The problems referred to under the above designation are those which involve the double survivorship contingency of A living after the death of B before C. The following solutions of these cases are quite general, and consequently applicable to any mortality table whatever.

I have taken the problems in the order in which they appear in the work of Mr. Milne, whose notation I have also followed. By means of an obvious relation which exists between the value of the compound survivorship assurance and the corresponding annuity, the whole of these cases are reduced to the single fundamental annuity value combined with the values of simple survivorship assurances. Consequently, if we should ever possess a complete table of the values of the simple survivorship assurance and also of the values of the annuity we shall be able to calculate the numerical value in any case with the greatest facility.