I. Introduction. No consideration appears to have been given in the literature to the design of beam apparatus for studying the atomic spectra of gases. Considering our uniquely complete theoretical knowledge of the spectrum of hydrogen, and the inconclusive nature of our present experimental knowledge of the structure of the alpha-line, atomic beam studies of this line are needed. II. Geometrical consideration. The pressure ratio of the final and initial chambers must be far smaller than the solid angle subtended by the first slit at a point in the field of view; and the region of space in which the atoms are excited should not extend, in the line of view, far beyond the full (non-penumbral) portion of the beam. III. The Doppler effect. Five independent contributions to the Doppler effect, for a line emitted from an atomic beam, are studied: (1) Original atomic velocity; (2) atomic velocity gained by excitation (in particular, for hydrogen excited by electron impact); (3) atomic velocity gained by emission; (4) spread of light in the optical system; (5) error of orientation of the optical system with respect to the beam. Some of these factors tend to produce broadening, and some to produce frequency shifts. The broadening can probably be kept low enough for the complete resolution of the electronic structure of the alpha-line, $\frac{\nu }{\Delta \nu }=4.2\mathrm{}\times {10}^5$. IV. Design of the apparatus. An atomic beam apparatus is described which has been designed and built with a view to the conditions outlined above.

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