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



A is supposed to remain the same large quantity throughout this 

 investigation, in fig. 4, LB being the reflector and Ox its axis. 



Fig. 4. 



Let P 1 be a point for which v/A is small. 



P 2 be a point for which v/A is large. 



A 1 and A 2 points for which v/A = /x moderate, but v and A 

 both large. 



A be a point for which v = A. 



The value of V x at P x is given by (46) which increases as v 

 increases. 



The value of V x at P 2 is given by (61) which decreases as v 

 increases. 



Suppose the ordinates of the curve EFO to represent roughly 

 the values of V x at the various points of the axis at which they 

 are taken, then the curve will take some such form as that shown in 

 the figure, and we might surmise that there might be a maximum 

 ordinate somewhere about A that is somewhere about midway 

 between P x and P 2 , and we shall find presently (Art. 29) that this 

 surmise is verified. But here a caution is necessary. In the 

 present investigation one of the most interesting things is to 

 endeavour to find the point on the axis where the sound has 

 greatest intensity, but we must remember that this intensity is 

 not measured by V x at any point, but (Art. 5) by 2dV 1 /dv, 

 which multiplied by a time factor gives us the velocity of the air 

 particle at the point considered. If then we suppose the ordinates 

 of the curve to represent, not V 1 but dVJdv, it will be found that 

 the curve will have the same general form as before, and in the 

 following articles we will shew that dVJdv has its maximum 

 value at a point a little to the left of A. 



26. We will first examine the value of V x at a point A Y (fig. 4) 

 to the left of A. In (12) drop the dashes and put 



v = Afi (62), 



