Supposing the jerks to be so timed as to cause each hump to be one-third of the tube’s length. At the end of one-third of a second from starting the pulse will be in the position _a b_ (1), Fig. 38. In two-thirds of a second it will have reached the position _b b′_ (2), Fig. 38. At this moment let a new pulse be started at _a_; after the lapse of an entire second from the commencement we shall have two humps upon the tube, one occupying the position _a b_ (3), the other the position _b′ c_ (3). It is here manifest that the end of the reflected pulse from _c_, and the end of the direct one from _a_, will reach the point _b′_ at the same moment. We shall therefore have the state of things represented in (4), where _b b′_ wishes to move upward, and _c b′_ to move downward. The action of both upon the point _b′_ being in opposite directions, that point will remain fixed. _And from it, as if it were a fixed point, the pulse b b′ will be reflected, while the segment b′ c will oscillate as an independent string._ Supposing that at the moment _b b′_ (4) begins to be reflected at _b′_ we start another pulse from _a_, it will reach _b_ at the same moment the pulse reflected from _b′_ reaches it. The pulses will neutralize each other at _b_, and we shall have there a second node. Thus, by properly timing our jerks, we divide the rope into three ventral segments, separated from each other by two nodal points. As long as the agitation continues the tube will vibrate as in (6). There is no theoretic limit to the number of nodes and ventral segments that may be thus produced. By the quickening of the impulses, the tube is divided into four ventral segments separated by three nodes; quickening still more we have five ventral segments and four nodes. With this particular tube the hand may be caused to vibrate sufficiently quick to produce ten ventral segments, as shown in Fig. 38 (7). When the stretching force is constant, the number of ventral segments is proportional to the rapidity of the hand’s vibration. To produce 2, 3, 4, 10 ventral segments requires twice, three times, four times, ten times the rapidity of vibration necessary to make the tube swing as a whole. When the vibration is very rapid the ventral segments appear like a series of shadowy spindles, separated from each other by dark motionless nodes. The experiment is a beautiful one, and it is easily performed.