1893. BIOLOGICAL THEORIES. 425 
The diameter of the circular orbit of a particle at the surface is 
equal to the height of the crests above the troughs, as has already 
been seen. The point which is of most importance to the jelly-fish, 
however, is the amount of movement and of deformation at various 
depths below the surface. This has been investigated by mathema- 
ticians, who express the result as follows :—-Calling the diameter of 
the circular path of any particle the ‘‘ extent ”’ of its movement, and 
writing a for the extent of movement of a superficial particle, that is, 
for the height of the crests above the troughs, and X for the distance 
between one crest and the next, then a particle which in the undis- 
turbed water is at a distance / below the surface will in the disturbed 
anh 
water move to the extent expressed in the formula ae~ 1 
At a quarter of a wave-length from the surface 4h = A, and the 
extent becomesae ”7 =” or one-fifth of extent of movement at the 
surface. At half a wave-length below the surface 2h = A, and the 
extent, therefore,ae ”= one twenty-third of a. At one wave-length 
the extent is ae~?”= <1. of a. (The calculations are only rough 
approximations. ) 
From this it is obvious that, however violent the movement may 
be at the surface, there is always a zone to be found not far from the 
surface where the jelly-fish may swim and feed in safety, but above 
which it would be exposed to danger from the violence of the move- 
ments of the water. This zone we will call the ‘‘ zone of safety,” 
but it appears probable that the name ‘zone of maximum food- 
supply”? would be equally appropriate. Its depth below the surface 
varies with the violence of the movements at the surface. In still 
water it is at the surface. 
I have now to show reason for the belief that the tentaculocysts, 
without giving rise to any sensation, can automatically steer the jelly- 
fish in such way as to keep it close to this zone and to bring it back 
to this zone whenever it is forcibly carried away from it (as by 
currents), and that this will happen, whatever the distance of this zone 
below the surface may be. 
Before considering how the tentaculocysts can serve this 
important function, I would once more remind my readers that the 
only waves we have been considering are waves—not breakers or 
‘‘ white horses ’’—in the deep ocean, and not in shallow water. 
Suppose the jelly-fish to be some distance below this zone of 
safety and in water in which there is no appreciable disturbance, it 
will then, by virtue of the greater specific gravity of its oral portion, 
float with the mouth downward. Its rhythmic contraction will, under 
these circumstances, by increasing the mutual pressure between the 
water in the sub-umbrellar space and the inner surface of the 
umbrella, cause the animal to move upwards till it reaches a zone 
