(1.) It would be arbitrary to name any definite distance to which the ice must recede in order to constitute its re-advance a distinct ice epoch. It would be not so much a question of miles as a question of proportions. Considering this point alone, we presume it would be agreed that an ice-sheet should have suffered the loss of a very considerable proportion of its mass, and that it should have dwindled to proportions very much less than those subsequently attained, before its re-advance could properly be called a separate glacial epoch. To be specific, if the North American ice-sheet, after its maximum extension, retreated so far as to free the whole of the United States from ice, we should be inclined to regard a re-advance as marking a distinct ice epoch of the same glacial period, if in such re-advance the ice reached an extension comparable with that of the earlier ice-sheet. Especially should we be inclined to refer the second ice advance to a second glacial epoch, if it, as well as the preceding retreat, were accompanied by favoring phases of some or all the other three elements entering into the notion of a glacial epoch. In this statement we do not overlook the fact that a northerly region--as Labrador or Greenland--might be continuously covered with ice throughout the time of the two glaciations of the more southerly regions. But this is not regarded as a sufficient reason for discarding the notion of duality. Greenland has very likely been experiencing continuous glaciation since a time antedating that of our first glacial deposits. The renewal to-day of glaciation comparable in extent to that of the glacial period would certainly be regarded as a distinct glacial epoch, if not a distinct glacial period, even though Greenland's glaciation may not have been interrupted. Scandinavia and Switzerland have probably not been freed from ice since the glacial period. Their snow and ice fields are probably the direct descendants of the ice fields of the glacial period. An expansion of the existing bodies of ice in these countries to their former dimensions, would constitute a new glacial epoch, if not a new glacial period. Analogous subdivisions in pre-Pleistocene formations have been frequently recognized. (2) The application of the time element is hardly susceptible of quantitative statement. We are inclined to think that it would be generally agreed that, with a given amount of recession of the ice, its re-advance would be more properly regarded as a distinct glacial epoch if the interval which had elapsed since the first advance were long. Whether a longer time between the separate advances might reduce the amount of recession necessary in order to constitute the second advance a second epoch, we are not prepared to assert; but we are inclined to think it might.