In submitting a revised edition of the paper which I read before the Actuarial Society of Edinburgh more than six years ago, I wish to express the pleasure I feel that this, my first effort, should not only have proved of benefit to students, but that the Faculty of Actuaries consider it worthy of a place in their Transactions. The subject was taken up originally to condense the best actuarial opinions and bring together some of those practical questions which had been dealt with by actuaries of ripe experience. Premiums can be profitably discussed at almost any time, because an exchange of views is sure to shed light on some obscure point of more or less importance. The present time is peculiarly opportune for further discussion, because of the recent publication of the New Mortality Experience, and the knowledge of such statistics which we have all been gradually absorbing.