if n is the number of particles of A initially present. Now dQ, the increase of the number of particles of the matter B per unit time, is the number supplied by the change in the matter A, less the number due to the change of B into C, thus
Substituting in (1) the value of P in terms of n,
The solution of this equation is of the form
By substitution it is found that a = λ1/(λ2 – λ1).
Since Q = 0 when t = 0, b = -λ1(λ2 – λ1).
Thus
Substituting this value of Q in (2), it can readily be shown that
where
