D, E and F existing at any later time are given by the equations 3, 4, 5, section 197.
Since, however, the intermediate product E has a much more rapid rate of change than D or F, the equations can be simplified, without much loss of accuracy, by disregarding the change E, and by supposing that D gives out β rays and changes directly into the α ray product F.
Let λ 1 , λ 2 be the constants of change D and F respectively. Let n ₀ be the number of particles of D present initially. Then using the notation of section 197, the amount P of radium D at any time t