Augusts, 1878J 



NATURE 



381 



Uranometria Nova 6. This discrepancy may very easily occur 

 in the hurry of such a sensational observation, as on these occa- 

 sions the time at the disposal of the observer is so limited. 

 Royal Observatory, Greenwich, G. B. Airy 



August 3 



Floating Magnets 



I HAVE no intention of discussing the beautiful experiments 

 of Prof. A. M. Meyer on floating magnets ; but as a privately- 

 expressed opinion of mine has appeared in Nature, vol. xviii. 

 p. 260, I feel bound to defend it. The mutual repulsion of the 

 vertical floating magnets varies nearly inversely as the fourth 

 power of the distance at great distances, and nearly inversely 

 as the square at small distances. The horizontal attraction of 

 the magnet, held vertically over the water, varies nearly in- 

 versely as the fourth power at very great distances. At a certain 

 moderate distance it reaches a maximum, and close to the centre 

 it varies directly as the distance. It is easy to see that varia- 

 tions of the magnetisation of the lengths of the magnets, and of 

 the distance of the large magnet from the surface of the water, 

 may render configurations stable which would, under different 

 conditions, be forms of unstable equilibrium. Prof. Meyer 



thinks that the configuration . . can never be stable. It is 



easy to see that it is a form of equilibrium, and in fact that any 

 given size of hexagon will be brought into equilibrium by 

 placing the large magnet at a suitable distance. It may, there- 

 fore, be in equilibrium when the floating magnets are on the 

 circle of maximum attraction of the fixed magnet. Eut, in this 

 case, the equilibrium is stable ; for work would be expended in 

 altering in any way the position of any one of the floating mag- 

 nets. If this one is carried away from the others they repel it 

 less, and it will be brought back ; if it is carried nearer to the 

 others they repel it more, and again it will be brought back. 



The nature of equilibrium where there are several degrees of 

 freedom may be illustrated by considering a tract of country 

 upon which water can run. The hollows are positions of stable 

 equilibrium ; the summits and passes (saddles) are positions of 

 unstable equilibrium. Then, if any one speaks of the former as 

 more or less stable (as Prof. Meyer does of stable configurations), 

 he may be understood as. having reference to the curvature of 

 the hollow, or to its level, or to some vague and mixed charac- 

 ters. It is very easy to understand why the form . • . should 



be difficult to produce or maintain. It is because the floating 

 magnets are in this case at much greater distances from the 

 centre than when they assume the form * Hence, the poten- 

 tial energy of the former configuration is much greater than that 

 of the latter. The reverse is the case with ' • ' and • ' , and 



still more so with . . and • . • , and so with greater num- 



bers of magnets. C. S. Pierce 



Mons. A. Cavaille-Coll on Musical Pitch, the French 

 Diapason Normal, Scheibler's Tuning-Forks, &c. 



In the course of my researches on musical pitch, with the 

 view of discovering the source of the discrepancy between 

 Appunn's and Lissajous's measurement of the French diapason 

 normal, I have had the good fortune to enter into correspon- 

 dence with M. Aristide Cavaille-Coll, the celebrated Parisian 

 organ-builder, and in his long and obliging answers to my in- 

 quiries he has communicated some facts which I have thou<^ht it 

 important, with his permission, to lay before the readers of 

 Nature, as far as possible in his own language. 



Scheibler, and the Persistency of the Pitch of Tuningforks. 



M. Cavaille-Coll had the advantage of personally knowing 

 Heinrich Scheibler, silk manufacturer, of Crefeld, near Diissef 

 dorf, who died November 20, 1837. Scheibler's experiments 

 on tuning, ^ith which I had long been acquainted, are the most 

 important hitherto made ; but I had feared that his wonderfully 

 accurate tuning-fork tonometer was irrecoverably lost. I find 

 that M. Cavaille-Coll is fortunate enough to possess one, and 



Herr Amels, of Crefeld, another, that is, a series of fifty-six 

 forks, proceeding by degrees of four beats in a second, from 

 A 220 to A 440 double vibrations in a second, which last was 

 adopted by the Stuttgart Conference in 1836 as the best normal 

 pitch. This was chosen by Scheibler as his standard, because it 

 was the mean of the Viennese grand pianos in his day. Of him 

 M. Cavaille-Coll says :— 



"M. Scheiblei n'etait pas un savant, mais, en s'appuyant sur 

 les experiences faites par Sauveur en 1701 pour la determination 

 d'un son fixe, il etait arrive par ses patientes recherches a creer, 

 en 1834, un tonometre differentiel de la plus rigoureuse exacti- 

 tude et qui n'avait pas ete fait avant lui." 



