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



to discover if possible for what value of u, U^ has its greatest 

 value, that is the point in LO where the supply from the source is 

 strongest, u varies from to I. Of course I will vary according 

 to the reflector used. If portability be chiefly regarded, perhaps 

 we might consider the values of I chosen for my reflectors as not 

 unreasonable, say I = § for the large reflector and I = £ for the 

 small (or ear) one, taking one foot as the unit of length. Any 

 way we may perhaps practically regard I as < 1. 



If A be chosen so large that u/A is small, we have from (39) 

 approximately 



U 1 - 



cob {2 (Au)l-\ir} 



77-s (Au)i 



(82). 



If we take no notice of the variation of the numerator, (82) 

 shews us that generally U^ increases numerically as u diminishes, 

 that is that the strength of the source increases as we approach the 

 geometrical focus of the reflector, in fact when u = 0, (82) becomes 

 infinite, but we must carefully notice that (82) is not and does not 



Fig. 7. 



profess to be a true approximation to U x when u is very small or 

 zero. When u = (15) gives us U 1 = l. It seems certain there- 

 fore that, while A remains constant and u varies from up to I, 

 Z7j must somewhere have its greatest possible value, and that this 

 corresponds to some small value of u. We will endeavour to find 



