386 



SCIENCE, 



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



22. Velocities equal. 



23. Velocities unequal 



VII. Preceding case (IV) adjusted £or rotary 

 polarization. 



24. Plane and helical compounds. 



Vm. Waves of compression and l-arefaction. 



25. Longitudinal vibration. 



26. Reflection. 



IX. Component S. H. M's. ooplanar, with wave- 

 length ratio, 1:2. 



27. Harmonic curves. 



28. Waves. 



29. Case IX with component velocities unequal. 



30. Case IX with one component velocity reversed. 



X. Component S. H. M's. at right angles to each 



other, with wave-length ratio 1:2. 



31. Harmonic curves. 



32. Waves. 



33. Case X with component velocities unequal. 



XI. Components S. H. M's. coplanar with wave- 

 length ratio 2:3. 



34. Plane harmonics and waves. 



XII. Component S. H. M's. at right angles to each 

 other with wave-length ratio, 2:3. 



35. Transverse space waves. 



XIII. Component harmonics circular and vertically 

 simple harmonic of any wave-length ratio. 



36. Harmonic curves for equal component wave- 

 lengths. 



37. Waves. 



38. Curves and waves for other component wave- 

 lengths. 



XIV. Component harmonics both circular, of any 

 wave-length ratio, and opposite in direction. 



39. Remarks on the machine. 



40. Rotary polarization. Equal component wave- 

 lengths 



41. Do. Unequal periods and velocities. 



42. Unequal component wave-lengths. Equal 

 velocities 



43. Do. Unequal velocities. 



44. Right-handed circular component harmonics. 



45. Do Unequal velocitie<. Equal wave lengths. 



46. Do. Unequal wave-lengths. 



DESCRIPTION OF A WAVE MACHINE.* 



1. Introductory. — Although wave ma- 

 chines of a variety of special patterns are 

 well known, none of them, to my knowledge, 

 are sufficiently comprehensive in design to 

 embody in a single mechanism the types of 



* Compiled from notes on lectures delivered at 

 Brown University. 



harmonic motion met with in acoustics, 

 light, electricity and elsewhere, with a clear 

 bearing on their kinematic analysis. I will, 

 therefore, venture to describe such a ma- 

 chine, even at the risk of becoming prolix, 

 believing the apparatus to be more complete 

 than any similar machine which I have 

 seen, and having, after considerable expe- 

 rience, become assured of its usefulness in 

 class work. 



The machine which I have in view must 

 be able, in the first place, to compound any 

 two simple harmonic curves for any differ- 

 ence of amplitude period and phase. The 

 compound harmonic of two, or, at the most, 

 three, components is quite complex enough 

 for illustration, and whatever advantage 

 may be gained from further components is 

 more than counterbalanced by additional 

 complexity of apparatus. The wave ma- 

 chine must next be able to set all the com- 

 pound harmonics in vigorous motion,* thus 

 producing what I should like to call a train 

 of resolute complex waves (not decrepit 

 waves or waves of deficient vitality) ; it 

 must do this when the components (meet- 

 ing at the origin initially in any difference 

 of amplitude period or phase) travel with 

 the same or with different velocities in the 

 same direction or in opposite directions. 

 The latter adjustment affords an admirable 

 illustration of the phenomenon of station- 

 ary waves, either with fixed or with wan- 

 dering nodes ; the other an equally apt 

 illustration of musical beats for slight dif- 

 ferences of periods or slight differences of 

 wave velocity. Doppler's principle is thus 

 put in evidence. Relative to stationary 

 waves the adjustment is to be set either for 

 reflection with or without change of phase 

 in such a way as to clear up the wretched 

 confusion which usually surrounds this sub- 

 ject in elementary physics. 



With these possibilities for plane polar- 



* In this respect the photographs fail utterly to sug- 

 gest the beauty of the machine when in action. 



