Mr Sharpe, On the Reflection of Sound at a Paraboloid. 193 



It will be observed that as we pass from infinity along the axis 

 from X towards the maxima air-velocities gradually increase in 

 intensity till at Vi we have the greatest maximum. 



On the left of OR' we have a state of air- velocity at Ui, u^, u^, etc., 

 P\, P-2, p3, etc., exactly the image, in the line OR', of that which 

 exists on the right of OR'. Of course on the right of Vi,V2,V3, etc., 

 are real foci of reflection. But on the left of (as the figure is 

 drawn) only Ui and U2 are real foci, all the rest U3, u^, etc., are 

 virtual foci of reflection. And here it must be noted that the 

 point r^ in fig. 9 is supposed to be identical with the point L' in 

 fig. 8. The points L and L' being points of no air-velocity must 

 be made identical with some of the points ri, r^, etc., and p^, p^, etc., 



Fig. 9. 



in fig. 9 — taken in pairs as r^pi, r2p2, ^sps, etc. As we have 

 chosen the size of the Reflector so that L' coincides with r^ (fig. 9) 

 we shall have I (or. Art. 39, going back to the original notation) 

 pi = 7"01. Suppose ^ to be 8 inches (the size of a portable Sound 

 Reflector I actually made). Then |)=1051, a high note just 

 within the range of a piano. 



Suppose (fig. 9) we had made L' to coincide with r^ (instead 

 of Ta) we should have gotjjl = 3*83, and then p would be 5*74. We 

 thus see that as we experiment with higher and higher notes, 

 more and more points of maximum velocity are crowded into the 

 space LL' (see fig. 8) that is in the neighbourhood of the focus 0. 

 It must, however, be noticed that in this case where A = 0, which 

 we have been considering, is always a point of rest. 



