182 Lord Rayleigh on Porous Bodies 
conduction of heat ; but the influence of these is enormously- 
augmented by the contact of solid matter exposing a large 
surface. At such a surface the tangential as well as the nor- 
mal motion is hindered, and a passage of heat to and fro takes 
place, as the neighbouring air is heated and cooled during its 
condensations and rarefactions. With such rapidity of alter- 
nations as we are concerned with in the case of audible sounds, 
these influences extend to only a very thin layer of the air 
and of the solid, and are thus greatly favoured by attenuation 
of the masses. 
I have thought that it might be interesting to consider a 
little more definitely a problem sufficiently representative of 
that of a porous wall, in order to get a better idea of the 
magnitudes of the effects to be expected. We may conceive 
an otherwise continuous wall, presenting a flat face, to be per- 
forated by a great number of similar small channels, uniformly 
distributed, and bounded by surfaces everywhere perpendi- 
cular to the face. If the channels be sufficiently numerous, 
the transition from simple plane waves outside to the state of 
aerial vibration corresponding to the interior of a channel of 
infinite length, occupies a space which is small relative to the 
wave-length of the vibration, and then the connexion between 
the condition of things inside and outside admits of simple 
expression. 
Considering first the interior of one of the channels, and 
taking the axis of x parallel to the axis of the channel, we sup- 
pose that as functions of x the velocity-components u, v, w, and 
the condensation s are proportional to e iKX , while as functions 
of t everything is proportional to e int , n being real. The rela- 
tionship between k and n depends on the nature of the gas and 
upon the size and form of the channel, and must be found in 
each case by a special investigation. Supposing it known for 
the present, we will go on to show how the problem of reflec- 
tion is to be dealt with. 
For this purpose consider the equation of continuity as in- 
tegrated over the cross section of the channel o\ Since the 
walls are impenetrable, 
so that 
n^sda- + K^udc7 = (1) 
This result is applicable at points distant from the open end 
more than several diameters of the channel. 
Taking now the origin of w at the face of the wall, we have 
to form corresponding expressions for the waves outside ; and 
