388 0.8. Lyman’s new form of Wave apparatus. 
ing particle; their resultant, then, is represented by the third 
side of the triangle of forces, or the side formed by the wire 
pendulum. This resultant must be always normal to the wave 
surface, as the wire pendulum is seen to be always at right an- 
gles to the elastic wire representing that surface. 
9. The condition of a wave’s rupture at the erest. When 
the centrifugal force becomes equal to gravity (or the radius of 
the orbit to that of the large circle), the resultant force, for a 
particle at the highest point of its orbit, or crest of the wave, 
must be zero, and the particle consequently fly from its orbit, 
or the crest break in foam. 
10. The trochoidal form of the wave curve. The point of 
suspension of the pendulum, that is, the upper extremity of 
the vertical radius of the large circle, may be regarded as the 
instantaneous center about which an element of the wave curve 
at the point of normalcy of the pendulum is described. Con- 
sequently, if this circle be rolled under a horizontal straight 
line, a point within it distant half the height of a wave from 
the center, will trace the wave profile ; which therefore 1s & 
trochoid. The rolling circle is the same for all wave profiles, 
down to still water, the lengths of the tracing arm only dit 
ering. The circumference of this circle equals, of course, the 
wave’s | 
11. The greater sharpness of the crests than of the troughs 
of waves, This follows from the preceding, and is shown 1D 
the relative positions of the crank-pins—nearer together at the 
crests, farther apart in the troughs. The trochoids become, 
ty. 
13. The greater elevation of the crests above the level of still 
water, than depression of the troughs below it. The difference 
Sadie this elevation and depression is equal to twice = 
twice the height from which 
elocity; or, is a third proportional 
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