198 Loi'd Bayleigh on Diffraction of Sound. [Jan. 20, 



Such a system has been cut out of zinc, and is now hanging before 

 you. When the adjustments are correct there will be produced, under 

 the action of that circular grating, an effect much greater than would 

 result if the sound-waves were allowed to pass on without any obstruc- 

 tion. The only point difficult of explanation is as to what happens 

 when the system of zones is complete, and extends to infinity, 

 viz. when there is no obstruction at all. In that case it may be 

 proved that the aggregate effect of all the zones is, in ordinary 

 cases, half the effect that would be produced by any one zone 

 alone, whereas if we succeed in stopping out a number of the 

 alternate zones, we may expect a large multiple of the effect of one 

 zone. The grating is now in the right position, and you see the flame 

 flaring strongly, under the action of the sound-waves transmitted 

 through these alternate zones, the action of the other zones being 

 stoi^ped by the interposition of the zinc. But the interest of the 

 experiment is principally in this, that the flame is flaring more than 

 it would do if the grating were removed altogether. There is now, 

 without the grating, a very trivial flaring ;* but when the grating is 

 in position again — though a great part of the sound is thereby 

 stopped out — the effect is far more powerful than when no obstruc- 

 tion intervened. The grating acts, in fact, the part of a lens. It 

 concentrates the sound upon the flame, and so produces the intense 

 magnification of eflect which we have seen. 



[The exterior radius of the nth. zone being x, we have, from the 

 formula given above : 



1 1 _ wA_ 



a X- 



80 that if a and h be the distances of the source and imago from the 

 grating, the relation required to maintain the focus is as usual, 



i + l-i 



where /, the focal length is given by : 



•^ n\ 



In the actual grating, eight zones (the first, third, fifth, &c.) are 

 occupied by metal. The radius of the first zone, or central circle, is 

 3 inches, so that x- / 7i = 9. The focal length is necessarily a func- 

 tion of X. In the present case A = J inch nearly, and therefore 

 / = 18 inches. If a and h are the same, each must be made equal to 

 36 inches.] 



[Eatleigh.] 



* Under the best conditions the flame is absolutely unaffected. 



