A few remarks concerning the underlying assumptions may be appropriate. In applying the theory it is assumed that stellar atmospheres are of uniform composition, and that at marginal appearance all lines are unsaturated. These reasonable assumptions have been discussed above, and they are here explicitly restated. The third assumption, that the same number of atoms is represented at the marginal appearance of a line, whatever the element, is by far the most serious. It implies the equality of the absorbing efficiencies of the individual atoms under the conditions involved. This is assumed in default of a suitable correction, but it is not suggested that the use here made of the assumption would imply its universal validity. Its present application is made under conditions of extremely low pressure (
), and over a range of temperature from 7000° to 10,000°. Under such conditions the absorbing efficiency of an atom will depend almost entirely upon its energy supply and upon its inherent tendency to recover after undergoing an electron transfer. The pressures are so low that collisions will have no appreciable effect in disturbing the normal recovery of the atoms. The energy supply will vary with the temperature; but with the range of temperature considered the variation will probably not be very large. The reorganization time of an atom appears to be an atomic constant, and to be of the same order for all atoms hitherto examined in the laboratory or in stellar atmospheres. As a working assumption, then, the equality of the atomic absorption coefficients is assumed with some confidence in the discussion of observed marginal appearances.
[TABLE XXVIII]
| Atomic Number | Atom | Atomic Number | Atom | Atomic Number | Atom | |||
|---|---|---|---|---|---|---|---|---|
| 1 | H | 11 | 13 | Al | 5.0 | 23 | V | 3.0 |
| 2 | He | 8.3 | 14 | Si | 4.8 | 24 | Cr | 3.9 |
| He+ | 12 | Si+ | 4.9 | 25 | Mn | 4.6 | ||
| 3 | Li | 0.0 | Si+++ | 6.0 | 26 | Fe | 4.8 | |
| 6 | C+ | 4.5 | 19 | K | 3.5 | 30 | Zn | 4.2 |
| 11 | Na | 5.2 | 20 | Ca | 4.8 | 38 | Sr | 1.8 |
| 12 | Mg | 5.6 | Ca+ | 5.0 | Sr+ | 1.5 | ||
| Mg+ | 5.5 | 22 | Ti | 4.1 | 54 | Ba+ | 1.1 |
As stated above, the relative abundances of the atoms are given directly by the reciprocals of the respective fractional concentrations at marginal appearance. The values of the relative abundance thus deduced are contained in [Table XXVIII]. Successive columns give the atomic number, the atom, and the logarithm of the relative abundance,
.
COMPARISON OF STELLAR ATMOSPHERE AND EARTH'S CRUST
The preponderance of the lighter elements in stellar atmospheres is a striking aspect of the results, and recalls the similar feature that is conspicuous in analyses of the crust of the earth.[481] A distinct parallelism in the relative frequencies of the atoms of the more abundant elements in both sources has already been suggested by Russell,[482] and discussed by H. H. Plaskett,[483] and the data contained in [Table XXVIII] confirm and amplify the similarity.