

assume that there is an ultimate value toward which, 
with finer methods and greater numbers, the quantity 
tends. The upper, the median, and the lower thres¬ 
holds are similarly quantities toward which the 0.0022 %> 
the 50 %, and the 99.9978 % values tend to settle as the 
number of experiments increases. Aside from this there 
are no reasons for considering any values rather than 
others as the thresholds. 
The three thresholds will differ under different condi¬ 
tions for different persons, &c. For one condition the 
curve may run as shown in I. (Fig. 70), for another as 
in II., for still another as in III. Persons or conditions 
whose thresholds are lower are said to be “ more 
sensitive,” and likewise the reverse. 
We have every reason to believe that the curve of 
results for an extended series of careful experiments 
would follow the law for * (?) (see Appendix I.), where 
y = h D, D being the amount of the weight and h a 
quantity indicating the subject’s fineness* of sensation. 
For any given subject or condition we would, therefore, 
know the frequency of occurrence for each value as 
soon as we had determined it for one of them. 
In this explanation of the threshold we have supposed 
the number of experiments to be practically unlimited. 
In actual work, the number of experiments is not 
large. It is thus impossible to pick out directly the 
upper and lower thresholds. The median threshold can 
be picked out directly as the middle value M (p. 46). Of 
course, as the number of experiments is limited, there 
is a degree of uncertainty attached to it. This degree 
of uncertainty can be indicated, as in Chap. II., on the 
supposition of the validity of the $ (y) law for this case. 
Oft a similar supposition we can also deduce the upper 
and lower thresholds as follows. 
The general experience of science since thé time


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