14 SENSITIVE FLAMES AND SOUND-SHADOWS. 



medmm required for the propagation of light-waves, whether 

 through interplanetary space or terrestrial bodies, is the universal 

 ether, of whose existence we have no evidence except that, by as- 

 suming it and applying mathematics, the results of computation 

 are exactly corroborated by observation and experiment. The 

 elastic medium required for sound-waves may be solid, liquid, or 

 gaseous. In any case it must be material. 



Assuming, then, an obstacle in the path of a wave of sound 

 or light, a shadow should be produced ; but since the edges are 

 sources of secondary waves, according to Huygens's principle, 

 these should encroach upon the shadow. The degree of encroach- 

 ment can be expressed in a mathematical formula, and is thus 

 shown to be proportional to the wave-length. The average length 

 of a wave of green light is now known to be about -g-rJrr of an 

 inch. The encroachment on the geometric shadow is hence so 

 small that refined methods are needed to make it perceptible. In 

 the case of audible sound, on the contrary, when propagated 

 through air, the wave-length is ordinarily so great that the en- 

 croachment almost wholly masks the presence of any shadow 

 whatever. For the pitch C, 132 vibrations per second, such as is 

 often used by men in conversation, the wave-length is readily cal- 

 culated, if we know the velocity of sound in air. Taking this as 

 1,120 feet per second, there will be 132 waves strung out over this 

 distance in each second. The length of each is hence eight feet 

 and six inches, or more than five million times as great as that 

 of the average wave of light. For such waves it is hopeless to 

 attempt producing any well-defined shadows. 



One of the most familiar facts in physics is that the pitch of a 

 note becomes higher, and hence its wave shorter, in proportion to 

 the increase of vibration frequency. If well-defined sound-shad- 

 ows are possible, we must resort to sounds of very short wave- 

 length. If the sound is continuous instead of explosive, this short- 

 ness implies very high pitch. There are mechanical difficulties 

 to contend with which make it hard to give much intensity to 

 very acute sounds. The range of audition, moreover, is limited. 

 For persons of good ear the range may be roughly stated as from 

 25 to 25,000 vibrations per second for sounds of small intensity ; 

 indeed, many fail to perceive any pitch exceeding 15,000. To 

 exhibit sound-shadows, therefore, it becomes necessary either to 

 employ a source that sends forth sounds of such high pitch as to 

 be inaudible to most of those who are expected to perceive the 

 shadow, or to resort to a momentary sound of great intensity and 

 short wave-length. 



Every one has noticed the decrease in intensity of the sound of 

 a distant railway-train as it passes into a cutting. The observer 

 is in a shadow which is incomplete but nevertheless noticeable. 



