Alternation Phonometer for Balancing the Loudness of Tones of Different Pitch.—It has been found that if two tones alternate in the ear at a suitable rate, for instance 25 times a second, the interruptions of the louder tone are the more conspicuous, and it is possible to adjust the relative intensities until the interruptions are equally conspicuous. Two tones when balanced in this way are said to be equally loud. This definition is justified by the fact that if two tones each balance a third tone they are found to balance each other and are also accepted by the ear as equally loud. The electrical circuit, commutating relays, and other apparatus used in making a loudness balance are described. To enable the mean pressure of the sound at the ear drum to be calculated from the electrical energy input, either a thermophone, whose theory is known, or an electromagnetic receiver which had been calibrated (rather imperfectly) by means of an artificial ear cavity and an electrostatic transmitter, was used next the ear. Successive readings usually agree within 5 per cent.

Relative Sensitivity and Sensibility of the Ear, at Various Loudness Levels, for Frequencies of from 100 to 4,000 per Second.—(1) Phonometric comparisons with a thermal receiver were made by ten men and ten women over a limited range of loudness. The results correspond to the equation $log P_1=A+B log P_2$, where $P_1$ and $P_2$ are the acoustic pressures, computed from the thermophone theory, of the two balanced tones. This equation is in harmony with Fechner's law. The constant $-A$ is the sensitivity and depends only on the threshold pressures; $\frac{1}{B}$ is the relative sensibility at the two frequencies and is found to be constant, within 10 per cent., for the entire range of frequencies investigated. The curves for men and for women show no systematic differences except at the higher frequencies where resonance of the ear cavity begins to enter. (2) With an electromagnetic receiver a greater loudness range was possible, the pressure being varied up to 20,000 times the threshold values. Of 32 curves obtained with four observers making comparisons against 700 cycles, 25 were straight throughout, in agreement with the thermophone results, and only 7 were distinctly curved near the extremes. The slope at all frequencies is between 0.9 and 1.0; therefore the sensibility is practically uniform, at least to 2,000 cycles and at all loudness levels. No evidence of a phonometric Purkinje effect was observed, but it may be present for pressures near the threshold values. Since the pressures are all computed, the absolute values of $A$ probably contain small systematic errors, but these would not affect the values of $B$.

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