1. In considering the question of the calculation of Survivorship Assurances (excluding Compound Survivorship Assurances), it is only necessary to know how to obtain the values of Survivorship Assurances which determine on the first death. All Survivorship Assurances in which only one order of survivorship is involved may be expressed in terms of assurances determining on the first death. This is most easily accomplished by a process of general reasoning, but to those who prefer strictly analytical methods, an algebraical solution will be more acceptable. To take quite a simple example, suppose we are required to find the value of an assurance payable on the death of (x), provided (y) predecease him and (z) survive him, in symbols .