382 



NATURE 



\_August 8, 1878 



The difficulty of using the siren for the exact determination of 

 pitch is ordinarily very great, so that observations made by it 

 without proper precautions are, as a general rule, defective. 

 ITie causes of error (besides imperfect workmanship) are — 

 I. The difficulty of estimating with precision at what time the 

 continually rising pitch of the siren note reaches the height of the 

 continuous tone with which it is compared, precise equality of 

 pitch (as in the example just given) being always extremely 

 difficult to attain, and also to verify, except under the most 

 favourable circumstances, and with the siren the circumstances 

 are most unfavourable ; 2. The difficulty of obtaining a blast 

 under constant pressure to make the tone of the siren continuous ; 

 and 3. The difficulty of comparing the counter of the rotations 

 of the siren's disk with the seconds counter. Now M. Cavaille- 

 CoU, as an experienced, ingenious, and scientific organ-builder, 

 turned his attention in the first place to the second difficulty, 

 which when overcome would obviate the first. It is clear that 

 if the tone of the siren could be indefinitely sustained at the 

 same precise pitch, it could be completely compared with another 

 tone either by unison or by beats. In 1863 (Comptcs Rendus, 

 vol. Ivi. pp.309-443) M. Cavaille-CoU invented a "soufflerie 

 de precision " for giving a constant blast, applicable not only to 

 the siren but to many other scientific instruments. The com- 

 plete bellows, such as he furnished for the physical laboratory of 

 the Sorbonne, is expensive (about 80/.), but he has arranged 

 "un petit modele de soufflerie de precision pour des experiences 

 d'acoustique, et que j'es'.ime a5oo fr.," 20/. (not including the 

 siren), inclosed in an oak case about 27i inches long, 

 172 inches wide, and 324 inches high, and therefore of 

 most convenient dimensions for an experiment. " Cette 

 soufflerie," he says in his letter of February 8, 1878, in answer 

 to my inquiries, for the small model is not described in the 

 Comptis Rendus, "est mise en jeu par une pedale en fer a la 

 portee de I'operateur. Au dessus de ce bati est un grand 

 regulateur de pression communiquant avec un sommier de 13 

 notes sur lequel on pent monter toute espece de tuyaux ; de 

 chaque cote du grand regulateur et communiquant avec lui, j'ai 

 dispose deux petits regulateurs angulaires a poids curseurs, avec 

 leurs sommiers sur lesquels on peut monter soit la syrene, soit 

 deux tuyaux pour I'etude des battements. Sur le sommier du 

 grand regulateur de 13 notes j'ai place une serie harmonique de 

 tuyaux a bouche du ton de 8 pieds a partir du 3eme (67 de 2 

 pieds), et compose de 13 tuyaux d'etain exactement accordes, 

 donnant les sons 4, S, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 et 16. 

 Eicn que les trois premiers tuyaux de la basse manquent, cette 

 terie des sons harmoniques naturels permet neanmoins de faire 

 de bonnes experiences sur le timbre, et sur les sons resultants^ 

 I have given the description of this instrument at length, because 

 it is evidently precisely what is wanted for acoustical experi- 

 ments. The ordinary laboratory blowing apparatus I have 

 found quite useless for experiments on pitch and beats. By 

 means of these constant action bellows it is possible to maintain 

 any tone on the siren for many minutes, and hence the two first 

 difficulties are overcome. The third difficulty (of counting), not 

 to mention insufficient accuracy of workmanship in the siren, still 

 remained. 



"En general," remarks M. Cavaille-CoU in his letter of 

 February 8, " I'execution de ces appareils [les syrenes de 

 commerce] laisse beaucoup a desirer. Quand j'ai voulu faire 

 des observations exactes, j'ai du faire retoucher I'appareil avec 

 beaucoup de soin par un de mes employes ; mais apres avoir 

 obtenu la regularite du mouvement de la syrene, j'ai rencontre 

 une nouvelle difficulte pour marquer exactement la duree de 

 I'observation au moyen d'une pendule a secondes. C'est alors 

 que j'eus I'idee de completer la syrene par un compteur a point- 

 age, que me permet d'embrayer du meme coup le compteur de la 

 syrene et le compteur a seconder, de maniere a bien preciser le 

 point de depart et le point d'arrivee de I'obsei-vation. Je con- 

 struisis a cet effet un petit appareil en bois que je conserve dans 

 mon cabinet comme souvenir historique de mes essais, et qui 

 fonctionnait fort regulieremeut. Plus tard j'ai compose le dessin 

 d'un appareil plus elegant, pouvant se fixer sur I'armature de la 

 syrene, etj'en ai confie I'execution a I'opticien quiavait etabli ma 

 syrene, esperant que cela pourrait lui donner I'idee d'en con- 

 struire de semblables pour le commerce ; mais ce petit travail 

 fut mal construit, et ce n'est que longtemps apres que j'ai pu 

 faire executer sous mes yeux, dans mes ateliers, I'instrument que 

 j'ai montre, et qui est encore unique en son genre." 



By means of this complete regeneration of the siren, M. 

