In the special case where , the second curve, which represents the growth of the fraction , becomes a straight line parallel to the temperature axis, and the first, or ionization, curve, approaches the zero ordinate asymptotically at low temperatures. The ordinate of the curve representing is zero, and the resultant sum gives a curve identical with the curve for the ultimate lines. Ultimate lines thus appear as the special case of subordinate lines for which the excitation potential is zero. This fits exactly with the definition of ultimate lines as the lines naturally absorbed by the cold vapor—no initial excitation is required to bring the atoms into a state in which they can absorb. LINES OF IONIZED ATOMS [Pg 102] As soon as ionization sets in, the absorbing layer begins to contain a new kind of atom, derived from the neutral atoms by the complete ejection of one electron. These ionized atoms will absorb their own spectrum, which differs completely from that of the corresponding neutral atom; and the degree of absorption will again depend on the number of such ionized atoms present in the reversing layer. The ionized atom has in general a spectrum corresponding exactly to that of the neutral atom preceding it in the periodic table, but with a different Rydberg constant.[368][369] Two types of lines arise, as before—ultimate and subordinate lines. For the number of atoms which can absorb the ultimate lines of the enhanced spectrum, the formula reduces to Account is here taken of the residual neutral atoms by the middle term of the denominator, which is very small, and is only of sensible magnitude for the ultimate lines, when the numerator is equal to unity. Figure 7 Maximum of the ultimate line of an ionized atom. Ordinates are logarithms of computed fractional concentrations; abscissae are temperatures in thousands of degrees. The curve is drawn for the line 4554 of Ba+, on the assumption that is . The following curve shows the number of absorbing atoms. The flatness of the maximum is especially to be noted, suggesting that the ultimate lines of the ionized atom, like the ultimate lines of the neutral [Pg 103] atom, will be very persistent. The and lines of Ca+, and the corresponding lines 4077 and 4215 of Sr+, and 4555 of Ba+, would thus be expected to show over a considerable range in temperature and spectrum, and this is actually found to be the case.