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THE POPULAR SCIENCE MONTHLY. 



possible also, when the stereoscopic displacement is so small, that not 

 the slightest duplication of images can be distinguished with even the 

 keenest vision. When this displacement is large, the play of the eyes 

 is necessary to the completeness of the perception ; but, in any case, 

 the illusion is complex. The perception of double images is doubtless 

 one important element ; but when these are too minute to be distin- 

 guished, we are driven to other resources for an explanation. 



Every one has noticed that each instrument in an orchestra has its 

 own peculiar quality of sound, each singer in the cast of an opera his 

 own vocal timbre. The explanation of this is no longer a mystery 

 since Helmholtz analyzed, by the aid of resonators, what had eluded 

 analysis by the unaided ear, and showed that the difference in quality 

 between tones, nominally the same from different sources, is due to 

 minute modifications upon sensations, corresponding to small air- waves 

 accompanying those which produce the fundamental tone. By a well- 

 known system of graphic representation, let the curve in Fig. 17 stand 

 for the fundamental note ; if this be simple, the curve is perfectly 

 regular. But in fact it is accompanied by a group of smaller waves 



Fig. 17. Simple Sound Waves. 



Fig. 18. Complex Sound Waves. 



(Fig. 18, a V)\ when all are graphically combined, the curve is modified 

 (Fig. 18, c d), and so is the actual sensation. With the same funda- 

 mental a different series of overtones would have produced a different 

 resultant curve and sensation. The first of these resultants may rep- 

 resent c' from a soprano's voice, the other c' from that of the tenor, 

 each sending into the ear 264 complex thrills per second. Without 

 being absolutely unisonant, they constitute a pair of dissimilar musical 



