theories supply the basic interpretative perspective. Spectroscopes and other high-precision optical equipment relied on interference effects. A precise application of electromagnetic theory required detailed information concerning the material of a particular grating and the shape of its grooves.23 In calculating wave-packet qualities experimenters relied on Huygen's principle, physical optics, Fourier transforms, and geometrical optics. The underlying presupposition interrelating these different models, fragments of theories, and experimental arrangements is the assumption that characterizes a real periodic disturbance in space and time. Scattering experiments, the second basic source of information, related the controlled input and measured output by assumptions concerning single or multiple collisions, short-range forces, screening effects, radiation, excitation, ionization, energy loss and electron capture. These were not related by some all-encompassing theory, but by the underlying presupposition that electrons and alpha particles travel in continuous trajectories.
The Bohr theory of the atom modified the way experiments were interpreted24. Experiments, in turn, modified the interpretation of the theory. The quantum numbers, n and k, used in the B-S theory to characterize electronic orbits, were also used to classify spectral lines. New quantum numbers, j and m, and the new selection rules, k = 1, j = 0, 1, introduced as book-keeping devices in classifying allowed spectral lines, were soon extended to orbital states and eventually accepted as characterizing angular momentum.
Bohr organized this experimental-theoretical dialectic in terms of principles and concepts and accorded the mathematical formalism a merely instrumental role. The two quantum principles basic to his account of atoms and radiation were stationary states and discrete transitions between states. The concepts he took as basic were the two presuppositional concepts of experimental work already considered, particles and waves. They could be used within the limits set by his quantum principles. Thus, orbital electrons follow trajectories, but orbital transitions cannot be explained through trajectories or any particle model. A wave account covers radiation in free space, but not the production and absorption of radiation.
The crowning achievement of the B-S program, Bohr's account of the periodic table, relied on three formal principles: the correspondence principle, 25 the adiabatic principle; and the Aufbauprinzip (adding further electrons does not alter the assignment of quantum numbers to earlier electrons); and descriptive concepts. Bohr had been using a distinction between descriptive concepts and formal concepts, or concepts whose meaning depends on functioning in a system. Bohr no longer accorded a realistic significance to the way that the n and j quantum numbers characterized orbital properties, but claimed that it may be stated with certainty that the orbital properties indicated by the k quantum number (in contemporary notation k = l + 1) correctly describes orbital properties. The ellipticity of orbits was a crucial factor in Bohr's account of helium, carbon, and the rare earth elements. The descriptive significance accorded the k quantum
23 A general survey of the theory and practice of diffraction gratings may be found in Stroke (1967) or in Hecht and Zajac (1974), chap 10.
24 See Robotti for changes in the interpretation of spectral lines and Bohr (Collected Works, II, p. 410) for his reinterpretation of the Franck-Hertz experiment.
25 Bohr used the (forward) correspondence principle as a tool for guessing quantum formulas on the basis of classical formulas. Since the 1930's the term has come to refer to the (backwards) correspondence principle that quantum mechanics should merge with classical mechanics in the limits where 0, or n .