C. 8. Lyman’s new form of Wave apparatus. 387 
3. The genesis of the undulatory — from the circular 
motion of revolution. This is seen in the mode in which the 
crank-pins, in each transverse series, or ma 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 diffe- 
rent phases of a wave. A glance at the motion of the crank 
pins, shows that a particle at the wave’s 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 9 
ticle on the forward slope is rising, and one on the back slope 
descending. The same is true of particles in all the es gates] 
or surfaces of ome pressure, down to still water. 
6. The length of a pendulum keeping time with the wave. This 
is equal to ie radius of a circle whose circumference is the 
wave’s length. Such a circle is the we one drawn on the 
particle’s orbit (or length of a crank sag as the particle’s 
Weight is to its centrifugal force. Or, putting R and r for these 
radii respectively, and ¢ for the time ‘of revolution, we make 
4nty 
bee ce ae 
Whence | t=2n 
ndent of the length, as a pears | in the apparatus, and as may 
ay inferred Sak the nee given eg thek on. It depends 
on the centrifugal force of the particle, and this, ultimately, 
on the external forces rating it. - 
8. The varying aerection and intensity of the resultant force 
acting, at each instant, on a given en particle in a wave. The 
pate forces are two—the particle’s Sante 2 and its cen- 
he former is represent radius 
of the laced Seiad latter by the iene 
* 
