188 H. V. Gill — Theory of Singing Flames. 



As before, let us first consider the flame actually sounding. 

 At the node nearest the base (it is only necessary to consider 

 one of the notes) there are alternately condensations and rare- 

 factions. When the condensation is changing into a rarefac- 

 tion there is a current of air which issues from the tube ; this 

 is the first stage. When the rarefaction is becoming a conden- 

 sation this current enters the tube. During the first stage the 

 current due to the draught tends to cross the gauze with a 

 velocity y ; but the current due to the vibration is in the oppo- 

 site direction with a velocity x : therefore at this moment the 

 resultant current has a velocity x—y. This current is less than 

 if the flame had been silent, so that a smaller amount of gas 

 enters into the flame. But after a very small fraction of a 

 second the rarefaction at the node changes into a condensation. 

 During this second stage the current due to the vibration goes 

 up the tube and is in the same direction as the draught. There- 

 fore the resultant current has a velocity x-\-y. This current, 

 much more rapid than when the flame was silent, and than 

 that during the first stage, causes a greater quantity of gas and 

 air to enter into the flame than before. This sudden augmen- 

 tation of the flame gives an impulse to the vibrations already 

 taking place, and thus the note continues. 



This explanation is proved by several experiments. We 

 have stated that the gauze may be a certain distance below the 

 base of the tube. We have seen that the vibrations of the air 

 column extend a certain distance outside the end of the tube. 

 Many researches have been made to determine the exact law 

 which this distance follows, but though in individual cases it is 

 easy to determine the amplitude, it is difficult to formulate a 

 general law. It has been determined that this distance depends 

 on the diameter of the tube, and that when the wave length of 

 the note is great in comparison, this distance is somewhat 

 greater than two-thirds the radius of the tube. We have made 

 many experiments with the gauze in various positions, and find 

 that the gauze must be inside the limit assigned by this law, or 

 no note will be produced, whicii shows that the note depends 

 on these air currents. 



A second proof is that the note produced is not pure, but is 

 composed of a number of different ones. We have seen that 

 all the notes of the tube may be produced together and that 

 thus the resultant note is composed of tones proportional to 1, 

 2, 3, 4, 5. . . . If the gauze be placed at the middle of the 

 tube the note is much higher. We see at once why this must 

 be so if the whistling flame is proper to a loop. For the only 

 tones which have a loop at the middle of an open pipe are 

 those proportional to 2, 4, 6, 8, etc. Therefore since so many 

 of the lower tones are absent the resultant tone is higher than 

 in the former case. 



