276 NEWTON S PBINCIPIA. 



of the observed and calculated velocity was now found to 

 be very close. 



The value of x depends on the general temperature of 

 the air. By Amontem s law, we know that if K be the 

 value at any temperature, the value at any other exceeding 

 this by will be 



where a = -r^-. If, therefore, the temperature of the air 



be above 60, the velocity of sound will be 1124 



feet nearly - ! &quot; 



The demonstration we have given of Newton s propo 

 sition of the motion of sound in a tube may easily be 

 extended into a vigorous demonstration. For the accele 

 rating force on any element having been shown to be 



the equation of motion must be 



d t 2 dx 



putting a 2 for x (1 -f /3). This equation must be true for 

 the motion of sound in a tube under all circumstances. 

 Thus, the tube may be finite, open or closed, and the dis 

 turbance may be caused in any manner. The complete 

 integral of this equation is known to be 



where / and ty are unknown functions depending on the 

 nature of the disturbance and the other circumstances of 

 the tube. 



This investigation of the motion of sound in the air 

 depends on the assumption that the medium is a perfect 

 fluid. But this is not the case. The effect of internal 



