Abstract
THE proper replies to Prof. Runge's letter in last week's issue of NATURE are three in number: viz. (1) that, as I pointed out in my former letter (NATURE of May 12, p. 29), the reasoning in my paper is valid if, as I there proved and as Prof. Runge now admits in the first sentence of his letter, Fourier's theorem can be applied to motions which approximate to non-periodic motions in any assigned degree and for any assigned time; (2) that I am not aware of anything I have written which countenances Prof. Runge's supposition that “Prof. Stoney has not noticed that a distinct property of the function is wanted in order to get a proper” [rather, a mathematically accurate] “resolution into a sum of circular functions”; and (3) that Prof. Runge is mistaken when he supposes that “the amplitudes and periods” [or frequencies] “of the single terms … do not approach definite values when the interval” [i.e. the periodic time of the recurrence required by Fourier's theorem] “increases indefinitely.”
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STONEY, G. The Line Spectra of the Elements. Nature 46, 126 (1892). https://doi.org/10.1038/046126a0
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DOI: https://doi.org/10.1038/046126a0
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