March 17, 1899.] 



SCIENCE. 



397 



On the other hand, if the direct wave 

 meets a rarer medium at aa the reaction is 

 less than that of the original medium. The 

 pull up developed by the wave d in Fig. 12 

 is not resisted by an excessive pull down as 

 before. The reaction (which from its 

 rhythmic character develops the reflected 

 wave) i.s an additional pull up, such as 

 would correspond to a wave r' in Fig. 12. 

 Both waves r' and d are in the same phase 

 as regards their effect on the initial particle 

 at aa, but they differ in direction of motion. 

 In other words, the direct wave d and the 

 reflected wave prolonged r', are not initially 

 contiguous parts of one and the same wave, 

 meeting without displacement at the wall. 

 Half a wave-length is necessarily lost at the 

 inception. 



This determines the method of setting 

 the pointers of the machine for equal dis- 

 placements of the same sign at the origin, 

 beginning with opposite null displacements ; 

 for the two waves d and r' if traveling in 

 the same direction (cf. Fig. 12) would then 

 annul each other. 



Summarizing ; the reflected wave from a 

 denser plane boundary normal to the axis 

 is obtained from the incident wave by tioo 

 rotations of 180° each ; one around the axis 

 of motion, the other around the trace of the 

 wave plane on the plane of the obstacle ; 

 these correspond respectively to the substi- 

 tution of reaction for action, and of an op- 

 posed direction for the given direction of 

 motion — two reasons for change of phase. 

 The wave advancing crest on (crest fore- 

 most) returns trough on and vice versa. 



The reflected wave from a rarer plane 

 boundary is obtained from the incident 

 wave by a single rotation around the trace 

 in question. The only reason for change 

 of phase is change of direction. The wave 

 advancing crest on returns crest on, and the 

 trough returns a trough. Cf §26. 



If the component amplitudes are made 

 unequal the nodes show a correspondingly 



slight vibration, the case corresponding to a 

 medium at the origin neither absolutely im- 

 permeable nor absolutely rare. 



19. Wandering Nodes. — If with equal am- 

 plitudes the velocities or periods of the com- 

 ponents be unequal in value and opposite 

 in sign the case becomes one of stationary 

 waves with continually drifting nodes. 

 Thus if the 3 : 4 pulley be cross-belted four 

 turns of the rear or faster cam axle will 

 continuously move the node half a wave- 

 length onward. The stationary character 

 is, nevertheless, very thoroughly retained. 



In the extreme and transitional case where 

 the velocity of one wave is zero and the 

 other of any value a single turn at the 

 crank moves the nodes half a wave-length 

 and thus reproduces the original curve. 



IV. Component S. H. Motions at Eight 

 Angles to Each Other of the Same Amplitude 

 and Wave-Length. 20. Elliptic Polarization. — 

 Using cam axles with two waves each and 

 adjusting rear ends of levers (Fig. 4) , while 

 the vertical riders L engage the cams, two 

 simple harmonic curves are available to be 

 compounded at the particles. This is usu- 

 ally an elliptic helix. It is advisable to 

 tip the machine up in front with the object 

 both of relieving the work of the springs 

 and of exhibiting the wave symmetrically 

 with reference to a horizontal plane through 

 the axis. 



In order that circular polarization maybe 

 obtained, the amplitudes of the particles 

 must be equal. The rear cams contribute 

 their full swing independent of the levers. 

 The fore cams enter with an amplitude 

 which may be more than doubled, though 

 the fulcrum of the levers is now at the 

 rollers. Thus the levers are to be shortened 

 from 1 meter to about 70 cm. to obtain cir- 

 cular paths 3" in diameter for the single 

 particles. Shorter levers would give oblate 

 ellipses, larger levers prolate ellipses, for 

 their central figures. Cf. §36. 



The two S. H. motions will meet and 



