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



by displacing a chair in the room next that in which the flame 

 was placed). We have seen, too, that the slight changes of 

 pressure produced by blowing across the end of the tube were 

 sufficient, even when the flame was not small enough to begin 

 of itself; therefore a lesser cause will suffice when the flame is 

 still smaller. The air inside the tube is at a higher tempera- 

 ture than that of the atmosphere ; this causes a current of air 

 to pass upwards through the tube with a velocity which we can 

 calculate.* This current as it passes the edges of the tube pro- 

 duces a faint note. The variations of pressure caused by this 

 note are sufficient to put the flame in action. This conclusion 

 is justified by the following facts: 



(a) A flame begins much more easily in a long tube than in 

 a short one, and we know the current due to the temperature 

 of the air is proportional to the length of the tube, so that the 

 note produced in a long tube is more intense than in a short one. 



(h) On placing the ear near the lower extremity of a tube 

 60 cm long, inside which a silent flame burns, one hears the note 

 produced by the current of air passing up. 



(c) A consideration of the various ways in which a flame 

 may be caused to sing leads to this conclusion. 



Although this reaction is the chief one which causes the 

 flame to begin to sing, we must bear in mind that there are 

 innumerable other minor ones which, in certain cases, may play 

 a part. Thus in the case of a very small flame inside a short 

 tube (8'0 or 10*0 cin ) the expansion of the air near the flame, 

 and accidental changes of the pressure of the gas, may be of 

 importance. 



We think we have made it clear that the pressure on the gas 

 plays the important part in this phenomenon, and that a con- 

 sideration of the reactions we have described will be found to 

 explain the many facts noted in the case of a singing flame, 

 some of which we have alluded to. We look therefore on the 

 chief cause as a mutual reaction between the pressures in the 

 tube and on the gas ; the energy necessary to sustain the note 

 being supplied by the pressure on the gas and the action of the 

 flame. We may compare the singing flame to the siren, in 

 which the current of air causes the disk to rotate, the note 

 being produced by the reaction of the disk on the current of air. 



* Dr. Everett investigates in his " Natural Philosophy." part II. the condi- 

 tions for a good draught up a chimney and applies the formula of Torricelli for 

 the efflux of liquids from orifices. This formula for the velocity of the air 

 current is 



2 = 2gha (t-f) 

 1 + at 



in which #=gravity; fe=length of chimney (or tube); a = the coefficient of 

 expansion for air ; fc=the temperature inside the chimney, and if that of the 

 exterior air. 



