PHYSICS: A. G. WEBSTER 
277 
Let Xi = be the volume introduced by the piston X2 that entering by 
the hole. Then 
p^Zo (Xi + X2) = - Z2X2, (5) 
and inserting values, 
X,= - 7T-. (6) 
1 + Vk 
/ki 1\ 
\2t~ c / 
Disregarding phase by taking the modulus and putting k = n/a we have 
the phone formula for the strength of source. 
A = 
where 
dX 
dt 
S^m, (7) 
n 
^ = 
If instead of sending the air out through a hole it goes into a cone or any 
other horn, we must use for the impedance Z2 that given below, and we arrive 
at the theory of the phonograph, and are thus able to answer the question as 
to the function of the horn in persuading the sound to come out of the phono- 
graph when the motion of the diaphragm is given (it is well known that very 
little sound is emitted by the phonograph or the telephone with the horn taken 
off, although in the former case the motion of the diaphragm is exactly the 
same). 
The phonometer was formerly arranged with the back of the diaphragm 
protected from the sound, figure 3. Let F be the external pressure, then, as 
before, 
p = Zo(Xi + X2) (9) 
and in addition, 
--P = Z,X,, (10) 
P- p = Z2X2, 
from which 
Xi= , (11) 
"l~ ^1^2 ~\~ Z2Z0 
giving the formula for the measurement of the pressure, 
P = ^k/S (12) 
(13) 
