I. Introduction. One of the most interesting problems connected with glacial geology is the explanation of the glaciation of those group~ of islands which lie at some distance from the north-east corner of the mainland of Scotland. It is now almost universally admitted, by those who have carefully weighed the evidence, that during the maximum cold of the glacial period, Scotland, Ireland, and the greater part of England were buried underneath an ice-sheet, which moved off the high grounds towards the sea-level. This has been clearly proved by the careful mapping of the ice-markings indicating the trend of the old glaciers, as well as by a minute examination of the stones in the Boulder-clay which accumulated underneath the ice, and was rolled along with the onward motion of the mass. So far most geologists are agreed; but when the glaciation of the Orkney and Shetland Isles has been discussed, it has given rise to considerable difference of opinion. Doubtless this want of uniformity has been largely due to the imperfect evidence hitherto obtained from the isles regarding the direction of glaciation and the nature of the various superficial accumulations. There has been no systematic examination of Shetland, or even of Orkney, with a view to determine these questions ; and hence the absence of reliable observations has given scope for some latitude of opinion, and has likewise retarded the final settlement of the question. The group of islands to which this paper especially refers may be said to form a