Passage of Waves through Apertures in Plane Screens, 259 



focns lenses, especially if the polish is impaired, the central 

 spot may be somewhat distorted, but its centre can be found 

 pretty accurately by taking the semi-diameter of the outer 

 rings. The angle between the planes may conveniently be 

 fixed so that chord = 01 or thereabouts. This will serve for 

 the majority of lenses, but the apparatus is so simple that 

 several gauges of different angles may be kept ready. 



I have not found any inconvenience from the use of marine 

 glue to fasten the plates together, any variation of the angle 

 that may result from changes of temperature being too small 

 to affect the result appreciably. 



21, Norham Road, Oxford, 

 January 1897. 



XXXVII. On the Passage of Waves through Apertures in Plane 

 Screens, and Allied Problems. By Lord Rayleigh, F.R.S.* 



THE waves contemplated may be either aerial waves of 

 condensation and rarefaction, or electrical waves propa- 

 gated in a dielectric. Plane waves of simple type impinge 

 upon a parallel screen. The screen is supposed to be infi- 

 nitely thin, and to be perforated by some kind of aperture. 

 Ultimately one or both dimensions of the aperture will be 

 regarded as infinitely small in comparison with the wave- 

 length (X) ; and the method of investigation consists in 

 adapting to the present purpose known solutions regarding 

 the flow of incompressible fluid. 



If <fi be a velocity-potential satisfying 



d 2 <£/^ 2 =V 2 v 2 & (1) 



where 



V 2 = d*/d.v* 4- d 2 /df + d?ldz\ 



the condition at the boundary may be (i.) that d(f)/dn = 0, or 

 (ii.j that </>=•(). The first applies directly to aerial vibrations 

 impinging upon a fixed wall, and in this connexion has 

 already been considered f- 



If we assume that the vibration is everywhere proportional 

 to e int , (1) becomes 



(V 2 + * 2 )<£ = ; (2) 



where 



k = n/Y = 27r/\ (3) 



It will conduce to brevity if we suppress the factor e inf . 



* Communicated by the Author, 

 t « Theory of Sound/ § 292. 

 X2 



