598 



SCIENCE. 



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



exist throughout in the same phase if the 

 pointer on the rear eccentric is 90° ahead of 

 the other, supposing, in accordance with the 

 above table, that directions upward and 

 rearward are positive. The zero of phase 

 thus begins with front pointer left and rear 

 pointer up. If the pointers are parallel and 

 in the same direction the front harmonic is 

 90° in phase ahead of the other. The com- 

 pound harmonic is circularly polarized and 

 the corresponding wave advances with 

 counter-clockwise rotation if seen in the 

 direction of advance, i. e., from left to right 

 to the observer in front. Dephasing the 

 front axle 90° farther (180° advance) pro- 

 duces plane polarization at 135° to the hori- 

 zontal ; 90° farther (total advance 270°) 

 finally a circularly polarized harmonic 

 curve with a wave advancing in the direc- 

 tion of the components with clockwise rota- 

 tion, as seen from the origin. All interme- 

 diate cases are elliptically polarized with 

 intermediate I'otation. 



The sunshine picture on a screen normal 

 to the axis with rays parallel thereto is in 

 general an ellipse with the appropriate 

 rotation discernible with remarkable clear- 

 ness. 



V. Preceding Case {IV) with Compoiient 

 Velocities or Periods Unequal. 21. — If the com- 

 ponent waves do not advance with the same 

 velocity (necessarily implying difference 

 of period in the present case) the differ- 

 ence of phase of the first pairs of cams is 

 continually changing, and the phase differ- 

 ence of all succeeding cams is changed in 

 like measure. Hence the compound wave 

 passes continuously through all the differ- 

 ent harmonic curves in turn. If the belt 

 be placed on the 3:4 pulleys four turns of 

 the rear axle restores the original form 

 through all intermediate forms, beginning, 

 for instance, with plane polarization at 

 45°, passing through circular clockwise 

 polarization (seen from the origin) into 

 plane polarization at 135° ; then back with 



counter-clockwise rotation into plane polar- 

 ization at 45°. 



The sunshine shadow of this case is 

 identical with the Lissajous figures from 

 two tuning forks slightly different in pitch 

 but of the same amplitude. The directions 

 of rotation are particularly evident, en- 

 hancing the instructivenes of the figure. 



VI. Preceding Case {IV.) with Either Cowpo- 

 nent Velocity Reversed. 22. — If with equal am- 

 plitudes and wave-lengths the component 

 waves travel in opposite directions (pulleys 

 cross-belted) the compound wave is a pecu- 

 liar form of stationary wave in which the 

 form of vibration of all particles is sustained, 

 but in which the motion of each particle 

 differs uniformly in regard to the phase dif- 

 ference of its components, i. e., in ellipticity, 

 from its neighbors. Thus a group of parti- 

 cles a wave-length apart are plane polarized 

 at 45° ; particles midway between plane 

 polarized at 135° ; particles midway between 

 both groups circularly polarized with alter- 

 nately opposite rotations and all other par- 

 ticles correspondingly elliptically polarized. 

 The envelope of the harmonic curve would 

 be given by a thin tube 3" in diameter, com- 

 pressed at equal distances by a pair of 

 shears to lines at right angles to each other, 

 but alternately in the same direction. The 

 case is thus thoroughly different from the 

 case of unequal velocities in the same 

 direction, where all the particles under ob- 

 servation are instantaneously in the same 

 ellipticity. 



23. Velocities Reversed and Unequal. — If the 

 two component waves of the same wave- 

 length have unequal velocities (and periods) 

 of opposite sign the plane polarized groups 

 wander. Thus if the 3 : 4 pulleys be taken 

 4 turns of the rear crank reproduces the 

 original wave. The transitional case is 

 again that in which one cam axle is sta- 

 tionary (wave velocity zero) while, the 

 other rotates. A single turn reproduces 

 the original figure. 



