404 



SCIENCE. 



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



two of the rear axle, peculiar apparently 

 beknotted wave forms are obtained, well 

 adapted to give a notion of the complexity 

 resulting from simple compounding ; but it 

 is needless to refer to them further. 



XIV. Component Harmonics Both Circular, 

 of any Wave- Length Ratio and Opposite in 

 Direction. 39. Remarks on the Machine. — 

 After the description of the machine and 

 the remarks already made in the successive 

 paragraphs above, it is not necessary to 

 enter at length into a consideration of the 

 present experiments. As to matters of ad- 

 justment in Fig. 6, I may note that the 

 common horizontal locus of the centers of 

 the approximate circles described by the 

 free ends of the levers (they are really 

 curves of the 6th degree), and the respec- 

 tive cam axles, must be equidistant from 

 the perforated cross laths, C/and V. In 

 the given apparatus the effective lever 

 length is about 18". In this case the lever 

 ends describe curves which do not differ 

 more than 1/8" from circular circumfer- 

 ence, a departure not discernible with 1/2" 

 balls. Nevertheless, the angular velocity 

 in the quasi-circles is not uniform, a circum- 

 stance which from symmetry is without 

 bearing on the vertical compound vibra- 

 tions, but becomes more marked in propor- 

 tion as the vibration is twisted around into 

 the horizontal. The latter, therefore, ap- 

 pears somewhat convex downward unless 

 very long levers are chosen. The adjust- 

 ment in § 24, where the circles are nearly 

 quite perfect, is thus in many respects to be 

 preferred, though the levers are necessarily 

 farther apart and the lever ends incapable 

 of resisting much tension. There is incon- 

 venience, however, in constructing special 

 pairs of front and rear cam axles. 



To find whether the circles at the lever 

 ends have a common cylindric envelope 

 the cam axles should be rotated in like di- 

 rection. Coincident ends should then re- 

 main nearly coincident throughout. The 



cross laths, U and V, are adjustable with 

 this test in view. 



40. Rotary Polarization. Equal Component 

 Wave-Lengths. — Let the front cam axle be a 

 left-handed, the rear axle a right-handed, 

 screw (Fig. 6). Let them be equal in wave- 

 length and amplitude. Then the compo- 

 nent harmonics (loci of the lever ends or 

 eyelets) will be respectively right and left 

 circular helices, otherwise equal. The vibra- 

 tion lines of the particles, W, in Fig. 10) 

 will all be coplanar, the plane being parallel 

 to the cam axles at any angle to the hori- 

 zontal depending on the phase diiierence of 

 the initial cams. The compound harmonic, 

 or longitudinal arrangement of the particles 

 in the plane stated, is a simple harmonic, 

 curve whose amplitude is the common 

 diameter of the component circular har- 

 monics. 



This case has already been referred to in 

 §24 and there exemplified. The compound 

 curve, as constructed by the machine, is on 

 a scale of one-half. 



If the cam axles are rotated with the 

 same velocity, opposite in dii-ection (cross- 

 belt), the corresponding plane- wave will 

 result, unchanged in obliquity. One may 

 note in passing that, whereas, in all the 

 above compounding, plane-waves were ob- 

 tainable in one or two special altitudes 

 merely, they may now be obtained in all 

 altitudes. 



41. If the axles are rotated with un- 

 equal velocities, components of equal wave- 

 length differ in period and velocity. The 

 plane of the compound wave will, there- 

 fore, rotate about the axis of the component 

 circles. Hence, if the oscillation of the 

 first particle be put back into the same line 

 after each oscillation (in general, continu- 

 ously), i. e., if oscillation is continually 

 supplied at the origin in this line, the amount 

 of rotation resulting will be proportional 

 to the distances between particles. The 

 rotary polarization so produced is due to a 



