394 



SCIENCE. 



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



The amplitudes of the horizontal vibra- 

 tions do not admit of change without giving 

 useless complexity to the machine. Ad- 

 vantageous lever ratios will be given with 

 the experiments. 



I. Components. H. Motions Coplanar, of the 

 same Wave-Length. 13. Plane Polarization. — 

 Let cam axles each with two complete turns 

 be selected and the rear plate adjusted to 

 the vertical (Fig. 3). For harmonic curves 

 this implies the same wave-length for the 

 coexisting S. H. motions. With the cams 

 swinging nearly as 2:3, and lever ratios 

 I. + I' and I' (§ 12) as 3:2, the occurrence 

 of no displacement along the line of parti- 

 cles may be looked for in case of opposite 

 phases. This furnishes a method of adjust- 

 ing the particles at the outset. Practically 

 the condition of no displacement is reached 

 with relatively short levers, say a meter 

 long. When the pointers on the initial 

 cams are away from each other the com- 

 ponents meet in the same phase, with the 

 first particle in the axis of motion just about 

 to start vibrating. The double amplitude 

 given by the machine to this compound 

 harmonic (25" long) of maximum displace- 

 ment is about 9". If a beam of parallel 

 rays (sun light) be shot along the axis of 

 the wave, the shadow of the balls on a 

 screen normal to the axis necessarily be- 

 trays slight curvature ; the double ampli- 

 tude, instead of being vertical and straight, 

 is concave toward the cams. But the 

 chord deviates from the arc (9") by less 

 than 1/2" at the center, and hence with 

 balls 1/2" in diameter the curvature is 

 negligible to the eye of an observer in front. 

 It must be remembered, however, that 

 curvature is superimposed in all subsequent 

 higher figures. 



If the front cam axle be dephased 90° 

 clockwise the amplitude of the compound 

 curve is diminished, the curve remaining 

 sinusoidal but beginning with 1/8 wave- 

 length. If the rear cam axle is also de- 



phased 90° clockwise the compound cvirve 

 of the first case is restored in the shadow 

 (maximum amplitude), but the phase of 

 the first particle has advanced 1/4 period 

 and the curve itself 1/4 wave-length, etc. 

 I allude to these points because of their 

 value in instruction. (Cf. table, § 10.) By 

 the very make-up of the machine a S. H. 

 curve is seen to result when the phase dif- 

 ference of two particles varies as their dis- 

 tance apart. In drawing such a curve it is 

 simpler to place the circle of reference in 

 the plane of the harmonic ; in the machine 

 the circle of reference is preferably placed 

 at right angles to the curve. The addition 

 of two such curves is another S. H. curve of 

 the phase and amplitude directly specified 

 by the machine. 



14. Waves of Constant AmjMtude.— Belting 

 the two equal pulleys and rotating uni- 

 formly, waves corresponding to each of the 

 harmonic curves produced in §13 may be 

 sent along the axis of motion. Thus making 

 the phase difference between two particles 

 proportional to their distance apart, and 

 then setting each pai-ticle in S. H. M. of a 

 common period and amplitude, is object- 

 ively seed to be the realization of simple 

 wave motion. The wave-length being fixed 

 by the apparatus, velocity and period must 

 vary reciprocally. 



Particularly striking is the case for oppo- 

 site phases in the two wave cams. Both 

 component waves are seen travelling in the 

 same direction along the axes with full 

 vigor, whereas the compound effect at the 

 liue of particles is permanently nil. 



The warped surface of the levers now has 

 a linear directrix at the particle edge and a 

 sinusoidal directrix at the roller edge. It 

 should be noted that the case of maximum 

 amplitude in the compound harmonic pre- 

 sents an approach to a similar linear direc- 

 trix between the cam axles. 



15. Waves of Varying Amplitude. — Change 

 of amplitude is given to the levers by draw- 



