92 Dr. A. M. Mayer on the Experimental Determination 



Such a method, which relies only on chance, can be of little 

 value, on account of its uncertainty and the tediousness of its ap- 

 plication. 



The above difficulty I have entirely removed by the following 

 means. I cut a piece out of one of the tubes equal in length to 

 a half- wave of the note we are experimenting on, and replace 

 this piece of tubing with a glass tube of the same length, into 

 which slides, air-tight, another glass tube, also half a wave in 

 length. The experimentation now becomes expeditious and 

 certain. Sound both bodies continuously, and place in a fixed 

 position one of the resonators. Move the other to a certain 

 distance from its sounding body, and then pull out the inner 

 glass tube until exact opposition of phase of the impulses is 

 brought to the manometric membrane. This condition will 

 be known when the serrations have dropped to their minimum 

 of elevation. If the latter do not entirely disappear from the 

 band of light in the mirror, we must place the moveable reso- 

 nator at another distance and readjust the sliding tube. A few 

 trials will give in the mirror a band of light with a straight, un- 

 ruffled top border; then we have opposed phases of vibration 

 at the confluence of the branches of the forked tube, and pulses 

 of equal intensity are traversing the two tubes leading from the 

 resonators. 



The distance of each resonator from its sounding body is now 

 measured ; and the inverse ratio of the squares of these distances 

 will be the ratio of the intensities of the vibrations at the sources 

 of the sounds, if the intensities of the pulses sent through a tube 

 from a resonator varies directly with the intensities of the vibra- 

 tions of the free air in the plane of the mouth of the resonator. 



It will be observed that the accuracy of the determinations by 

 this experimental method depends on three conditions : — First, 

 that the vibration-effects of the same area of a spherical sonorous 

 wave diminish in intensity as the reciprocals of the squares of 

 the distances of this area from the point of origin of the wave. 

 There is every dynamic reason to believe in the truth of this 

 proposition. The second necessary condition is, that the elon- 

 gation of one of the resonator-tubes beyond the other by a half 

 wave-length of firm glass tubing does not diminish the intensity 

 of the impulses which have traversed it. Numerous experiments, 

 especially those of Biot and Regnault on the aqueduct-tubes 

 of Paris, show that so short a connecting-tube of glass cannot in 

 any way affect the accuracy of the measures. The third condi- 

 tion is, that the intensities of pulses sent through a tube from a 

 resonator vary directly with the intensities of the vibrations of 

 the free air in the plane of the mouth of the resonator. This is 

 a very important consideration ; and as I believe there is no en- 



