In no department of chemistry have the methods of spectrum analysis proved of more value than in the field of the rare earths. They provide the chemist with a means of following and controlling his processes of separation which is far more delicate and decisive than the older method of determining the equivalent weight. Whilst the examination of emission spectra, and especially of arc spectra, is of decisive value in every case, it has the disadvantage of requiring delicate and complicated apparatus and great experimental skill; wherever possible, therefore, the examination of the absorption spectra is preferred, though this is useful only for a few of the elements, and varies considerably with the conditions employed. ~The Absorption Spectra.~--Absorption in the visible region of the spectrum is observed only with those rare earth compounds which are coloured, and is of value, therefore, chiefly for identification in the case of praseodymium and neodymium among the cerium elements, and of erbium among the yttrium metals; these give characteristic absorption bands, even in dilute solution. The absorption spectra of the rare earth compounds are highly characteristic, the bands being well defined and sharply bounded, whereas coloured compounds of the common elements show general absorption, or at best diffuse bands, under the same conditions. In observing an absorption spectrum, the light from a Nernst lamp, or incandescent burner, is passed through a layer of a suitable solution of the coloured compound, of known concentration and thickness, and after collimation is analysed by a suitable prism; the spectrum is observed by a telescope in the ordinary way. Where accurate readings are not required, as, for example, in testing for the presence or absence of a particular element, the position of the bands may be read to a sufficient degree of accuracy by means of a scale, the image of which is adjusted to coincide with the spectrum as seen through the eyepiece; but in mapping a spectrum accurately, more refined methods must of course be used. The photographic method, in which a photograph of the spectrum is taken on a plate which bears, for purposes of measurement, a comparison spectrum of known lines, is very convenient for examining the absorption in the violet and ultraviolet regions.