810 



SCIENCE, 



[N. S. Vol. IX. No. 232. 



reach the receiving resonator from the 

 telescope- fork, for it also was carefully 

 boxed. The box was provided with glass 

 windows for the transmission of the beam 

 from the refractometer, which was similarly 

 boxed in such a way that a portion of the 

 receiving resonator protruded and pulsa- 

 tions of sound acted only upon the side of 

 the sensitive plate which faced the mouth of 

 the resonator. The adjusting screws of the 

 refractometer were brought outside the box. 

 The whole was small and portable. Equal 

 care was taken to keep all sounds from 

 motor and cylinder from reaching the re- 

 ceiving resonator, and all these pieces 

 rested upon little piers of soft rubber and 

 tin in layers, this to prevent vibrations from 

 being transmitted through the table and 

 supports. Careful tests were made for im- 

 munity from such disturbances. 



Results obtained thus far give promise of 

 a high degree of constancj', and of sensitive- 

 ness greater than the human ear, i. e. , 

 ability to detect both extremely faint sounds, 

 such as escape the sense of hearing, and 

 also the most minute differences in intensity 

 For this reason this instrument may prove 

 useful in the psychological laboratory. 



The limits of this sketch allow but an 

 outline of the mathematical theory of the 

 source, and of the receiver, by which the 

 intensity of a tone is reduced to absolute 

 measure. For a measure of intensity can 

 be made independently bj^ each, and one 

 may be used as a check on the other. 



ENERGY OF SOURCE. 



The energy emitted bj^ the source re- 

 sonator in sound may be measured in a 

 manner analogous to one employed by Eay- 

 leigh* in determining the minimal sound. 

 The rate at which the source fork expends 

 its energj'' is readily shown to be 



- ^ (£J = KE^e-"'" = A'^„ per sec, 



*P;»7. il/rt?., 1894, p. 365. 



and this energy is constantly supplied by 

 the current driving the fork. But not all 

 this energy is converted into sound. In 

 fact K is composed of three distinct parts : 



A'l peculiar to the fork 

 a; " " " plate 

 IC " " " resonator 



alone, 



If the resonator is made very smooth within 

 we may neglect the dissipation of energy in 

 other forms within the resonator and say 

 that the production of tone is due to K^ for 

 the system. Accordingly the energy of the 

 tone produced is K^ E^, when E^ represents 

 the sum of the energy of fork, plate and 

 connection at the time. The energy of fork 

 and connection are approximately 



E, = 1 pU -'■ {2r,Y- Vr2 for fork, 



E, = ^-''- M, (27j)' V^' " connection. 



The energy of the plate is an infinitesimal 

 of the second order. 



Since 2/; = Ae "'= '''*, K can be obtained by 

 noting the time required for the amplitude 

 to fall one-half The resonator plate is 

 mounted upon a separate ring so that the 

 resonator may be removed without disturb- 

 ing the plate. Then a differential measure 

 serves to determine K,. First, K is deter- 

 mined with resonator in place ; then the re- 

 sonator is removed and K^ + K.^ is deter- 

 mined ; thence 



K,^K- (R\ + A'J = 21og,2 CA - '/Q- 



A galvanometer, or millivoltmeter, is in- 

 terposed in the circuit containing the source 

 forks, so that a few measures, taken 

 through some range of intensities, suffice to 

 calibrate the current in terms of absolute in- 

 tensity at the mouth of the resonator. From 

 tills a simple assumption regarding propa- 

 gation gives the intensity at any point- 

 Since the intensitj' can be varied at will, 

 this instrument alone, with the ear for re- 

 ceiver, can be employed for a considerable 

 number of investigations. 



