If we assume that the antiquity of man is as great, or even approximately as great, as Sir Charles Lyell and his followers affirm, the question naturally arises, what has he been doing during those countless ages, prior to historic times? what evidences has he afforded of the possession of an intelligence superior to that of the brute creation by which he has been surrounded? what great monuments of his fancy and skill remain? or has the sea of time engulphed any that he erected, in abysses so deep that not even the bleached masts project from the surface, to testify to the existence of the good craft buried below? These questions have been only partially asked, and but slightly answered. They will, however, assume greater proportions as the science of archæology extends itself, and perhaps receive more definite replies when fresh fields for investigation are thrown open in those portions of the old world which Asiatic reserve has hitherto maintained inviolable against scientific prospectors. If man has existed for fifty thousand years, as some demand, or for two hundred thousand, as others imagine, has his intelligence gone on increasing thoughout the period? and if so, in what ratio? Are the terms of the series which involve the unknown quantity stated with sufficient precision to enable us to determine whether his development has been slow, gradual, and more or less uniform, as in arithmetical, or gaining at a rapidly increasing rate, as in geometric progression. Or, to pursue the simile, could it be more accurately expressed by the equation to a curve which traces an ascending and descending path, and, though controlled in reality by an absolute law, appears to exhibit an unaccountable and capricious variety of positive and negative phases, of _points d'arrêt_, nodes, and cusps. These questions cannot yet be definitely answered; they may be proposed and argued on, but for a time the result will doubtless be a variety of opinions, without the possibility of solution by a competent arbiter.