in the Theories of Light and Sound. 217 



position in nature in many cases. Thus, if two similar organ- 

 pipes are sounded near each other in exact unison, they always 

 arrange their vibrations in opposite phases, and the two tones 

 destroy each other. No doubt also the explanation given by 

 Airy of the doubling of intensity by use of two candles points 

 in the correct direction. As, however, it takes no account of 

 the alteration of the plane of polarization in common light, a 

 matter of which we know scarcely any thing, it can only be re- 

 garded as an illustration. The complete explanation cannot be 

 given or recognized till we know more about the alteration of the 

 plane of polarization. We must note, however, that the doubled 

 light of two candles is not to be regarded as an axiom, but as a 

 fact ascertained in the every- day processes of photometry. 



Still it may often happen that two such vibrations may be 

 superposed with coincident phase; it happens, for instance, at 

 the loudest part of the beats given by two organ-pipes nearly in 

 unison. In these cases we must not treat each vibration as a 

 cause in itself, invariable under all conditions. If we regard 

 the two vibrations as unaltered by the superposition, we shall in 

 general be wrong. We must go back to the sources of energy ; 

 and we shall in general find that the delivery of the vibrations is 

 materially affected by their superposition. By the superposition 

 of the vibrations we increase the work to be done by each, if con- 

 sidered to remain unaltered. Take an illustration from electri- 

 city ; then it is like interposing an additional resistance in an 

 electric circuit, only that heat is developed instead of sound. If 

 the battery be arranged for quantity, as it is called, the current 

 may be materially affected by the new resistance ; if for tension, 

 the new resistance may have a small influence only. So with 

 an organ-pipe. Let two pipes be nearly in unison, and at the 

 swell of the beat, when the vibrations are superposed with the 

 same phase; then the state of things may vary a good deal, 

 but necessarily lies between the following extreme cases. 



First, let the wind be very light, passing with freedom through 

 the wind way, and wasting little of its pressure there on the over- 

 coming of friction, imparting velocity to the external air, and so 

 on ; then most of the pressure at the windway is due to the work 

 converted into sound. The pressure at the orifice, and thence 

 the rate of issue, are then different as more or less work is con- 

 verted into sound ; when the work to be done is increased, the 

 pressure at the windway is increased and the velocity lessened. 

 Thus on superposition the amplitude of each vibration will be 

 diminished, until the work of the compound vibration is such 

 as the sources are able to furnish ; and in the extreme case each 

 amplitude would be diminished in the ratio of 1 : \/2. This is 

 analogous to the introduction of a resistance into an electrical 



