186 LETTERS ON NATURAL MAGIC. 



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 

 atmosphere; 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 AB, as in Fig. 41, No. 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 same manner as we have already explained 



