The phenomena of rotatory dispersion are of special interest from two points of view. To the chemist they afford the most hopeful clue to the solution of the difficult and much discussed question as to why a particular substance possesses a given rotatory power. To the physicist, they contribute important data for the discussion of the mechanism involved in the propagation of light through matter, on the lines laid down by Maxwell, in 1869, and extended by the subsequent work of Sellmeier, Von Helmholtz, Larmor, Drude, and others. On the chemical side, progress depends mainly on the accumulation of data as to the rotatory dispersion of a large number of substances for a few selected wave-lengths ; in particular also upon the development of simple and effective laboratory methods, permitting of the measurement of rotatory dispersion being made a part of the ordinary routine of every laboratory in which polarimetric studies are undertaken. Progress on the physical side demands that a few selected substances shall be examined with light of many ave-lengths, extending over the whole of the available range of the spectrum, and that the measurements shall be made with the highest degree of accuracy. The present investigation of rotatory dispersion, which has been in progress continuously since 1905, is concerned with the natural rotatory power of crystals and of optically active liquids, and also with the rotatory power induced in them by a magnetic field. It was undertaken primarily from the chemical standpoint with a view to obtaining information as to the variations of rotatory power with wave length in organic liquids. But it was soon found that the two lines of investigation indicated in the preceding paragraph were inseparable, since the only satisfactory way of establishing standard laboratory methods for everyday use was to make measurements of rotatory dispersion with light of every available wave-length and to strive persistently to increase the degree of accuracy attained. Only in this way could adequate experience be gained as to what was possible in work of this kind. Thus, after making observations with light of some thirty wave-lengths, it was found that measurements of the highest degree of accuracy could be made with twenty-four lines in the spectra of the elements Li, Na, Tl, Zn, Cd, Hg, Cu, Ag; nine of these were used in the earliest series of laboratory-measurements, but the number was soon reduced to seven and finally to four (or even two) lines, which were found to give an adequate representation of the rotatory dispersion of the simpler organic compounds.