370 Scientific Proceedings, Royal Dublin Society. 



the second order, as this theory requires, then by withdrawing the 

 two primaries from the sensitive jet — or allowing them to die 

 down as was done — the combination-tone should fall off more 

 quickly than the generating tones ; but this was not the case. Is, 

 then, the view of the critics of Helmholtz correct ? Do " the beats 

 of the generators, with their alternations of swellings and pauses, 

 pass into the differential-tone of like frequency, without any such 

 failure of superposition as is invoked by Helmholtz " ? Employing 

 a sensitive jet as a delicate phonoscope, it certainly would appear 

 that the greater amplitude of the disturbance produced at the 

 beats gives a definite and disintegrating shock to an unstable jet 

 of flame or water. This disturbance being periodic and recurring 

 with sufficient rapidity, the successive shocks in some way became 

 audible as the difference-tone, or what Konig called the beat- 

 tone. 



In the case of the sensitive water- jet falling on a membrane, 

 this is the explanation suggested by Mr. Belas. The sound 

 actually heard is due to the impact of the drops of water on the 

 membrane, and those drops which break off high up on the jet, 

 and have therefore a greater distance to travel, must strike the 

 membrane with greater momentum than the others. Now the 

 photographs clearly show that the jet does disintegrate higher up. 

 When, therefore, the phases of the two primary tones coincide, 

 the difference - tone should be heard more loudly than the 

 primaries, as is the case. 1 



1 Professor Poynting, d.sc, f.k.s., was good enough to read the proof of the 

 foregoing paper, and writes to me as follows : — " It appears as if Mr. Belas had got a 

 good mechanical explanation of this particular difference-tone. Another similar case 

 occurs to me. Suppose a reservoir is at the sea-shore, just below the level of the highest 

 spring-tide, and with some contrivance for emptying it slowly. Then it will fill once 

 a fortnight, and its rise and fall will have a frequency equal to the difference in 

 frequencies of the solar and lunar tides. Its oscillations will, of course, not be 

 harmonic, but its chief vibration will be fortnightly. This appears to me to be very like 

 the water-jet experiment as explained by Mr. Belas. We have a mechanical explanation 

 then of the beat-tones. And now I remember a case where summation-tones appear to 

 occur ; perhaps worth troubling you with, but not bearing on the case in point. I 

 used to live near a railway incline where an engine was used at the rear to help to 

 push the train. The puffing of the two engines, front and rear, could be heard, some- 

 times coinciding, sometimes alternating. Suppose they each gave two puffs per second ; 

 when they alternated, it sounded as if an engine was giving four puffs per second, 

 and the frequency was the summation-tone. I suppose — but perhaps there is some 



