The prevailing system of life contingency calculation is one not of variable but of invariable quantities. At the very threshold the admission of two such important assumptions is asked for, as that the rate of mortality is always invariable at the same age, whether old or young, and that the rate of interest is equally invariable for all periods, whether long or short. Upon these admissions of invariability a system is formed for assessing the relative values of different cases, thereby necessarily in every instance indicating an invariable answer; and with such indications the system rests content. Whether such assessments, however logically fair in connection with agreed postulates of invariability, are themselves eventually justified by the same invariability of actual result as was à priori assumed, has not hitherto been commonly brought within the general scope of the actuary’s studies. Directly, however, he is called on to take upon himself the practical responsibility of upholding this theory of invariability, he is somewhat surprised to find that, good as the mere logic of his studies may have been, it is by no means an easy task to connect such logic with the nature of the events he may see passing around him.