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THE POPULAR SCIENCE MONTHLY.

soon accorded in acknowledgment of his merit. Among these may be mentioned a gold medal, in I860, from the SociƩte d'Encouragement at Paris; a gold medal, in 1867, from the International Exhibition at Paris; in 1868 the honorary degree of Doctor of Philosophy, from the university of his native city, Koenigsberg; and, in 1876, a medal from the Centennial Exhibition at Philadelphia. Before scientific assemblies he has been called upon to give the results of his investigations, including in them the Assembly of German Naturalists, in 1868, at Dresden; the American Association for the Advancement of Science in 1876 at Buffalo, and again in 1882 at Montreal; and the Electrical Exhibition at Paris in 1881, when he was specially visited by a large company of the most renowned of living physicists, including Helmholtz, Kirchhoff, Du Bois-Reymond, Clausius, Quincke, Mach, Kundt, Pahlzon, and Sir William Thomson.

The scientific papers of M. Koenig have been published almost entirely in the Annalen of Poggendorff and of Wiedemann. Most of these have been translated into French and published, in 1882, in a volume entitled Quelques ExpƩriences d'Acoustique. To give an adequate idea of what is included in them would be impossible without going into detail. The volume includes a full account of Koenig's application of the graphic method and that of manometric flames. Both these methods are applied in an exhaustive investigation of the beat tones which result from the combination of two or more primary tones. Helmholtz discussed "differential tones" and "summation tones," whose existence was inferred from the results of mathematical analysis; and certain phenomena seemed for a time to confirm the conclusions of the great German physicist. But Koenig subsequently applied the most patient care and consummate skill in the experimental examination of these phenomena. Without detracting at-all from the credit due Helmholtz for his splendid researches, it may now be safely said that Koenig's experiments have shown that differential and summation tones are due exclusively to the beats which the ear perceives when impressed simultaneously by systems of waves differing in length. The effect is physiological, and such combination tones are not at all re-enforced by resonators like the separate primaries that enter into combination. It is not necessary that beating tones shall be nearly in unison, as is stated in so many of the text-books.

The subject of musical quality was long an unsolved enigma for physicists. The principle underlying its explanation was foreshadowed early in the present century by the French mathematician Fourier, and soon afterward applied to acoustics by Ohm, whose name is now so familiar in connection with electricity. But to Helmholtz is due the full experimental proof that the