54 8 THE POPULAR SCIENCE MONTHLY. 



soon accorded in acknowledgment of his merit. Among these 

 may be mentioned a gold medal, in I860, from the Societe d'En- 

 couragement at Paris ; a gold medal, in 1867, from the Interna- 

 tional Exhibition at Paris ; in 1868 the honorary degree of Doctor 

 of Philosophy, from the university of his native city, Koenigs- 

 berg ; 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 Exhi- 

 bition 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 Experiences 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 manomet- 

 ric flames. Both these methods are applied in an exhaustive in- 

 vestigation 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 phenom- 

 ena seemed for a time to confirm the conclusions of the great Ger- 

 man 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 sum- 

 mation 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 combi- 

 nation tones are not at all re-enforced by resonators like the sepa- 

 rate 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 mathe- 

 matician 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 



