Prefatory Remarks. It is necessary to preface the part which here commences, by stating that we must suppose that the reader has acquired an ordinary knowledge of the technicalities of logic, and has some acquaintance with the speculations of modern logical writers, especially with those of the late Sir W. Hamilton, and those of Mr. J. S. Mill. To be obliged to explain all the terms which we shall have occasion to use, would be inconvenient and irksome, and not at all in consonance with the brevity which it is necessary to observe in this place, and especially with that distinctness which is so needful to the successful exposition of what we have here undertaken. And why should we exercise our ingenuity in varying descriptions of mental processes already expressed with such abundant variety in the works of able logicians? Since then we do not seek to afford a systematic account, but merely to record the leading results which we have yet obtained from examining the landmarks on ground not recently explored by the investigators of logic, much minuteness will not be demanded from us. And we desire to state that all that is peculiar in these contributions arises from adopting this separate course.