At the lowest temperatures, then, the ultimate lines will predominate. As the temperature of the absorbing layer is raised, ionization—the complete ejection of the electron from the atom, instead of a displacement from one stationary state to another—will set in, and the tracing of the resulting spectral changes is the salient feature of the Saha theory. “Ionization can be effected in many ways. To expel an electron against the attractive force of the remainder of the molecule, work is required, and the necessary energy may be furnished by X rays or rays, or by collision with other electrons.... At high temperatures, when the conditions of maximum entropy demands an appreciable amount of ionic dissociation, the requisite energy is drawn from the environment.... The work required to ionize a single molecule, when expressed as the number of volts through which an electron must fall to acquire this energy, is the ionization potential; it may be regarded as the latent heat of evaporation of the electron from the molecule” (Milne).[366] [Pg 98] The analogy between ionization and evaporation illustrates very well the scope of the Saha theory, in which the process is treated as a type of chemical dissociation. Corresponding to each temperature there is a definite state of equilibrium, where the forward and backward velocities of the ionization process are equal—in other words where ionization and recombination are proceeding at the same rate. The method of statistical mechanics has been applied to this problem by Fowler and Milne.[367] Here the analysis will not be reproduced, but the formulae are required in order to illustrate the process of ionization. The number of atoms which are unionized at any given temperature is given by the expression where = number of atoms ionized. = the “partition function.” , where is the partial pressure of electrons. = absolute temperature. = Boltzmann’s constant, = . = the ionization potential. This is the number of atoms which is effective in absorbing the ultimate lines at that temperature. For low values of , the number of unionized atoms falls off at first very slowly with rising temperature, up to a point depending only on the ionization potential. Beyond this temperature the number of neutral atoms falls off with great rapidity. The diagram (Figure 5) illustrates the fall in the number of neutral atoms, and the consequent decay in strength of the ultimate lines. So steep is the gradient of at the higher temperatures that the quantity is best plotted logarithmically. The ultimate lines will persist, with almost undiminished intensity, up to the temperature at which the gradient of begins to increase. [Pg 99] This critical temperature increases with ionization potential, and neutral atoms of high ionization potential should display very persistent ultimate lines as the temperature rises. Figure 5