On C. S. Lyman's new form of Wave- apparatus. 17 



equally represents a wave whose length is 36 feet and height 

 4 feet, with period 2'63 ; and similarly for other proportional 

 dimensions. 



Among the particular points in wave-phenomena which are 

 elucidated by this apparatus may be enumerated the following : — 



1. The undulating surface-profile. — This is shown in the mo- 

 tion of the upper flexible wire, which presents a continuous 

 contour-line, of the exact curvature throughout of a true normal 

 wave — instead of a broken contour of arbitrary form, by means 

 of rising and falling balls, as in the ordinary wave-apparatus. 



2. The undulatory motion of all subprofiles y or lines of equal 

 pressure down to still water. — The representative of such lines is 

 the lower transverse wire, which moves similarly to the upper 

 one, but with a less curvature. Every such line of equal pres- 

 sure is a continuous one, composed of particles in a state of dy- 

 namical equilibrium^ and constituting an ideal moving wave 

 exactly as if at the surface, the corresponding phases of all such 

 waves being on vertical lines. 



3. The genesis of the undulatory motion from the circular motion 

 of revolution. — This is seen in the mode in which the crank-pins, 

 in each transverse series, or the particles which they represent, 

 come in regular succession into a given position as they revolve 

 synchronously in their orbits. 



4. The equality of the height of a wave from trough to crest, 

 with the diameter of the orbits of the surface particles. — This is 

 obvious in the apparatus, and follows directly from the mode in 

 which the wave-surface is generated. 



5. The direction of motion of particles of water in the different 

 phases of a wave. — A glance at the motion of the crank-pins shows 

 that a particle at the wavers crest is moving forward, or in the 

 direction in which the wave is propagated, and a particle at the 

 trough in the reverse direction, or backward, that a particle on 

 the forward slope is rising, and one on the back slope descending. 

 The same is true of particles in all the subwaves, or surfaces of 

 equal pressure, down to still water. 



6. The length of a pendulum keeping time with the wave. — This 

 is equal to the radius of a circle whose circumference is the 

 wave's length. Such a circle is the large one drawn on the 

 background, as shown in the figure. Its radius is to that of a 

 particle's orbit (or length of a crank-arm) as the particle's 

 weight is to its centrifugal force. Or putting R and r for these 

 radii respectively, and t for the time of revolution, we make 



47r 2 r 

 R:r::g: -^-, 



whenCC ^2tt X /5; 



V 9 



Phil. Mag. S. 4. Vol. 36. No. 240. July 1868. C 