 Cavaille-Coll say?, in his memoir in the Comptes Rendus, that he 



has been able to " faire des experiences qui ont dure plus de dix 

 minutes, avec une telle exactitude, qu'en repetant plusieurs expe- 

 riences les resultats n'ont jamais varie que de quelques vibrations 

 sur 50,000 environ." In his letter he says: — " J 'ai fait i cette 

 epoque (1858-9) avec mon appareil, plusieurs observations dont 

 la moyenne concordait avec les nombres constates au tonometre 

 de Scheibler." 



Pitch of the French Diapason Normal, and how Lissajous de- 

 termined it. — As regards its pitch, M. Cavaille-Coll has carefully 

 compared the French diapason normal with Scheibler's 440 

 double or 880 single vibrations, the accuracy of which, after the 

 striking proof already given of Scheibler's exactness, admits of 

 no question. He says, on January 24: — "J'ai trouve aloi's, 

 que notre diapason normal de 870 vib. simples, donnait exacte- 

 ment 871*75 vib. par seconde, d'ou il resulteque notre diapason, 

 au lieu de 435 vib. doubles, donnent 435*875 vib., soit pres 

 d'une vibration sonore en plus que le chiffre de 435 vib. assign^ 

 par le rapport de la commission." 



This is a most important piece of information. Copies of the 

 French normal are easily procured, but they almost all vary by 

 some vibrations in ten seconds, even when costing 20 to 35 francs. 

 I have given means of making forks of 440, 256, 512 vibrations, 

 according to Scheibler, and hence also of the exact pitch of the 

 French normal, to Messrs. Valentine and Carr, 76, Milton 

 Street, Sheffield, successors to, and long workers with, Mr. 

 Greaves, from whom physicists can be pretty sure of getting 

 any pitch they like, within a few tenths of a vibration, for 3^-. a 

 fork, small size, but sounding 20 to 30 seconds. I mention the 

 names of there workers because people do not generally know 

 where to go for such work, and it is not safe to give orders 

 secondhand through the music-sellers. For larger forks and 

 greater accuracy, and of course much greater cost, perhaps Mr. 

 Ladd, of Beak Street, would be the best person to consult, but 

 he uses Koenig's pitch. Messrs. Valentine and Carr can also 

 make large forks if required. Time must also be given. To 

 make a fork with perfect accuracy is often two or three weeks' 

 work, for after filing, the pitch rises, and the fork has to rest 

 three days at least before it can be tried again. This was 

 Scheibler's experience, fully confirmed by my own. 



Now, my observations on Appunn's instrument, just finished, 

 but not reduced, show that his numbers are in excess about one per 

 cent., a little more or less. His tonometer, when in perfect con- 

 dition, gave the pitch of Broadwood's copy of the French nor- 

 mal, presented by the French Coiftmission in 1859, as 439 

 exactly. As Koenig's forks showed perfect intervals when 

 measured by this tonometer, we may take it as almost, if not 

 quite, exactly correct that the accelercttion of the beats in that 

 instrument is uniform throughout. This would show that 

 Appunn's numbers should be reduced in the proportion of 

 435*875 to 439, in order to obtain Scheibler's pitch, which is 

 probably as accurate as we can hope any measurement to go. 

 But I have since found that Broadwood's copy was not quite 

 accurate, and that the best approximate rule is to throw out i in 

 123 vibrations. Thus the fork of the Liceo Musicale of Bologna, 

 sent officially to the Society of Arts in 1869, and measured 

 "graphically " at Bologna as 443*89, but measured by me with 

 Appunn's tonometer as 447*2, would be 443*6 by Scheibler's 

 pitch, and this agrees with actual measurement by Scheibler's 

 440. Again, by Appunn's tonometer, Koenig's Uts was 258*4, 

 which, corrected as above, gives 256*3. Now the measure- 

 ments of Koenig's Utj, by Prof. Alfred Mayer and Prof. M'^Leod, 

 with their own special instruments, give the pitch nearly as 

 256*3, and this agrees with actual measurement by one of 

 Scheibler's own forks given me by M. Cavaille-Coll. 



For some time I had vainly endeavoured to learn the method 

 employed by M. Lissajous to determine the pitch of the diapason 

 normal, which I regarded as of great importance in the history 

 of practical music. I am indebted to M. Cavaille-CoU for the 

 following information (on February 8) : — 



"M. Lissajous s'est servi de la syrene de M. Cagniard de 

 Latour, mise en jeu par ma soufflerie de precision, munie d'un 

 regulateur de pression, pour determiner le ton du diapason 

 normal. Quant au compteur a secondes dont j'ai arme ma 

 syrene, je ne pense pas que M. Lissajous en ait eu connaissance 

 lors de la determination du diapason normal, et c'est peut-etre a 

 cela qu'est due la petite erreur que j'ai constatee par mes ex- 

 periences a la syrene et par comparaison avec le tonometre de 

 Scheibler." " Je n'ai pas assiste," he had written, on January 

 24 ; "aux experiences de M. Lissajous pour la determmation du 

 ton normal, vu qu'a cette epoque nous n'etions pas d'accord sur 



