The methods which can be adopted in attempting a separation are of two kinds. The first includes those processes which take advantage of the gradual variation in basic strength of the hydroxides as the atomic weight changes; the most important of these are fractional precipitation of the hydroxides, and fractional decomposition of the nitrates. Fractional precipitation of the hydroxides is generally effected by gradual addition of ammonia, soda, magnesia, or other base, to a solution of the mixed salts; such a solution may also be digested with the oxides obtained by ignition of another fraction of the rare earth compounds. If the digestion be sufficiently complete, the precipitate in each case will be richer in the less basic hydroxides, whilst the solution will be richer in the salts of the more electropositive elements. The fractional decomposition of the nitrates is based on the fact that when a mixture of the salts is heated gradually, the nitrate of the least positive element begins to decompose first. The temperature is maintained for some time at the point at which decomposition begins; when nitrous fumes cease to be evolved the mixture is cooled, and extracted with water or dilute acids. The insoluble portion--basic or superbasic nitrate (see p. 128)--will then be richer in the less electropositive elements; the solution is evaporated, and the solid so obtained subjected to a somewhat higher temperature, and the process repeated several times. In this way, a series of fractions is obtained, in which the elements tend to distribute themselves in order of electropositive character. By a sufficient number of systematic repetitions of such steps, the elements may eventually be obtained in the form of compounds of approximate purity, which may then be refined by one of the methods of the second kind described below. Experience has shown, however, that a quicker and more complete separation may generally be effected by combining two or more methods of separation; one method will give the best separation up to certain limits, but then becomes much less valuable; the separation at this point is therefore taken up by another process. A process depending on differences of basic strength of the hydroxides is generally supplemented by a method of the second class, i.e. a process of fractional crystallisation; where the basicity method is not used (as, for example, in most of the recent processes for separation of the cerium elements), two or more different methods of fractional crystallisation will supplement one another.