is then introduced, when it will be necessary to rotate the analyser 23° to the right, in order that the light may be extinguished. This is the amount of rotation for that particular fluid at a given density and that height of column. As the arc varies with increase or decrease of density and height of the fluid, it is needful to reduce it to a unit of height and density. The following formula is that given by Biot:--P = quantity of matter in a unit of solution; _d_ = sp. gr.; _l_ = length of column; _a_ = arc of rotation; _m_ = molecular rotation. Then _m_ = _a_/(_l p d_). The application of the polarising apparatus to the microscope is of much value in determining minute structure. It may also be defined as an instrument of analysis; a test of difference in density between any two or more parts of the same substance. All structures, therefore, belonging either to the animal, vegetable, or mineral kingdom, in which the power of unequal or double refraction is suspected to be present, are those that should especially be re-investigated by polarised light. Some of the most delicate of the elementary tissues of animal structure, the ultimate fibrillæ of muscles, &c., are amongst the most interesting subjects that might be studied with advantage under this method of investigation. The chemist may perform the most dexterous analysis; the crystallographer may examine crystals by the nicest determination of their forms and cleavage; the anatomist or botanist may use the dissecting knife and microscope with the most exquisite skill; but there are still structures in the mineral, vegetable, and animal kingdoms which will defy all such modes of examination, and will yield only to the magical analysis of polarised light. Formation and Polarisation of Crystals. The inorganic kingdom will afford to the microscopist a never-ending number of objects of unsurpassed beauty and interest. The phenomena of crystallisation in its varied combinations can be made a useful and instructive occupation. Although ignorant of the means whereby the great majority of minerals and crystals have been formed in the vast laboratory of Nature, we can, nevertheless, imitate in a small degree Nature’s handiworks by crystallising out a large number of substances, and watch their numerous transformations in the smallest appreciable quantities, when aided by the microscope. Among natural crystals we look for the material for the formation of our lenses, while the varieties of granites present us with the earliest crystallised condition of the earth’s crust as it cooled down, the structure of which is beautifully exhibited under polarised light. In Plate VIII. various crystalline and other bodies are displayed. In No. 158 is a section of new red sandstone; 159 of quartz; and 160 of granite. Special reference is made to others in the following list of salts and other substances which form a beautiful series of objects for study under polarised light:-- SALTS.