Mr Sharpe, On the Reflection of Sound at a Paraboloid. 197 



Then U^JA^vh^JA^^^A' ^' 



As J. is large and fi about 1, we get nearly 



^^cos(2i^^i-i7r) 



This shews that the air-velocity curve near the points defined 

 as above is wavy and cuts the axis. It seems probable that this 

 solution will take the same form whether /x differs from 1 in 

 excess or defect. 



47. I will now give a figure (fig. 10) which will illustrate at 

 one view the chief results arrived at in Arts. 42 to 46. The 

 figure is of course not drawn to scale. The Numbers 42 (1) etc. 

 refer to Art. 42, First Part, etc. The little dots clo.se together 

 near a large point on the axis mean that the air-velocity curve 

 near the point is wavy, like that in fig, 9, and cuts the axis. 



U HJH m\m — \ — I 1-^^ — f-wKi 1 H^w 



H I t " i . , 



42 L. A 43 O 43 44 A' 45 L' 42 



(1> 46 (1) (2) (2) 



Fig. 10. 



In this figure LAO A' is the axis of the Reflector of which is 

 the focus and L the vertex. OA is measured to the left o( = A 

 and OA' to the right = A. One curious result is that at all points 

 between and A' on the right of the velocity curve is 

 " exponential." 



