Graduation of all kinds is most attractive. The highest mathematical minds have apparently lingered upon it with delight, and when I glance down the weighty list, I feel that I, of all persons, should have shrunk from touching it. Most of these men have treated the subject in a highly theoretical manner, and have furnished formulæ that are extremely difficult to apply. A few, however, have followed in their footsteps and elaborated something that is practical. Other enthusiasts have searched for and have thought that they had found a ‘Law of Mortality.’ Some are still searching for it, and more will continue the search in all time coming. A Law of Mortality seems to me to be as illusive as the rainbow. The law found is only the law of some mathemathical process of summation.

The method of graduation indeed should vary with the matter to be graduated. When applied to the probability curve, it is intensely fascinating, and there appears to me to be occasional opportunities in our business of so applying it. I do not profess to put forward any new scheme. I do not propose to electrify the subject. I possess no wizard's wand. All I propose to do is to elaborate a very simple exposition of the most elementary principles on the subject of differences, but I am bold enough to state that, in my opinion, it is all that is necessary in the graduation of a table of mortality.