Abstract
I SEE by Prof. Stoney's letter that I have not yet succeeded in making myself understood, as he does not enter on the subject of my objection. A function of the time may well, with any assigned degree of accuracy and for any length of time, be approximately represented by a sum of circular functions, and nevertheless the periods, amplitudes, and phases may not approach definite values when the length of time for which the approximation is to hold good is increased indefinitely. I think this is quite clear from the example I have given in my last letter (p. 100), and it is not necessary to write out other examples. Now, Prof. Stoney shows how one may find by Fourier's theorem the amplitudes, periods, and phases of a sum of circular functions if one only knows the values of the sum. This deduction is not new to me. I worked out the same equations in a slightly different form, when Prof. Stoney's first letter made me further think about the subject. The deduction does also apply to functions that are approximately represented by a sum of circular functions, but only under the restriction that the time for which the approximation holds good is long in comparison to the longest period of the circular functions. In chapter iv. of his paper βOn the Cause of Double Lines, &c.β (Transactions of the Royal Dublin Society, 1891), Prof. Stoney should have added this restriction. Then the question would naturally have arisen how the restriction follows from Prof. Stoney's hypothesis on the origin of the line spectra. I do not venture to say that it does not, but the author would have to prove it.
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RUNGE, C. The Line Spectra of the Elements. Nature 46, 200 (1892). https://doi.org/10.1038/046200b0
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DOI: https://doi.org/10.1038/046200b0
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