94 Mr W. N. Shaw and Mr F. M. Turner. [Feb. 28, 
From these results we may conclude (1) that the wave-length 
in free air is considerably greater than four times the length of 
the whistle. (2) They do not shew any marked difference be- 
tween the whistles. (3) The wave-length perceptibly diminishes, 
i.e. the pitch increases, as the pressure of air increases. 
As to the second result, although the figures do not shew 
distinctly any difference between the ‘whistles, a difference is easily 
heard by the ear at certain wave-lengths. If they are all supplied 
from tbe same air-bag and set to the same length, say 5 mm., one 
will give a good clear note while another only gives a fizz. Owing 
to this difference the measurements could not be taken with 
different whistles at the same pressure. The flame however 
shewed the existence of definite nodes in many cases when the 
sound seemed by hearing very impure, the note being well within 
the limits of audibility. 
The difference between the wave-length in free air and the 
quadruple of the length of the whistle may be attributed partly 
to the diminution of velocity of the sound in the narrow pipe, but 
mainly to the fact recognised, even in the case of pipes of ordinary 
diameter, that the le neth between the whistle opening and the 
closed end requires a correction so that the formula for the 
: v : 
frequency is V, = ——— where = is the correction to the mea- 
4 (1+ 2) 
sured length. 
For a brass pipe, 40 millimetres in diameter and length 7 times 
as great, Wertheim found the value of w to be 1°5 times the dia- 
meter. Assuming the correction proportional to the linear di- 
mensions, the correction in the case of the whistles would be about 
lilmm. This correction would for particular pressures make the 
calculated pitch agree with the observed pitch for the lengths 
50 mm., 71 mm. and 7:6 mm., though the correction would be 
too large for the observations at 3°0 mm. and 3°3 mm. 
We have not been able to find sufficient data to enable us to 
calculate the effect of the pipe upon the velocity of sound. The 
Helmholtz-Kirchhoff formula, ¢=C is le quoted by 
Qr Jan 
Willner (Vol. 1. p. 799), has been investigated experimentally by 
Schneebele and Ad. Seebeck and verified in certain cases, but doubt 
was thrown upon the calculation of the correction by substitution of 
the value of n for a note of given pitch. As the pitch of the notes 
we have to deal with is very high indeed, this objection becomes 
: : if : 
very important. In fact if as suggested 7 should be taken in- 
1 : 
stead of —— the correction for our results would be thereby reduced 
n 
from 2 p.c. to 1/20th per cent. 
