ERRATA.

Page 141, line 14, for "in Fig. 2", read "above".

Plate VII., column 6, line 13 of the Computation: the signs for degrees, &c., are

erroneously given as figures (0, 1, 11).

Plate XIII. The numbering of Figs. 3 and 4 should be transposed.

WHEN first I commenced to write an address for this evening, I intended to call your attention chiefly to some special subjects which have been prominently brought before our Society during the last year or two. I never contemplated entering into certain questions with which I am so little acquainted practically that it would be presumptuous to express any confident opinion of my own. I thought it would be far better to enter at greater length into the consideration of such special subjects as I have studied sufficiently as to be able to treat them in a more or less original manner. I proposed to lay before you an account of some further observations of my own in connection with the visibility of very minute objects, and to discuss what has been done and said by others in relation to this subject; and also to consider some points in the construction of object-glasses, which have more particularly attracted my attention during the last few years. However, when I came to write out only a superficial account of another subject, I soon found that it alone was even more than enough to occupy your attention this evening. Being an almost entirely new application of the microscope, I thought it sufficiently suitable for the present occasion, and that it would be better to treat of it in some detail, rather than say so little as to make it scarcely intelligible, in order to find room for several other subjects. I propose, therefore, now to describe some simple additions to the microscope, which

DESCRIPTION OF PLATE I.

FIGS. 1 to 6 represent the images of a small circular hole, viewed with a microscope through various crystals.

FIGS. 7 and 8 are diagrams of mounted objects.

FIGS. 9, 10, and 11 show the appearances seen on viewing the cross lines of the grating through different crystals.

VOL. I.

B

enable us to study certain classes of objects in a far more satisfactory manner than heretofore. The very striking facts on which this method is based were first shown publicly at our scientific evening meeting on the 18th of April last year, when their true explanation was still unknown; and were again shown at a subsequent meeting on the 31st of October, after the general principles of the subject had been sufficiently well established. The various facts seemed to attract so much attention, that I have often felt desirous to bring the subject before this Society, and now take the opportunity, since I fear another may not occur for some time to come.

In the first instance my attention was exclusively directed to the application of the method to the study of comparatively large portions of minerals, having a thickness of of an inch or more, in order that the various measurements might be made with sufficient accuracy to establish general principles, and to verify or correct certain theoretical deductions of Professor Stokes, who undertook that part of the subject. The results fully convinced me that the method would enable us to determine, with very considerable accuracy, some of the most important optical constants of crystalline minerals, provided that the section be cut in the plane of any two of the axes. This alone was a great gain for mineralogy, since, in order to determine them by the methods previously adopted, more numerous and complex measurements were necessary, and it was requisite to cut the section in one very special direction. The new method enables us to approximately determine several important particulars, no matter what may be the direction in which the section is cut. This is of course a very great advantage when we come to apply it to the study of thin sections of rocks, in which the minerals lie in every possible position. Even when comparatively large specimens and a low magnifying power are used, the special characters observed by this method depend entirely upon the collection by an object-glass of more or less divergent rays. It is not, as so often happens, a case where the microscope merely magnifies an appearance which might be seen with the naked eye or a simple lens, but a new class of properties is, so to speak, created by the peculiar optical conditions of a compound microscope. Though the deductions have a direct bearing mainly on mineralogy and theoretical optics, it would not therefore be out of place to enlarge even on this department of my subject, but still I will not say more than is absolutely necessary, since I am anxious to describe more fully the applications of the new method to the study of minute objects somewhat highly magnified.

Before proceeding any farther it will, I think, be well to give a short history of this subject.

At the meeting of the Royal Microscopical Society, November, 1876, Dr. Royston-Pigott exhibited and described an instrument