March 17, 1899.] 



SCIENCE. 



403 



best adapted for recognition. They corre- 

 spond respectively to like phases at the 

 origin with maximum or miminum dis- 

 placement of both components ( W- and M- 

 shaped forms) , or to opposite phases at the 

 origin with maximum and minimum, mini- 

 mum and maximum displacements of the 

 components ( V- and j^ -shaped forms). 



If the component waves are to advance 

 with the same velocity the rear cam axle 

 rotates twice while the fore axle rotates 

 thrice, thus establishing a period ratio of 

 3 : 2. Hence each wave contains two of the 

 specified harmonic curves in succession, or 

 only one-half of it is seen at once. The 

 progressive character of these waves as 

 they dash along is singularly pronounced. 



If the axles rotate equally fast in the 

 same direction the wave assumes a station- 

 ary type, with one node at the middle of the 

 component harmonics meeting at the origin 

 in the same phase. If the latter meet at 

 the origin in opposite phases, nodes occur 

 at the two ends with marked vibration for 

 intermediate parts of the compound wave. 

 If the cam axles rotate equally fast, but 

 in opposite directions, the compound wave 

 shows 6 nodes if the components meet in 

 opposite phases at the origin, and 5 nodes 

 under other conditions. 



Finally, if the wave velocities are equal, 

 but opposite in sign, there is permanence in 

 the vibration form of each particle, with dif- 

 ference of phase between them, but no nodes. 



XII. Component Simple Harmonics at Right 

 Angles to Each Other, ivith Wave-Length Ratio 

 2:3. 35. Transverse Space Waves. — The results 

 are similar to the above cases, only more 

 complex. The sunshine shadow on the nor- 

 mal screen shows the 2 : 3 Lissajous figure 

 in permanent form if the axes are rotated 

 at angular velocities of 3 : 2. The compo- 

 nent waves are then transmitted with equal 

 velocity and the period ratio becomes 2: 3. 

 If the component waves are transmitted 

 with other velocities the compound wave 



continually changes form, as does also the 

 Lissajous shadow curve. The rotation 

 within it is here again exhibited as to di- 

 rection, etc., with remarkable clearness. 

 To obtain steady results for this case the 

 balls must be small and the ratio workman- 

 ship of the machine accurate, otherwise the 

 inconmensurable cases supervene. Experi- 

 ments are made as above. 



XIII. Component Harmonics Circular and 

 Vertically Simple Harmonic of any Wave-Length 

 Ratio. 36. Harmonic Curves for Equal Com- 

 ponent Wave-Lengths. — The present curves 

 are interesting, inasmuch as they present 

 an intermediate stage between the above 

 cases of S. H. composition and the next 

 cases relating to the composition of circular 

 motions. The wave machine is put into 

 adjustment, as shown in Fig. 5, with cam 

 axles and pulley ratios 1:1. The machine' 

 is tipped up in front. 



Inasmuch as the S. H. M. of the front 

 axle interferes with the vertical component 

 of the circular motion of the rear axle, the 

 phase diflference is best specified in terms 

 of these coplanar vibrations. For like 

 phases, therefore, the Lissajous figure of the 

 compound curve is a tall vertical ellipse, 

 say 9" high and 3" broad. Advancing the 

 front phase +90° inclines this ellipse -to 

 the rear, shrinking it throughout. Advanc- 

 ing the front axle +90° farther produces 

 the simple harmonic curve in the .horizon- 

 tal with a double amplitude of 3". The 

 further advance of the front phase of +90° 

 expands the Lissajous figure into an oblique 

 ellipse inclining to the front, etc. 



37. Waves. — The rotation in the waves is 

 always clockwise for a clockwise circular 

 component. In this and other respects 

 (pronounced prolateness combined with 

 horizontal plane polarization) they diifer 

 from §20. 



38. Waves and Curves for Other Component 

 Wave-Lengths. — On replacing the front cam 

 axle with one of one or three waves to the 



