And here a difficulty presents itself. The stopped end _b_ of the tube Fig. 110 is, of course, a place of no vibration, where in all cases a nodal dust-heap is formed; but, whenever the column of air was an exact multiple of the wave-length, M. Kundt always found a dust-heap close to the end _a_ of the vibrating rod also. Thus the point from which all the vibration emanated seemed itself to be a place of no vibration. [Illustration: FIG. 112.] This difficulty was pointed out by M. Kundt, but he did not attempt its solution. We are now in a condition to explain it. In Lecture III. it was remarked that in strictness a node is not a place of no vibration; that it is a place of _minimum_ vibration; and that, by the addition of the minute pulses which the node permits, vibrations of vast amplitude may be produced. The ends of M. Kundt’s tube are such points of minimum motion, the lengths of the vibrating segments being such that, by the coalescence of direct and reflected pulses, the air at a distance of half a ventral segment from the end of the tube vibrates much more vigorously than that at the end of the tube itself. This addition of impulses is more perfect when the aërial column is an exact multiple of the wave-length, and hence it is that, in this case, the vibrations become sufficiently intense to sweep the dust altogether away from the vibrating segments. The same point is illustrated by M. Melde’s tuning-forks, which, though they are the sources of all the motion, are themselves nodes.