250 LETTERS ON NATURAL MAGIC. 



remain fixed during the opposite excursions of the spiral 

 springs : nay, if we remove the partition, and hook the 

 end of one spiral spring to the end of the other, the node 

 or point of junction will remain stationary during the 

 movements of the springs, because at every instant that 

 point is drawn by equal and opposite forces. If three, 

 four, or Jive spiral springs are joined in a similar manner, 

 we may conceive them all vibrating between their nodes 

 in the same manner. 



Upon the very same principles we may conceive a long 

 column of air without partitions dividing itself into two, 

 three, or four smaller columns, each of which will vibrate 

 between its nodes in the same manner as the spiral spring. 

 At the middle point of each small vibrating column the 

 air will be of its natural density like that of the atmo- 

 sphere, while at the nodes B, &c., it will be in a state of 

 condensation and rarefaction alternately. 



If, when the air is vibrating in one column in the pipe 

 A B, as in Fig. 41, Nos. 2, 3, we conceive a hole made in 

 the middle, the atmospheric air will not rush in to 

 disturb the vibration, because the air within the pipe and 

 without it has exactly the same density. Nay, if, instead 

 of a single hole, we were to cut a ring out of the pipe at 

 the middle point, the column would vibrate as before. 

 But if we bore a hole between the middle and one of the 

 ends, where the vibrating column must be either in a 

 state of condensation or rarefaction, the air must either 

 rush out or rush in, in order to establish the equilibrium. 

 The air opposite the hole will then be brought to the 

 state of the external air like that in the middle of the 

 pipe, it will become the middle of a vibrating column, 

 and the whole column of air, instead of vibrating as one, 

 will vibrate as two columns, each column vibrating with 

 twice the velocity, and yielding harmonic sounds along 

 with the fundamental sound of the whole columns, in the 



