260 PROCEEDINGS OF THE AMERICAN ACADEMY 



responding distance of the pair as 1 : s/^. If three resonators be 

 opposed to one, the distances should be 1 : V 3 ; if four resonators, 

 1:V4 or 1:2, &c. 



It will be seen that the accuracy of the above method depends 

 ujjon the following conditions : — 



1st, That the resultant wave from the combination of two resonators 

 has twice the intensity of that coming from one. 



2d, That the decrease in intensity of a sound, in passing through a 

 tube, is inconsiderable. 



3d, That the intensity of resonance is proportional to the intensity 

 of vibration at the mouth of the resonator. 



Let us first see the arrangement of the apparatus used, and then 

 determine how nearly these three conditions are satisfied. 



As a source of sound, a Co closed organ-pipe was used, blown by a 

 stream of air from a large gas-holder having an arrangement for keep- 

 ing the pressure constant. The pipe was mounted on a small standard, 

 raised some four feet above the floor, so that the sound-waves pro- 

 duced might have opjjortunity to diverge equally in all directions. At 

 a measured distance from the embouchure of the pipe were placed 

 two resonators, each cylindrical in shape, and capped with a hemi- 

 sphere at one end, through which ran a tube ^-in. in internal diameter, 

 and at the other end with a flat plate, in which was a circular aper- 

 ture of 1.5-inch diameter. The resonators were telescoped, so as to be 

 readily adjusted for pitch and intensity. From the small tubes of the 

 pair of resonators pieces of rubber tubing led to the two prongs of a 

 forked brass tube, in which the waves from the two resonators came 

 together, and augmented each other. From the stem of the fork 

 another tube led to one arm of the trombone interference apparatus of 

 Herschel. The third resonator was placed at an appropriate distance 

 from the embouchure of the pipe, and so arranged that it could be 

 moved to or from the iii])e, and, at the same time, one arm of tlie 

 interference apparatus could be moved to compensate for the change in 

 phase due to such motion. From the small opening of this resonator 

 a rabl>er tube extended to the other arm of the interference apparatus ; 

 and in this tube was insei'ted a bi'ass fork precisely like that used for 

 the pair of resonators, excepting that one of its arms was stopped, so 

 that the conditions of reflection for this wave might be as similar as 

 possible to those from the jiair of resonators. If all these conditions 

 of reflection be the same, it follows that two resonators give twice as 

 great an intensity as one placed at the same distance from the source 

 of sound. 



