Prof. Tyndall on the Vibrations of Strings. 69 



separated from each other by the appropriate number of nodes. 

 With a certain rapidity of vibration on the part of my hand I cause 

 the rope to swing to and fro as a whole. Twice that rapidity divides 

 it into two equal vibrating parts ; three times that rapidity into three 

 vibrating parts, and so on. The number of vibrating parts, or ven- 

 tral segments, as they are called, is in fact directly proportional to 

 the rapidity of my hand's vibration. 



5. In these cases, where every point of every ventral segment 

 moves to and fro at the same time, we have examples of stationary 

 undulations. 



6. My hand, which produces this vibration, does not move through 

 more than half an inch of space, while the ventral segments oscil- 

 late through a space of four-and-twenty. This wide vibration is in 

 fact produced and maintained by the addition together of small im- 

 pulses properly timed. The nodes, moreover, though apparently 

 motionless, are not strictly so ; for if they were, the vibration of the 

 segments would soon come to an end. In fact, it is by the motion 

 transmitted through the nodes that the vibrations of the rope are 

 sustained. 



7. I might attach the free end of this rope to any suitable vibra- 

 ting body instead of taking it in my hand. If the rate of vibration 

 of the body were that of any aliquot part of the rope, it would 

 divide itself accordingly. 



8. The effect may also be produced by causing the vibrations of 

 an aliquot part of our rope to excite vibrations in the remaining 

 portion. Stretched vertically from top to bottom of this wooden 

 frame is an india-rubber tube. I encircle the middle of the tube 

 with the finger and thumb of my left hand, and pull the lower half 

 aside with my right. The lower half vibrates, but the upper half 

 vibrates also. In fact the small amount of play permitted by my 

 hand has enabled the pulse to transmit itself, to be reflected, and to 

 accumulate its motion to this extent. I withdraw my left hand : 

 the tube continues to vibrate in two equal parts, divided from each 

 other by a node. 



9. I encircle the tube at one- third of its length from the lower 

 end, and pull aside the shorter segment ; it vibrates more quickly 

 than the half tube, and the vibration immediately causes the upper 

 and longer'portion to divide into two equal parts. I now withdraw 

 my hand, and the tube continues to vibrate in three equal segments, 

 which are separated from each other by two nodes. 



10. In like manner I encircle the tube at one quarter of its length 

 from its lower end, and pull the lower and shorter segment aside ; 

 itjvibrates, and forthwith the longer segment above divides into three 

 vibrating parts. I now withdraw my hand, and the tube continues 

 to oscillate in four equal segments, separated from each other by 

 three nodes. 



11. Again, from side to side of the room is stretched this stout 

 iron wire 24 feet long. I seize the wire at the point which 

 divides it into two parts, one three times as long as the other, and 

 pulling the shorter segment aside permit it to vibrate ; the remain- 

 ing p ortion of the wire divides itself into three ventral segments. I 



