OF AIR OBSERVED IN KUNDT’S TUBES. 
9 
A few corresponding values of fiy and of —(sin /3y +fe ^)e ^+f are annexed, in 
order to show the distribution of velocities within the thin frictional layer. 
ft/- 
ft/- 
7T 
3tt 
+ •055 
16 
-•038 
"8 
7T 
8 
-•054 
7T 
2 
+ 151 
377 ’ 
Id 
-•049 
7T 
+ •374 
7T 
37T 
+ •384 
4 
-•025 
“2 
It appears that (sin 2 kx being positive) the velocity is negative from the plate out¬ 
wards until /3y somewhat exceeds y7r, after which it is positive, until reversed by the 
factor (1 — 2 ky). The greatest negative velocity in the layer is about y of that which 
is found at a little distance outside the layer. 
Faraday found that fine sand, scattered over the bottom, tended to collect at the 
loops. This is in agreement with what the present calculation would lead us to 
expect, provided that we can suppose that the sand is controlled by the layer at the 
bottom whose motion is negative. The exceeding thinness of the layer, however, pre¬ 
sents itself as a difficulty. The subject requires further experimental investigation ; 
but in the meantime the following data may be worth notice, though in some respects, 
e.g., the shallowness of the liquid in relation to the wave-length, the circumstances 
differed materially from those assumed in the theoretical investigation. 
The liquid was water (^—•014 C.G.S.), and the period of vibration was yy, so that 
v = 2nX 15. The thickness of the layer 
7T 
4 
= '0135 centim. 
Measurements of the diameters of the particles of sand gave about '02 centim., so 
that the grains would be almost wholly immersed in the negative layer, even if isolated. 
It seems therefore that the observed motion to the loops gives rise in this case to no 
difficulty. But it is possible that the behaviour of the sand is materially influenced 
by the vertical motion of the vessel by which in these experiments the liquid vibra¬ 
tions are maintained.* 
§ 2. In the problem to which we now proceed the motion will be supposed to have 
its origin in the assumed motion of a flexible plate situated when in equilibrium at 
y— 0. Thus for a first approximation we take u— 0, v = y 0 sin kx e lnt , when y= 0, and 
the question is to investigate the resulting motion of the fluid in contact with the 
plate. 
* See a paper “ On the Crispations of Fluid resting upon a Vibrating Support,” Phil. Mag., July, 1883. 
MDCCCLXXXIV. C 
