POPULAR SCIENCE 253 



meet, there is no interference between the two notes, no addi- 

 tional vibration ; but if their frequencies are different — say one 

 possessing A vibrations per second, the other A+2 vibrations — 

 it is obvious that in half a second the second note makes one 

 vibration more than the first ; each would therefore be in 

 exactly the same phase of the wave in each half-second. A 

 particle under the influence of the two vibrations will therefore, 

 once every half-second, be subjected to a maximum one, due to 

 the combined waves ; it is obvious that this maximum displace- 

 ment represents an additional vibration or rhythm of two per 

 second. The number of these " beats " or additional vibrations 

 per second corresponds to the numerical difference in the fre- 

 quencies of the two notes, which as far as we know remain 

 themselves unaltered. Such interference between two waves, 

 if insufficient to produce destruction of the fundamental notes, 

 will unavoidably produce reinforcement : this is what we mean 

 by an assortment of Forces in its simplest aspect. Another 

 example in sound vibration of a superadded rhythm is the over- 

 tone, which has probably an origin in analogous interference. 



The interaction between wave lengths of all sorts is ubiquitous 

 in nature, and obeys the same laws of interference. In a suitable 

 medium, when the rays of white light pass through a prism, 

 dispersion reveals vibrations of other wave lengths in the colours 

 of the spectrum ; wave lengths that in a repassage through another 

 prism produce again white light. White light is thus an " over- 

 tone " ^ produced by the suitable adjustment of vibrations of the 

 fundamental colours of the spectrum. That the fundamental 

 vibrations of colours is not seen in white light in the same way that 

 the fundamental notes are audible along with the superadded 

 vibrations is, of course, not opposed to this assumption. That 

 these two types of vibration obey the same laws of interference 

 is shown by the fact that complete interference between two 

 waves will in either case cause destruction. Another example 

 of the creation of an overtone is shown in the magnetic action of 

 an electric current : it is known that, if a small single electric 

 cell be floated in water and a loop of insulated copper wire be 

 connected to its poles, the cell will in every way behave like a 

 magnet. We know certain wave vibrations are emitted from 

 a current conveying wire even though insulated, for these are 

 shown to deviate a magnetic needle. Magnetism can thus be 

 considered as much the overtone of electric vibration as a 

 superadded vibration is of two discordant notes. It must be 

 noted that an induced current is not an overtone of magnetism, 

 but an overtone of an interrupted magnetic induction only. 



^ This term, for the sake of simpUcity, will be used to signify a super- 

 cycle of vibration, irrespective of the nature of the fundamental waves, unless 

 otherwise specified. 



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