In introducing a consideration of this subject to the Institute, I do not purpose putting forward any new theories; many papers have been written upon the different methods of valuation and the modes of distributing profits, which have been most valuable contributions for determining the best theoretical basis to be adopted. I need only refer to the papers of Messrs. Jellicoe, Sprague, Bailey, Meikle, Manly, Valentine, King, and others, all of which are to be found in the Journal of the Institute, in order to remind you how fully these subjects have been considered at different times. The present paper, however, is intended to investigate the practical effect of applying the respective theories, not upon any theoretical assumption, but as they have to be applied in actual practice, and to see how far they are influenced by the different rates of premium actually charged by the different companies.