Velocities of Two Groups of Rays and their Absorption Coejfficie)its. 79 
this last case the ions represented by the shaded toe are lost. This area 
equals that of the shaded toe of the curve Fig. 4, h. 
It is to be remembered, however, that the ordinate on the cathode-ionisa- 
tion curve at any given pressure p represents the area of the ionisation- 
density curve in Fig. 4 included between the two faces of the chamber. The 
ordinate CC (Fig. 3) is a measure of the unshaded area in Fig. 4, h, and, 
therefore, if at the critical pressure the ionisation-density curve is given by — 
then — 
which equals the total number of ions existing at a given instant in a slab 
of half the thickness of the chamber, in this particular case. 
It will be seen that x = ^P/V and that if the form of the function 
represented by the experimentally obtained cathode ionisation curve can be 
found, the first differential coefficient of this function gives the density dis- 
tribution function of the ions across the chamber, with the possibility of 
determining the absorption coefficient. 
First Approximation. 
It will be seen from the figure that the cathode-ionisation curves 
proximate to Nj. = No (1 — e"^'^), and therefore the density ionisation in the 
chamber itself will be of the form = jOo^~^'% where p„ = N^x and X is the 
absorption coefficient. If x be taken as the distance across the chamber at 
which the ionisation density becomes one-half of what it is at the gold 
screen, we obtain — 
^ = ^^^}^A o where x = "^^ x 1-45 cm., 
X X -4343 p 
since the depth of the chamber was 1-45 cm., P is the critical pressure for 
the gas in question, and p^ that pressure at which one-half of the ions that 
'2 
could be produced by the cathode particles are missing through the electrons 
having been absorbed by the opposite wall of the chamber. It will be noted 
that the absorption coefficient so found will be that at a pressure P, and 
therefore — 
X Sit N.T.P. = ^^^io2 X 76 X 
p. X 1-45 X -4343 273 ' 
It will be noticed that P is absent. 
The results obtained in this manner are tabulated in Table I. I have put 
them in this form for comparison with Beatty's results for air and hydrogen. 
