In a circular strip the rate of the waves is uniform over the whole extent of the strip; so that the time of their transit from one point to another varies directly as the length of the strip. But on now narrowing such a strip, although the rate is thus slowed, the relation between the narrowing and the slowing is not nearly so precise as to admit of our saying that the rate varies inversely as the width. The following figure will serve to show the proportional extent to which the passage of contraction-waves is retarded by narrowing the area through which they pass:—
Fig. 13.
Fig. 14.
In such experiments it generally happens, as here represented, that reducing the width of a circular strip by one-half produces no effect, or only a slight effect, on the rate, while further narrowing to the degree mentioned produces a conspicuous effect. I may also state that if, as occasionally happens, the immediate effect of narrowing a circular strip to one-half is to temporarily block the contraction-waves, when the latter again force their passage, their rate is slower than it was before. It seems as if the more pervious tissue tracts having been destroyed by the section, the less pervious ones, though still able to convey the contraction-wave, are not able to convey it so rapidly as were the more pervious tracts.
In order to ascertain whether certain zones of the circular contractile sheet in all individuals habitually convey more of the contractile influence than do other zones, I tried a number of experiments in the following form of section. Having made a circular strip, I removed all the lithocysts save one, and then cut the strip as represented in Fig. 14. On now stimulating the end a, or on watching the lithocyst there discharge, the resulting contraction-wave would be observed to bifurcate at b, and then pass on as two separate waves through the zones, b c, b d. Now, as these two waves were started at the same instant of time, they ran, as it were, a race in the two zones, and in this way the eye could judge with perfect ease which wave occupied the shortest time in reaching its destination. This experiment could be varied by again bisecting each of these two zones, thus making four zones in all, and four waves to run in each race. A number of experiments of this kind showed me that there is no constancy in the relative conductivity of the same zones in different individuals. In some instances, the waves occupy less time in passing through the zone b c than in passing through the zone b d; in other instances, the time in the two zones is equal; and, lastly, the converse of the first-mentioned case is of equally frequent occurrence. Very often the waves become blocked in b c, while they continue to pass in b d, and vice versâ. Now, all these various cases are what we might expect to occur, in view of the variable points at which contraction-waves become blocked in spiral strips, etc.; for if the contractile tissues are not functionally homogeneous, and if the relatively pervious conductile tracts are not constant as to their position in different individuals, the results I have just described are the only ones that could be yielded by the experiments in question. Considering, however, that in these experiments the central zones are not so long as the peripheral zones, I think it may fairly be said that the conductile power of the latter is greater than that of the former; for, otherwise, the above experiments ought to yield a large majority of races won by the waves that course through the central zones, and this is not the case. Indeed, it is surprising how often the race is, as it were, neck and neck, thus showing that the relative conductivity of all the zones is precisely adjusted to their relative lengths; and forasmuch as in the unmutilated animal this adjustment must clearly serve the purpose of securing to the contraction-wave a passage of uniform rate over the whole radius of the umbrella, I doubt not that, if it were possible to perform the race-course section without interrupting any of the lines of conduction-tissue, neck and neck races would be of invariable occurrence.
Interdigitating cuts, as might be expected, prolong the time of contraction-waves in their passage through the tissue in which the cuts are interposed. For example, in a spiral strip measuring twenty-six inches in length, the time required for the passage of a contraction-wave from one end to the other is represented by the line a b in the annexed woodcut. But after twenty interdigitating cuts had been interposed, ten on each side of the strip, the time increased to c d, the line e f representing one second. And more severe forms of section are, of course, attended with a still more retarding influence.
Fig. 15.