Dr. It. Konig on Manometric Flames. 7 



those positions where the long flames are at their longest, the 

 short flames are at their shortest, and vice versa. 



In fig. 4, PI. I. the picture of the seventh (8 : 15, or 8 : 16 — 1) 

 shows this process, although in a very short period. The fifth 

 (2 : 3) shows a period of three, the fourth (3 : 4) of four, the 

 third (4 : 5) of five, and the second (8 : 9) of nine in the 

 range of the increasing and then decreasing flames. 



If the proportion is not of the form n : n + 1, then there 

 takes place in the whole period not only a rise and fall of the 

 flame-summits, but the curve connecting them shows as many 

 elevations and depressions as the difference between the two 

 ratios. For example, see the picture of the sixth (3 : 5) (fig. 4, 

 PL I.). 



The more complicated the interval of the two notes, the more 

 carefully we must bring it into perfect purity of tune, until no 

 further movement whatever can be discerned in the flame, 

 because otherwise the recurring periods of the flame- pictures in 

 the mirror suffer continual change by the change of phase, and 

 in that case it becomes difficult to recognize them. But this 

 exact tune becomes still more imperative if we wish to combine 

 more than two notes while making them act on one flame. It 

 will be remarked, besides, in these experiments, how difficult it 

 is to retain absolutely constant notes with organ -pipes, even 

 when we make use of a well-regulated bellows. 



Coexistence of two Tones in the same Air-column, 



The investigation of the combination of two related tones in 

 one flame-picture is especially useful, because it teaches us from 

 the flame-picture of a combination of tones, of which the com- 

 ponents are unknown, to find the single tones of which it is 

 composed. 



A passage to the trial of such a combination of tones as, e. g., 

 each sound offers, is the combination formed by a fundamental 

 with a known overtone in the same air-column. Very suitable 

 for such an experiment is the above described closed organ-pipe 

 with three flames, since the node of the fundamental as well as 

 one node of the first overtone are situated at their ends. 



If we blow the fundamental (1) very gently, the flame- 

 picture in the mirror shows the vibrations of this tone ; if now 

 we blow the overtone (3) strongly, each single vibration will be 

 replaced by three flames. With a rather weaker blast both tones 

 are produced together, and we always see three flame-summits 

 over every fundamental flame (fig. 5, Plate I.) . Therefore several 

 tones present at the same time in the air-column give exactly 

 the same flame-picture as the combination of the same tones 

 when each is produced by its own particular organ -pipe. 



