March 17, 1899.] 



SCIENCE. 



401 



(when an opportunity to show the rear har- 

 monic alone is afforded as the levers now 

 ride on a common iixed axle in front), after 

 which the single wave axle is easily inserted 

 and the levers dropped down upon it by 

 lowering the cross-lath. 



Refei'ence to the scheme of phases com- 

 piled in §10 shows that 16 generically dis- 

 tinct compound harmonics with an indefi- 

 nite number of intermediate curves are 

 obtainable. The variation is further en- 

 hanced by changing the component ampli- 

 tudes by drawing out the levers. Among 

 forms for equal amplitude the symmetric 

 types are distinctive. They are obtained 

 concave upward more or less )F-shaped for 

 components meeting at the origin both at 

 maximum displacement ( + to), and more 

 or less ikf-shaped when both components 

 meet at the origin at minimum displacement 

 ( — m). Similarly symmetrical forms are 

 seen when the components at the origin are 

 in opposite phases, viz., F-shaped when the 

 front harmonic is at -\-m and the rear har- 

 monic at — m, and ^-shaped when the 

 front harmonic is at — m and the rear 

 at +m. 



28. Waves. If these curves are to be 

 transmitted in a compound wave which does 

 not change its form each component must 

 travel equally fast. Hence the rear axle 

 with two wate- lengths must be rotated 

 twice as fast as the front axle with one wave- 

 length (pulleys 2:1) The periods are now 

 also in the ratio of 1 : 2. Thus it appears, 

 that it takes two rotations of the rear axle 

 to exhibit the complete wave, or beginning 

 with a symmetric type, for instance, the W 

 and jl curve together make a single har- 

 monic curve ; whereas the M and V curve 

 make another, in relation to waves ; etc. 

 for non-symmetrical forms. The character 

 of the wave is markedly progressive, each 

 little kink as well as large elevations or de- 

 pressions running along the axis in turn. 



Referring again to the above table §10, 



the present succession of phases is a march 

 along a diagonal passing from left to right 

 downward across the diagram. 



29. Case IX. with Component Velocities Un- 

 equal. — If the component waves are trans- 

 mitted unequally fast the compound wave 

 continually changes form. Thus, if the 2 : 3 

 pulleys be used, it takes 3 turns of the rear 

 axle to reproduce the original form ; in 3 : 4 

 pulleys, four turns ; in 1 : 1 pulleys, but a 

 single turn. In the last instance the waves 

 produced are much like stationary waves, 

 with two nodes at the ends if the compo- 

 nents meet at the origin in opposite phases, 

 and one node in the middle if they meet in 

 the same phase, phase difference being 

 maintained constant at each cam. The 

 table, §10, shows that the passage is now 

 from left to right across the diagram, along 

 a single row. 



If one axle alone rotates a single turn 

 again repi-oduces the original form, but the 

 wave has now a progressive character, which 

 is an inversion of the result in §28. In 

 other words, the W and V types or the M 

 and^ types of curve are successive. In the 

 table of phases, §10, the present succession 

 for any single cam is given by a column 

 passed from top to bottom. 



30. Case IX. with One Component Velocity 

 Reversed. — If the axles rotate with equal 

 velocity in opposite directions the wave 

 presents the succession of forms of the first 

 (normal) case, but its character is now non- 

 progressive, each particle retaining its pecu- 

 liar form of vibration, which differs regu- 

 larly from that of neighboring particles. 

 But half the full wave is represented at 

 once. No particle is permanently at rest 

 and the stationary character is less pro- 

 nounced than for the case in §29 with equal 

 pulleys. Particles at the end of the curve in 

 view are in like figures of vibration. In the 

 above table, §10, the passage for any single 

 pair of cams is now diagonally across the 

 diagram, but from right to left, downward. 



