k2
k2n2Xe = ------- I,
k1 + k2

/[alpha]\^1/2 I
X = ( ------- ) ----------.
\ q / e(k1 + k2)

These solutions cannot, however, hold right up to the surface of the
plates, for across each unit of area, at a point P, k1I/(k1+k2)e
positive ions pass in unit time, and these must all come from the
region between P and the positive plate. If [lambda] is the distance
of P from this plate, this region cannot furnish more than q[lambda]
positive ions, and only this number if there are no recombinations.
Hence the solution cannot hold when q[lambda] is less than k1I/(k1 +
k2)e, or where [lambda] is less than k1I/(k1 + k2)qe.

Similarly the solution cannot hold nearer to the negative plate than
the distance k2I/(k1 + k2)qe.

[Illustration: FIG. 12.]

The force in these layers will be greater than that in the middle of
the gas, and so the loss of ions by recombination will be smaller in
comparison with the loss due to the removal of the ions by the
current. If we assume that in these layers the loss of ions by
recombination can be neglected, we can by the method of the next
article find an expression for the value of the electric force at any
point in the layer. This, in conjunction with the value

/[alpha]\^1/2 I
X0 = ( ------- ) ----------
\ q / e(k1 + k2)

for the gas outside the layer, will give the value of X at any point
between the plates. It follows from this investigation that if X1 and
X2 are the values of X at the positive and negative plates
respectively, and X0 the value of X outside the layer,

/ k1 I \^1/2 / k2 I \^1/2
X1 = X0 ( I + -- --------- ) , X2 = X0 ( I + -- --------- ) ,
\ k2 [epsilon]/ \ k1 [epsilon]/

where [epsilon] = [alpha]/4[pi]e(k1 + k2). Langevin found that for air
at a pressure of 152 mm. [epsilon] = 0.01, at 375 mm. [epsilon] =
0.06, and at 760 mm. [epsilon] = 0.27. Thus at fairly low pressures
1/[epsilon] is large, and we have approximately

/k1\^1/2 I /k2\^1/2 I
X1 = X0 ( -- ) ---------------, X2 = X0 ( -- ) ---------------.
\k2/ [root][epsilon] \k1/ [root][epsilon]

Therefore X1/X2 = k1/k2,

or the force at the positive plate is to that at the negative plate as
the velocity of t