Koenig's Tuning-Forks and the French “Diapason Normal”

Abstract

HAVING had occasion to measure a series of Koenig's tuning-forks, kindly lent me for that purpose by Professors Tyndall and Guthrie, by means of Appunn's tonometer, now in the South Kensington Museum, I was much struck, and for a time puzzled, by finding that though the forks were perfectly consistent with each other, they did not answer to their names, that is, the numbers of single vibrations marked on them, did not answer at all to the double vibrations measured by Appunn's tonometer. The workmanship of Koenig's forks is so good and the intervals between them so exact, that one might be at first inclined to suspect the accuracy of the absolute numbers of the reeds on Appunn's instrument. But there can be no doubt of the accuracy of the differences of the number of vibrations between any reed and any other, for these admit of ready control by counting, and I have counted them all. Hence such a thing as this is quite certain. The difference of the vibrations of C 256 and G 384 is 128 vibrations, as on Appum's instrument; but the difference in the vibrations of Koenig's corresponding forks is 1292 vibrations. Now, I have no doubt about the perfection of Koenig's fifth C to G. If then his C make x vibrations, his G makes x+1292 vibrations. Putting this = 3/2a we obtain x = 2584 as the number of the vibrations of his C, and this is the precise number furnished by Appunn's tonometer, according to a very careful measurement made by Mr. A. J. Hipkins, of Messrs. Broadwoods, who has had great experience in counting beats, and myself. The discrepancy, therefore, becomes an excellent proof of the perfection of Appunn's instrument. But how could Koenig have hit on this strange number 2584, in lieu of 256? It was some litttle time before the solution presented itself to my mind, but I believe that this, which is decidedly sufficient, will prove substantially correct.