The uncertainty as to the length of the pace-making circuit that the nerve-impulse takes around the ring may be avoided by stretching the inner edge of the ring until it is of the same diameter as the outer, thus transforming the ring into a cylinder or belt. Such a ring can be stretched further and behaves in a strikingly reversible manner. Since Mayer (1917) has shown that the rate of nerve-conduction in Cassiopea depends on temperature and electric conductivity of the sea water, it should be noted that all the experiments in this paper, unless otherwise stated, were made in sea-water of 30° and Cl = 20. Mayer found a variation of only about 2.5 per cent over the range of pH = 5.6 to 8.26, and this variation includes experimental errors and changes due to unknown causes. In the present experiments the pH was about 8.2 unless otherwise stated. The only difficulty in estimating the rate of the contraction-wave arose from the fact that the rate is 1 to 5 per cent faster in the ring that has just been stretched than in the ring that has just been relaxed, depending on the degree of recent stretching or relaxation. If, however, the circumference of the ring is allowed to remain constant for 5 minutes after each short step of stretching or relaxation, the rate will approximate a mean value.
This behavior of the ring may be regarded as a form of hysteresis, since the number of revolutions per second of the contraction-wave tend to remain constant immediately after stretching or relaxation. I do not see how this can be explained on the assumption that the stretching of the neuraxon is the only factor, and it is significant to note that Carlson records no such hysteresis in the stretched nerve of the slug, where synapses are less numerous or entirely absent. One explana tion of the increased rate immediately after stretching might be the thinning of the plasma membrane of the neuraxon, the regeneration in thickness taking appreciable time. Another suggestion is made that the immediate effect of stretching is increase in length of the neu raxon, but that this may be proportionately less than the increase in length of the strip of tissue, since the nerve-paths may be straightened, and that the apparent hysteresis is due to the possibility that after the nerve is stretched synapses gradually open, due to the tension, until the nerve-paths are proportionately as zigzagged as at the start. This supposition may similarly be applied to the fact that by prodding a cassiopea (having a trapped wave) with a stick, the number of revolu tions of the wave per second is reduced, although no apparent increase in length of the conducting-path remains. The local stretching of the subumbrella with the stick might break some of the synapses.
Such complicated suppositions are not very useful, however, since they are not easily tested. A more probable hypothesis is given below in connection with the amplitude of the contraction-wave. The sig nificant fact is that (ignoring the period of readjustment) the ring may be stretched until the circumference is increased 72 per cent with practically no change in rate (millimeters per second), although in order to accomplish this the number of revolutions per second or pass ages of the wave through the same tissue may be reduced 46 per cent.
This is analogous to the effect of stretching a metallic wire on the passage of an electric current through it, with the difference that the process is completely reversible in Cassiopea after an increase of 84 per cent in length due to stretching. The results on two rings are shown in table 18, the rate being given in millimeters per second.
If the rate of wave propagation is the same, we would expect that in umbrellas of cassiopeas of different sizes the number of revolutions of the wave per second would be inversely proportional to the diam eter. The diameter is measured before the wave is started and there is a progressive shrinkage in the diameter, due to starvation and decrease in volume, tension of the regenerating tissue after re moval of the rhopalia, and in creased tonus of the musculature . .
(sometimes transforming the into a cup-shape). This decrease in the diameter is associated with increase in revolutions per second, but agitation decreases the rev°. lutions per second. It is there fore necessary to make the deter minations under the same con ditions for strictly comparative results. The determinations in table 19 were rough, but serve to indicate the general features.
A comparison of these experi ments with those on the actual velocity of the wave shows the circumference of the potential pace-making circuit to be about 1.8 times the diameter.
If the contraction-wave is stopped by pressure and after a rest of some minutes or hours is started again, it is slower than just before stopping, but if it is started again as quickly as possible after stoppage the rate is the same. This effect of a rest may be associated with nutrition or recovery from fatigue, since the amplitude of the contrac tion-wave is greater in the rested umbrella, although the number of revolutions per second is decreased. Whether the actual rate of propagation is changed would be difficult to determine. It seems evi dent that the wave of nerve-impulse precedes the wave of muscular contraction. The contraction of the muscle must stretch the adjacent regions, and hence stretch the region through which the nerve-impulse is passing, thus increasing the distance traveled in one revolution and decreasing the revolutions per second. When the amplitude of con traction is increased, the stretching of the nerves is increased and the revolutions per second are decreased, but whether this can account for the total decrease has not been determined. The speeding-up of the revolutions per second after the trapped wave is started is at first more abrupt and later more gradual, and is associated with both de crease in amplitude of contraction and decrease in diameter of the umbrella, due to starvation and contraction of scar-tissue.