Open Organ-Pipe Problem in Two Dimensions. 481 
effects, as the large discrepancies seem to show that the limit 
has not been reached. Nevertheless, we think it highly 
improbable that these electrical effects are a direct result of 
chemical action, but believe rather that they are a secondary 
effect due to the enormous amount of heat set free by chemical 
union. 
It can, in fact, be shown that the energy required for the 
formation of the ions is quite insignificant in comparison with 
that produced by the combination of hydrogen and oxygen. 
For the heat evolved when one gram of hydrogen enters 
into combination is 34,000 calories. In other words, when 
vc.c. of hydrogen and oxygen are exploded at p mm. pressure, 
34,000 x a x up X 4:2 joules are formed, where p is the 
density of hydrogen at 15° C. and 760 mm. pressure. This 
equals 1:06 x 10-? x pv joules. Again, to produce Q coulombs 
of electricity of one sign in a gas by ionisation, Q pairs of 
e 
ions must be generated where e! is the charge on an ion 
measured in coulombs, and this will not require more than 
5Q joules, since the energy necessary for the formation of 
each pair does not exceed 5e! joules (J. 8. Townsend, Phil. 
Mag. Feb. 1901, p. 220). In our experiments p was about 
80 mm., v 356 c.c. and Q not greater than 12 x 10-° coulombs. 
The heat set free was therefore approximately 300 joules, while 
the energy required for ionisation did not exceed 6x 107-5 
joules, which is only one five millionth of the former quantity. 
We wish to express our thanks to Professor Townsend for 
his valuable suggestions and criticisms. 
XLVI. On the Open Organ-Pipe Problem in Two Dimensions. 
By Lord Rayuricu, O.M., F.R.S.* 
N the usual symmetrical organ-pipe of radius R, supposed 
to be provided at the mouth with an infinite flange, we 
know that the correction (a) that must be added to the 
length in order that the open end may be treated as a loop, 
lies between ¢77R and 8R/37. The wave-length of vibration 
is here supposed to be very great, so that in the neighbour- 
hood of the mouth the flow follows the electrical law. If we 
use this analogy and regard-the walls of the pipe and the 
flange as non-conductors, the question is one of the resistance 
of the air-space, measured from a section well inside, the 
pipe to an infinite distance beyond the mouth. And in spite 
* Communicated by the Author. 
Phil. Mag. 8. 6. Vol. 8. No. 46. Oct. 1904. 2. 
