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



violence of these changes of pressure is so great that it extin- 

 guishes the flame altogether. 



Though this method shows us that there is a considerable 

 change of pressure, it does not give any numerical measure- 

 ment. Such measurements have been made by Kundt and 

 others. Kundt employed a water manometer for this purpose. 

 As the changes of pressure follow each other very rapidly it is 

 clear that an ordinary manometer would be useless, and hence 

 he used one which, by means of a valve, could only be acted 

 upon by changes of pressure of a given sign. With such an 

 apparatus he found that, at a node of an open pipe sounding 

 loudly, the increase of pressure during a condensation was 

 equivalent to that exerted by a column of water about 15 cm 

 high, and a diminution of equal amount during a rarefaction. 

 Others have found lower values. 



We have next to examine another pressure which comes into 

 play in the case of the singing flame, one which has been alto- 

 gether neglected by those who have proposed explanations of 

 this phenomenon, but which we shall show to be an essential 

 element in the production of the musical note. 



The pressure of the gas which produces a flame of suitable 

 size for a singing flame may be easily determined by means of 

 the apparatus we have described. We have only to extinguish 

 the flame which has been singing and close up the aperture. 

 The water will then rise in the pressure-tube. This pressure 

 is one, or two, or even more centimeters of water, according 

 to the note which the flame produced. One might be inclined 

 to think that the pressure under which the gas of the flame 

 issues is always that on the gas supply of the house, but it is 

 easy to show that when the tap which connects the flask to the 

 main pipe is turned so as to let a small quantity of gas issue, 

 that the pressure is proportional to the passage thus modified, 

 the reason being the friction and viscosity of the gas. 



The figure will assist us in our explanation : I represents the 

 column of air during a condensation, II during a rarefaction 

 (fig. 2). The flame is situated at a node. 



We shall suppose the maximum pressure of either sign to 

 be 5 cm of water, since a singing flame does not produce a very 

 loud note, and will take 2 cm as the pressure on the gas. Here 

 is roughly what happens when the flame sings : 



During a condensation the air is being compressed in the 

 direction of the small arrows with a pressure represented by 5. 

 As the burner of the singing flame is not in communication 

 with the air in the tube except at the small aperture from 

 which the gas issues, this pressure acts in the direction A on 

 the gas. But the gas is issuing from this aperture under a 

 pressure 2 in the direction G-. Therefore the resultant of 



