Perhaps I owe to the Institute an apology for bringing forward so late in the day this second part of my paper. When first I resolved to enter on the investigation of which I have now the honor to submit a second series of results, the ground, at least in so far as the experience of the 20 Offices was concerned, was practically unoccupied; for although Mr. Sprague had written on the mortality prevailing among assured lives, yet, as he had not touched on financial matters, I conceived that there remained ample room for another worker. It was only when I was on the point of sending in the part of my paper which has already been printed in the Journal, that I heard of Mr. Berridge's labours; and not till the other day, when the calculations for this second part were all but finished, did I become aware that Mr. Sprague intended to deal with the question of the premiums for the insurance of recently selected lives. Had I known that these gentlemen were engaged very similarly to myself, I should probably have been deterred from my task: but seeing that in ignorance of their movements it has been completed, perhaps the results will not be considered valueless.