246 



LETTERS ON NATURAL MAGIC. 



the finger, or with a feather at the middle point C, Fig. 

 40, it will give out a more acute but fainter sound than 

 before, and while the extent of its vibrations is diminished, 

 their frequency is doubled. In like manner, if we touch 

 the string A" B", Fig. 40, at a point C, so that A" C is 

 one-third of A" B", the note will be still more acute, and 

 correspond to thrice the number of vibrations. All this 

 might have been expected, but the wonderful part of the 

 experiment is, that the vibrating string A' B' divides 

 itself at C into two parts A' C, C B', the part A' C 

 vibrating round A' and C as fixed points, and the part 

 C B' round C and B', but always so that the part A' C is 



Fig. 40. 



at the same distance on the one side of the axis A' B' as 

 at A m C, while the part C B is on the other side, as at 

 C n B. Hence the point C, being always pulled by equal 

 and opposite forces, remains at rest as if it were absolutely 

 fixed. This stationary point is called a node, and the 

 vibrating portions A' m C, C n B' loops. The very same 

 is true of the string A" B", the points C and D being 

 stationary points ; and upon the same principle a string 

 may be divided into any number of vibrating portions. 

 In order to prove that the string is actually vibrating in 

 these equal subdivisions, we have only to place a piece of 

 light paper with a notch in it on different parts of the 



