The subject to which I invite your attention is one which has never been directly submitted to the Institute of Actuaries, although reference has on various occasions been incidentally made to it. In the discussion which followed the reading of my essay of 1895, to which was awarded the Messenger Prize, it was suggested that I should give a whole set of forms of books necessary for conducting the business of an office, and a classification book for valuation purposes, showing how the information in each would afford a perfect check in the end, and this paper is, to some extent, the outcome of that suggestion. While this is the position of matters in the Institute, it is otherwise with the Faculty, which has now undertaken the functions hitherto performed by the Actuarial Society of Edinburgh. There the subject has frequently been brought before them, more particularly by Mr. McLauchlan, and, on the last occasion, reference was made to the suggestion I have referred to, and it was added that it was a point to which attention might profitably be given. In these circumstances, I do not offer any apology for bringing the matter before you, but I shall not attempt, on this occasion, to give a whole set of forms of books. I shall confine my remarks chiefly to premiums, as I think that in this way the paper will be more easily followed, while it will be possible, within this compass, to show the application of the various checks by means of the Valuation Books described in my essay.