May 31, 1877] 



NA TURE 



85 



KOENIGS TUNING-FORKS AND THE 

 FRENCH " DIAPASON NORMAL " 



T T AVING had occasion to measure a series of Koenig's 

 ■'■ -'• tuning-forks, kindly lent me for that purpose by 

 Professors Tyndall and Guthrif, 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 th° reeds on Appunn's instrument. 

 But there can be no doubt of the accuracy of the differ- 

 ences 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 Appunn's instrument ; 

 but the difference in the vibrations of Koenig's corre- 

 sponding forks is 129-2 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 .!■+ I29'2 vibrations. 

 Putting this = f.r, we obtain x = 258-4 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, there- 

 fore, becomes an excellent proof of the perfection of 

 Appunn's instrument. But how could Koenig have hit 

 on this strange number 258-4, 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 suffi- 

 cient, will prove substantially correct. 



The French normal A was settled at 435, and since 

 Lissajous superintended the publication of the fork of the 

 French Commission in 1859, the whole world has ac- 

 cepted that fork as having exactly 435 vibrations. Now 

 the French Commission gave to Messrs Broadwoods, in 

 return for their courtesy in sending them their forks, an 

 authorised copy of this fork, stamped with their stamp (a 

 lyre between D and N, at the end of each pron") and 

 made by Secretan. This fork I assume to be an authentic 

 representative of the French diapason normal, made at 

 the time. I have examined many others made by Secre- 

 tan, and also officially stamped, and one by Koenig, and 

 they mostly agree within two- or three-tenths of a vibra- 

 tion in a second. Two of Secretan's, however — one 

 bought in Paris by the Society of Arts, and one sent to 

 that society officially in 1869 through the Foreign Office, 

 as representing the French pitch used in the Grand 

 Duchy of Baden, differ as much as six-tenths of a vibra- 

 tion, the extreme difference observed in authorised forks. 

 Other copies differ as much as two vibrations. But I 

 take as my standard the copy given to Messrs. Broad- 

 woods (which through the kindness of Mr. Hipkins I 

 have carefully measured), and the one made by Koenig 

 (which Dr. W. H. Stone was so obhging as to allow me 

 to measure). These differ only by o/ir-tenth of a vibra- 

 tion, and that tenth may be my own fault in counting. 

 All these forks show that the real French diapason 

 normal is A 439, that is, four vibrations sharper than 

 was supposed. This is really a result of prime importance 

 as brought out by Appunn's instrument, and it fully 

 accounts for Koenig's differences as follows : — 



Koenig having to make a C 256, observed (I suppose) 

 that a major sixth above it would be A 4265 = j X 256, 

 and that this would beat 8J times in a second with A435, 

 which he assumed to be given by his diapason normal. 



Constructing such a fork by beats, which is easy enough, 

 he necessarily obtained one exactly four vibrations too 

 sharp, that is, A 430H-. From this, by the Lissajous figures 

 most probably (certainly /loi by interposing new forks and 

 counting the beats, for that would have shown him his 

 error), he obtained first the correct major sixth below it, 

 C 258-4 = f X 4305, and then got his other forks by true 

 intervals obtained also by Lissajous' figures. This makes 

 all Koenig's forks harmonics of C 64-6, instead of C 64, as 

 he intended and as he marks his forks. 



Since Koenig's forks are extensively used by physicists, 

 and also for the purpose of obtaining other pitches from 

 them either for musical or for counting purposes, I think 

 it will be convenient to add a little table of the harmonics 

 of 64-6, with the marks on the forks observed (all of which 

 had Koenig's monogram) and the pitches as actually 

 measured by Appunn's tonometer. I am quite willing to 

 allow the small differences to be set down to my bad 

 counting and not to defective workmanship of either 

 Koenig or Appunn. 



The last four forks were difficult to measure. Those 

 left blank were not found either at the Royal Institution 

 or the School of Mines. The nth, 13th, 17th, and 19th 

 harmonics would not be easy to tune by Lissajous' figures. 

 Appunn's instrument gives them with perfect ease. I may 

 observe here with regard to the question of forks and 

 reeds, that though forks may be the most permanent and 

 portable records of pitch, reeds have a great advantage in 

 che number of their upper partial tones, which allow of 

 an extraordinai-y variety of verifications without any 

 assistance beyond the instrument itself. 1 have found 

 this reed tonometer easily checked ahd invaluable in 

 measurements. But the above table would allow any 

 tuning-fork maker to tune exactly to C 256, or from 

 C 254 to C 265, by means of beats from Koenig's forks. 



In trying forks to- day at King's College, Prof. Adams 

 drew my attention to the fact that Koenig's organ-pipes 

 are much flatter than his forks. On account of the diffi- 

 culty of getting a steady blast on the organ pipes, it was 

 not possible to measure them satisfactorily by Appunn's 

 tonometer (a copy of which is in the physical laboratory 

 there, and should be in all physical laboratories, as it is 

 the best instrument for illustrating the nature of sound, 

 partials, beats, and chords that I have yet seen), but they 

 seemed to give very nearly C 250, about eight vibrations 

 flatter than the forks. I cannot account for this, as this 

 would be about Koenig's 248. Alexander J. Ellis 



Kensington, May 18 



