ADDITIONAL DEDUCTIONS FROM IONIZATION THEORY [Pg 155] CHAPTER XI THE ASTROPHYSICAL EVALUATION OF PHYSICAL CONSTANTS IN the opening chapter the statement was made that “the astrophysicist is obliged to assume [the validity of physical laws] in applying them to stellar conditions.” The astrophysical evaluation of physical constants might therefore seem, from our avowed premises, to involve a circular argument. In certain special cases, however, the process appears to be legitimate, and the results of three investigations are contained in the present chapter. The first of these investigations involves the derivation of spectroscopic constants, assuming the series formula; the second consists of an extrapolation of the results of Chapter X to the estimation of unknown ionization potentials; and the third constitutes a discussion made possible by the knowledge of the stellar atmosphere that has been attained with the aid of ionization theory. THE RYDBERG CONSTANT FOR HELIUM The wave-lengths of a series of lines can be measured in the spectrum of a star, and the series identified with a series observed in the laboratory. The occurrence in stellar spectra of series that can be identified with the series given by terrestrial atoms presumably shows that similar relations govern the atomic processes in the two sources. That series formulae of the same type are applicable to the stellar and terrestrial atom is indeed rather an observational fact than an assumption. By inserting into the appropriate series formula the observed stellar frequencies, a physical constant involved may be evaluated, and the extent of the agreement with the corresponding value from the laboratory may be determined. [Pg 156] H. H. Plaskett[429] has measured the wave-lengths of the lines of the Pickering series () of He+ in the spectra of three stars, incidentally separating the alternate Pickering lines from the Balmer lines for the first time. The formula that connects the frequencies of the lines with the constants associated with the atom is Plaskett discussed the theory, and derived from the measured wave-lengths of five lines the mean value of 109722.3 ± 0.44 for the constant . The value determined in the laboratory by Paschen is 109722.14 ± 0.04. Plaskett’s comment on the agreement is as follows: “It was not to be expected that there would be any startling changes.... It is of interest, however, to note that these “stellar” determinations are in agreement with the terrestrial values, in so far as it shows that the implicit assumption of identical atomic structure, identical electrons, and identical laws of radiation on the earth and in the stars, is in some measure justified.” CRITICAL POTENTIALS