H. V. Gill — -Theory of Singing Flames. 187 



II. 



There is another case of singing flames which we shall briefly 

 explain by a reasoning similar to that we have just employed. 

 If a tube, say 30 cm long by 3 or 4 cm in diameter, be placed on a 

 piece of wire gauze, the whole 5 cm above a Bunsen burner, and 

 if the gas be lighted inside the tube, a high note of great 

 intensity is produced. This experiment was first made by 

 Lissajons, who called it a " whistling flame." As we have 

 never seen any explanation offered, we think the following will 

 be found interesting. We have determined the following facts : 



1st. The note depends on the length of the tube and the 

 volume of the flame. 



2d. The gauze need not be outside the tube, but if placed 

 inside, the note is also produced. 



3d. If the gauze be more than a certain distance below the 

 base of the tube, no note is produced. 



4th. The image in a rotating mirror shows periodic disturb- 

 ances at the base of the flame. 



Just as a node is the position most favorable for the singing 

 flame, a loop is that favorable for the whistling flame. There 

 is a loop at the end of an open pipe, and hence the flame 

 sounds when at this position. As every note which an open 

 pipe can produce lias a node at the base, we see that each can 

 be produced by the flame at this position, and hence it is that 

 the note is so high and shrill, for, as we shall see, a great num- 

 ber of tones are produced simultaneously. 



At a loop, or ventral segment, there is considerable motion 

 of the air, as is shown by placing a small tambourine with 

 some sand on it at a loop ; the sand is violently agitated by the 

 air currents due to the vibration. The motion of the air at 

 the extremities is sensible for some distance outside the tube. 

 Mach studied this movement, and found that for a pipe four 

 feet long the amplitude at this point was 4 mm . 



We can easily calculate the velocity of these air currents if 

 we know the amplitude of vibration and the period of the note. 

 However in the general investigation this will not be necessary. 

 Let .us call this velocity x. 



We have seen that the draught, or current due to the flame 

 inside the tube, can be calculated from the formula 



y2 = 2gha(t-t') 



l+at 



For a certain tube we have calculated that the current due to 

 the vibrations was 2 meters per second, the draught 1 meter 

 per second. Let us suppose the velocity of the current due to 

 the vibration is x, that due to the draught y. 



