262 



Mr HOPKINS ON AERIAL VIBRATIONS 



The above values of - were determined by means of a membrane 



2 •' 



and a tube closed at the upper end, nearly 100 inches in length. The 



distance of a node from the closed end being found = b, we must 



Or, if bf be the observed distance, sub- 



have n . - = o, or - = - , 

 2 2 w 



ject to an error /3, and therefore b ± (i the true distance, we have 

 - = - + —. The value of /3 will probably be less than ^ inch, and 



t^ Tt ft 



in the determination, for example, of the first of the above values 



of -, « was about 45, so that that value of - may probably not be 



subject to an error exceeding .001 inch. We may also remark, as an 

 indication of accuracy in the numbers 10.88 and 6.78, given in the third 



* The measures are all given in inches. 



t In the determination of the quantity b, the temperature at the time of observation must 

 be carefully noted, since the variation in the velocity of aerial undulations produced by a varia- 

 tion of temperature of even less than 1°, is sufficient to make a very sensible difference in the 

 value of h, this value being as much as nearly 100 inches. 



Since the distance of any proposed node from the upper end of the tube will be proportional 

 to the velocity of the undulation, it is manifest that by observing the values of b, corresponding 

 to different temperatures, we may estimate directly the effect of temperature on the velocitj' of 

 sound. This method is capable of great accuracy. 



