96 



SCIENCE PROGRESS 



Fig, 3. 



The shell, in passing through the air, is continuously setting 

 up pressure waves which travel onward with the velocity 

 of sound, and thus faster than the shell itself. It is impossible 

 to draw all these pressure-waves, so we will content our- 

 selves by indicating only those 

 that are set up at the end of 

 successive seconds. At the end 

 of the first second the pressure- 

 wave will originate from the 

 point /, and will have four 

 seconds left in which to travel, 

 so that its position at the end 

 of the fifth second will be as 

 shown by the arc b, the pressure- 

 wave set up as the shell leaves 

 the gun being coincident with 

 the sound-wave of the discharge 

 report, and so represented by 

 the arc a. 



At the end of the second 

 second the pressure-wave will originate from the point //, 

 and will have three seconds left in which to travel, so that 

 its position will be indicated by the arc c. 



Similarly, the pressure-waves at the end of the third and 

 fourth seconds will originate from points /// and IV, and will 

 have two and one seconds respectively in which to travel, 

 and so at the time we are considering will be represented by 

 the arcs d and e. 



An observer at the point P would hear the report of the 

 discharge, and then a continuous sound as the pressure-waves, 

 b, c, d, e, pass him ; then would come the shell and the sound 

 of its explosion as it burst. This continuous, long drawn-out 

 sound was the ordinary well-known " whine " of the howitzer 

 shell. 



On the sound-ranging film this was recorded as a sharp 

 break followed by a series of more or less wavy fluctuations, 

 as seen clearly in Fig. i. 



The case of the gun, however, is altogether different, for 

 the shell travels faster than sound, and so the pressure-waves 

 caused by it arrive at any given point before the sound of the 

 discharge, i.e. the report of the firing. This pressure-wave 

 is itself received by the ear as a sound-wave, so that in 

 the case of the gun two reports are heard. Fig. 4 will make 

 this clear. 



Suppose, for the sake of argument, that a high-velocity 

 shell loses one-tenth of its velocity per second and leaves the 

 gun with an initial speed twice that of sound ; its position 



