86 
provided the proportional rate of fall of temperature of the gas by radia- 
tion be small compared with the number expressing the pitch of the 
sound. In the experimental work described in the second part of this 
paper sounds of very high pitch were employed, so that the above condi- 
tion was satisfied. By this means a value for the constant radiation is 
finally deducted, and it is found to be small in comparison with the 
pitch-number of any ordinary sound, and so the solution obtained above 
may be considered as holding true, at least very approximately, for any 
sound of moderate pitch. 
PART II.—EXPERIMENTAL. 
Any attempt to compare sound intensities is attended by great diffi- 
culties. The term intensity can itself be understood in two ways—firstly 
in the subjective or physiological sense of loudness, and secondly, in the 
objective or dynamical sense of rate of flow of energy. T: e only case 
in which there seems to be a constant proportion between these two is 
when we compare sounds of the same pitch and quality. In deducing re- 
sults from the experiments, I have made the following assumption: 
When two faint and diminishing sounds are indistinguishable by the ear 
as regards pitch and quality, the minimum of energy flow required for 
audibility is the same. While this assumption cannot be fully justified, 
it seems at least inherently highly probable, and can at most differ but 
slightly from the truth. The errors consequent on this assumption prob- 
ably lie well within the experimental errors in the following method: 
A large number of very small whistles were made of as nearly as pos- 
sible the same shape and dimensions. From these the eight that seemed 
most similar were chosen and mounted on a wind-chest in such a way 
that any number could be blown under a definite pressure measured by a 
water monometer. The distances at which each pair and the whole 
eight just became inaudible were then determined. It was found that 
near the limits of audibility the sounds were indistinguishable in quality. 
Let R be the distance at which all eight whistles blown simultaneously 
became inaudible and r the mean distance at which two became inau- 
dible. Then at a distance r the mean rate of energy-flow from two 
whistles equals the minimum for audibility, and hence that of eight 
whistles equals four times the minimum for audibility, while at distance 
R, the rate of energy-flow of eight whistles equals the minimum for audi- 
bility. If now, in accordance with the above assumption, the minimum 
be the same in both cases, 
