text: Now consider the case of a chain of two decays: one nuclide  decaying into another  by one process, then  decaying into another  by a second process, i.e. . The previous equation cannot be applied to the decay chain, but can be generalized as follows. Since  decays into , then  decays into , the activity of  adds to the total number of  nuclides in the present sample, before those  nuclides decay and reduce the number of nuclides leading to the later sample. In other words, the number of second generation nuclei  increases as a result of the first generation nuclei decay of , and decreases as a result of its own decay into the third generation nuclei . The sum of these two terms gives the law for a decay chain for two nuclides:
  The rate of change of , that is , is related to the changes in the amounts of  and ,  can increase as  is produced from  and decrease as  produces .
  Re-writing using the previous results:
  The subscripts simply refer to the respective nuclides, i.e.  is the number of nuclides of type ;  is the initial number of nuclides of type ;  is the decay constant for  – and similarly for nuclide . Solving this equation for  gives:
  In the case where  is a stable nuclide ( = 0), this equation reduces to the previous solution:
  as shown above for one decay. The solution can be found by the integration factor method, where the integrating factor is . This case is perhaps the most useful since it can derive both the one-decay equation (above) and the equation for multi-decay chains (below) more directly.