THE HO N. J. AY. STRUTT OH THE THEORY OF RESONANCE. 
95 
fluid in the plane of the opening is by the symmetry normal, and therefore the velo- 
city-potential is constant over the opening itself. Over the remainder of the plane in 
which the opening lies the normal velocity is of course zero, so that <p may be regarded 
as the potential of matter distributed over the opening only. If the there constant 
value of the potential be called ip 15 the electrical resistance for one side only is 
the integration going over the area of the opening. 
Now 
fjgc7<7=2TX the whole quantity of matter; 
so that if we call M the quantity necessary to produce the unit potential, 
resistance for one side=— 
Accordingly 
c=tM . (23) 
In electrical language M is the capacity of a conducting lamina of the shape of the 
hole when situated in an open space. 
OR 
For a circular hole M=— . and therefore 
c= 2R (24) 
When the hole is an ellipse of eccentricity e and semimajor axis R, 
<=WY (25) 
where F is the symbol of the complete elliptic function of the first order. Results equi- 
valent to (23), (24), and (25) are given by FIelmholtz. 
When the eccentricity is but small, the value of c depends sensibly on the area (<r) of 
the orifice only. As far as the square of e, 
v=*B? s /T^e‘ 2 =7r'R 2 (l-ie 2 ), 
R=\/^( i+ET 
ViH-V;- (26) 
the fourth power of e being neglected — a formula which may be applied without sen- 
sible error to any orifice of an approximately circular form. In fact for a given area the 
circle is the figure which gives a minimum value to c, and in the neighbourhood of the 
minimum the variation is slow. 
Next, consider the case of two circular orifices. If sufficiently far apart they act 
