Having been engaged for many years in collecting and studying the corals of the Mountain Limestone of Scotland, I propose, in the present communication, to describe some of the new species which have come under my notice. Some of these were discovered in a thin bed of shale from five to nine inches thick, which overlies the low post of limestone in Trearn Quarry, near Beith, Ayrshire. Indeed, this horizon throughout Great Britain may be safely said to be the zone in which simple corals existed in greater abundance, and attained greater dimensions, than in any other section of the Mountain Limestone. There are a few forms found in the upper members of the period. So far, however, as my investigations have gone, these are limited both in genera and species; and, with only one or two exceptions, are all more or less simple in their organization. It is not my intention at present to enter into any elaborate stratigraphical arrangement of beds, or classification, or distribution of the different genera or species. That will form matter for a memoir, in which I hope to delineate not only the almost imperceptible gradation from one species into another, but also the persistent modifications that occur between the different genera. Indeed, those modifications are so constant, that it often becomes difficult to say where one genus begins, and its next ally ends. This is a result that can only be safely attained by examining an extensive collection of specimens, all of which must be sectioned with great care. From my own personal observations, assisted by my friends, I shall be able to note the stratigraphical distribution of the genera and species throughout the three kingdoms. Such a memoir is a great desideratum; and it can only be prepared from personal investigation and examination of sections. Only thus can we ascertain in what condition the genera and species are found.