A Treatise On Light

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It seemed natural to expect that the different lines in a spectrum might be caused by the different modes of vibration of the same system, and thus arose a search for a mathematical relation between their wave-lengths.
At first investigators were misled by the acoustical analogue and sought to show that the frequencies were to one another as simple whole numbers. Schuster proved that these early results were merely chance coincidences, and progress was not made until the introduction of Rowland
...'s gratings and the great increase in the accuracy of wave- length determination which they rendered possible. The first to achieve a decisive result was Balmer. In 1885 he showed that the wave-lengths of the first nine lines of the hydrogen spectrum can be represented by the formula where A is a constant and n an integer which varies from 3 to 11. The formula could not be verified further as there were no further measurements available then. Afterwards additional lines were dis- covered in the vacuum tube spectrum of hydrogen by Ames and also in the spectrum of solar protuberances and in the so-called flash spectrum by Evershed.

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