156 
PHYSICS: R. L. WEGEL 
Proc. N. a. S. 
the errors which obviously tend to raise this curve might be mentioned — 
lack of attention, low mentaUty of the observer, noise in the observing 
room, and abnormality of hearing. Care was taken to reduce all these 
errors to a minimum without actually making separate quantitative meas- 
urements of them on a rigorous statistical basis. 
Fig.l 
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FRCQUENCY 
AUPITORY SENSATION AREAS 
The statistical deviation from the mean varies irregularly with frequency 
very likely due mostly to the external anatomical variations which cause 
deviations in the dynamical constants of the transmission system from 
sound source to the ear drum. The dotted lines following the curve of 
minimum audibility represent approximately the "standard deviation." 
3. Maximum Audibility. — The curve marked "Maximum audibility" 
represents the pressure on the average of 48 normal ears required to pro- 
duce the sensation of feeling. A sound much louder than this is painful. 
The measurements were taken through a range of from 60 to 3,000 cycles. 
The standard deviation lines are also given from which it will be seen that 
this curve is quite as definite as that of minimum audibility. While this 
point of feeling probably has no relation to the auditory sense it does 
serve as a practical limit to the range of auditory sensation. A few ob- 
servations indicate that people with abnormal ears have a point of feeling 
sound which is not greatly different from that of normal ears, but this 
of course depends on the type of abnormality. The intensity for feeling 
is about equal to that required to excite the tactile nerves in the finger 
tips. 
4. Lower and Upper Frequency Limits of Hearing. — The curves of mini- 
