THE TROCHOIDED PLANE. 67 
of the eel as the type), and a series of waves be passed through 
each muscle, such that the thick part of one wave is abreast th 
thin part of the wave on the other side of the eel, the backbone 
and skin will necessarily take a trochoidal form, and as long as 
the gored are generated the eel must go 
will be observed that if the fish or eel is swimming with its 
a and the a on the back and belly are kept rigidly extended, 
they serve feeds rease the sag tay surface. The body swimming 
of fishes Hehe its extreme form in the sunfish, whose powerful 
body par otis of extreme eaats in proportion to their 
amplitude. 
Porpoises, when rolling, seem to cut vertical prolate-cycloidal 
waves, and they blow when passing the crests; the horizontal 
position of the tail is well adapted for this mode of progression. 
If the top edge of the tail of a —,- or — deep fish, be 
twisted to one side, and the lower edge to . side, and ‘the 
trochoidal action of the body continued, ae ons t once turns on 
its a and will thus be able to dive suddenly. 
effect on the water of this action of fishes that are long 
iieak to contain a number of waves in their length is a tendeney 
to produce right-handed vortices on one side, and left-handed ones 
on the other, so that after the fish has passed the two series gear 
together, as it were, like a train of equal sized cog-whee 
If we conceive the action of the back fin, as thus described to 
be communicated to a series of legs on each side, as in the centi- 
pede, the effect will obviously be progression along a surface ; and 
if we cut off all the legs but two pairs, separated by a distance 
equal to one wave length, we have the quadr cout action popu- 
larly assigned to the giraffe ; if the two pairs are only half a wave 
length apart, we have the trottin of a horse, and the various 
other paces become clearly dependent on the length of the wave 
used by the animal. The legs and body of an alligator or lizard 
Tinks of which are unknown, whilst any two ian links are 
hardly distinguishable. The swinging of the hands and arms, in 
walking or running, is evidence that bipedal is evolved from quad- 
rupedal progression, which to me seems to have developed from the 
trochoidal action of-a fin. 
When the amplitude of the waves is in a vertical plane, each 
pair of legs is moved together, and the form of the wave is plainly 
seen in the back of a dog when going full split ; this method of 
progression reaches its extreme form in the hopping birds. 
