400 



SCIENCE. 



[N. S. Vol. IX. No. 220. 



apart, while the compression and rarefac- 

 tion of such a wave is an incidental phenom- 

 enon. This essential structural character 

 of the acoustic wave is not generally enough 

 insisted on. 



In the same way any of the above or the 

 following complex plane polarized waves 

 may be converted into compressional waves 

 by using vertical bell cranks (horizontal 

 axes). For the case of stationary waves 

 this would be of some interest, but I have 

 not carried out the construction. Since 

 small displacements are wanted, the en- 

 gagement of levers should be located be- 

 tween the axles. 



26. Reflection. — There is bound to be con- 

 fusion if the reflection of a compressional 

 wave from a denser or a rarer medium is 

 to be explained without reference to the 

 elementary S. H. M. of the particles of such 

 a wave. Relatively to § 12 and Fig. 12 it 

 follows that the explanation there given is 

 at once applicable to S. H. M. in sound 

 waves, the only difterence being that for 

 pulls up and reactions down we have now 

 pulls towai-d the right and reactions toward 

 the left, etc., which in no way modifies the 

 reasoning. A wave advancing toward the 

 dense medium ' crest on ' returns ' trough 

 on ' ; advanci.ng toward the rare medium 

 with a crest returns a crest. Let no one 

 suppose, however, that crest and trough 

 mean compression and rarefaction. For it 

 is just here that a slough of despond awaits 

 the incautious interpreter. A glance at 

 Fig. 11, where the oscillations of particles 

 have all been marked, shows that the centers 

 of convpresdon and of rarefaction are ivithout 

 simple harmonic displacement (phases ± 0) ; 

 that the maxima and minima of displacement 

 (± m) lie in air of normal density. If the 

 wave is to advance with particles in the 

 wave front in the zero of displacement it 

 must advance the center of a compression 

 or the center of a rarefaction sharply into 

 normal air. Thus, the particles on one 



side only of the balls marked ± in Fig. 

 11 must indicate the status of an advanc- 

 ing sound wave ; moreover, if the former 

 begins a crest, the latter (particles on the 

 other side of ± 0) begin a trough, and vice 

 versa. 



In this structural fact lies the gist of the 

 true explanation : If a compression meets a 

 denser medium it is reflected as a com- 

 pression surely enough, but the two com- 

 pressions are not the same. The sym- 

 metrical half of the incident compression is 

 returned. The two halves lie on opposite 

 sides of no displacement, and are the con- 

 tiguous halves of crest and trough required 

 by Fig. 12. So the two symmetrical halves 

 of a rarefaction become incident and re- 

 flected wave, initially meeting the plane of 

 reflection as contiguous trough and crest. 

 In both cases crest returns trough, and 

 trough crest, even though two compressions 

 or two rarefactions are in question. 



If reflection takes place from a rarer 

 medium a compression returns a rare- 

 faction ; this, however, is the rarefaction 

 ending in a crest, while the given com- 

 pression begins one, and vice versa. In 

 other words, there are two crests advancing 

 in opposite directions ; or crest returns crest, 

 even though a half wave-length is initially 

 lost and though a compression returns a 

 rarefaction. 



The agreement with §12 is thus complete 

 and the whole explanation logically simple 

 throughout. 



IX. Component Simple Harmonics Coplanar, 

 with Wave-Length Ratio, 1 : 2. Harmonic 

 Curves. 27. — Replacing the front cam axle 

 by another containing a single wave-length 

 and 2" double amplitude, the plane com- 

 pound harmonics for period ratio 1 : 2, for 

 the same or different amplitudes and for 

 any difference of phase, may be exhibited in 

 succession. The cams are exchanged by 

 lifting all the levers above the front axle, 

 by aid of the notched swivelled cross-lath 



