258 



Mk HOPKINS ON AERIAL VIBRATIONS 



So far these phenomena are in accordance with the results of 

 theory, (Art. 22, VI.) ; but when we examine the length I just men- 

 tioned, we find it entirely at variance with them. In fact on 

 investigating the circumstances more narrowly, we find that the value 

 of / depends in a considerable degree on the small distance between 

 the vibrating plate, and the extreme section A of the tube, a cir- 

 cumstance which nothing in our theoretical deductions has led us 

 to anticipate. This will be seen in the results of the following ex- 

 periment made with an open tube. 



Diameter of the tube = 1 . 35 inches. 



Value of- ,.=4.82 for temperature 63°. 



Position of the mouth (^A) of the 

 tube (Fig. I.) 



Value of the length / 

 above mentioned. 



Theoretical value of /. 



As close to the plate as 

 possible without interfering 

 with its vibrations 



About T^ inch from thel 



lo I 



vibrating plate. 



.12.25 inches. 



* 1 1 . 46 inches. 



12. 6 



31. This discrepancy however between the theoretical and ex- 

 perimental results is only apparent. It arises from the circumstance 

 of one of the conditions assumed in our mathematical investigation, 

 not being accurately satisfied, namely, the perfect prevention of all 

 communication between the external air and that within the tube at 

 the extremity next the plate. And this is easily proved experi- 

 mentally, by placing the extremity of the tube as near as possible 



* In this value of Z I have taken account of the displacement of the nodes, which is .59 

 inches, as determined by experiment. (See Table, Art. S6.) 