Of the exactness with which Scheibler worked M. Cavaille- 

 Coll gives the following remarkable proof, which is at the same 

 time a proof that tuning-forks will preserve their pitch for at 

 least twenty-eight years ; so that there is no reason to suppose 

 that, when properly protected, they vdll not form a lasting 

 record. This was a point on which I dwelt much in my letter 

 to M. Cavaille-Coll, because it has been often thought that they 

 might vary considerably. See Zantedeschi {Sitzb. Vienna Acad, 

 vol. XXV., year 1857, p. 172), whose conclusions I believe to be 

 eiToneously based. M. Cavaille-Coll says, in his first letter 

 (January 24, 1878) : — 



"En 1862, j'ai eu I'avantage d'assister aux experiences faites 

 par M. Leon Foucault pour la determination experimentale de 

 la Vitesse de la lumiere. Ce savant experimentateur, que la 

 mort a enleve a la science en 1868, "se servait, pour mouvoir 

 son miroir tournant, d'un petit tambour mis en mouvement 

 par une soufflerie et un regulateur de pression que je lui avais 

 etablis ; laquelle turbine devait faire 400 tours a la seconde. Or 

 avec cette vitesse, la turbine faisait entendre un son d'axe dont 

 le nombre de vibrations correspondait au nombre de tours." In 

 a subsec^uent letter (February 8, 1878) M. Cavaille-CoU adds : — 

 " M. Leon Foucault, bien qu'il fit construire ses instruments par 

 les premiers constructeurs, etait toujours oblige de les verifier et 

 de les rectifier lui-meme pour arriver a la regularite de marche 

 qu'il avait en vue d'obtenir." 



" Pour mesurer la vitesse de la turbine, M. Leon Foucault. 

 avait imagine un moyen nouveau que je vais essayer de decrire.. 

 D'aboi-d une pendule de precision, construite par I'habile 'con- 

 structeur Froment, mettait en evidence une roue dentee de 400 

 dents, laquelle faisait un tour entier par seconde. Ensuite, la. 

 turbine etait disposee de maniere a reflechir un rayon lumineux 

 du miroir tournant sur les dents de la roue. Or la coincidence 

 des rayons lumineux avec le passage des dents de la roue de la 

 pendule permettait de reconnaitre, a I'immobilite apparente des 

 dents de cette roue, que la vitesse de la turbine etait alors 

 exactement de 400 tours par seconde." This description is 

 necessary to understand the extreme delicacy of the test of 

 Scheibler's work, which follows. " Un jour que j'assistais a une 

 de ses observations, M. Leon Foucault me dit : ' Si nous avions 

 un diapason exactement accorde de 400 vib. par seconde il devrait 

 se trouver d'accord avec le son d'axe de la turbine ? Sans rien 

 dire a M. L. Foucault, je cherchai dans mon tonometre de 

 Scheibler un diapason de 400 vib., et I'ayant compare avec le 

 son d'axe de la turbine, je le trouvai si exact que je fus eraerveille 

 de constater que par des moyens differents et a plus d'un quart 

 de siecle de distance ces deux savants experimentateurs avaient 

 atteint avec la meme perfection la determination d'un son fixe 

 donnant exactement 400 vib. par seconde. Cette circonstance 

 est venue confirmer dans mon opinion que le tonometre de H. 

 Scheibler pouvait etre regarde comme un instmment de la plus 

 haute precision." M. Cavaille-CoU concludes: — " Dans mon 

 opinion le diapason conserve le meme ton a la meme temperature. 

 II n'y a que I'alteration du metal lui-meme qui puisse faire changer 

 le ton ; mais si I'on prend les soins necessaires pour preserver les 

 diapasons des influences climateriques, comme le faisait H, 

 Scheibler, on peut etre a peu pres certain qu'ils conservent le 

 meme ton," * 



Improvements in the Siren, Bellows of Precision, Double-Actioii- 

 Counter. — M. Cavaille-CoU was also personally acquainted with 

 M, le Baron Cagniard de Latour, and was "initieases travaux.'* 

 He calls him " un des plus savants acousticiens fran9ais du 

 siecle present," and says he is "sans contredit le veritable 

 inventeur de la syrene ; " adding, "la date de la creation de ce 

 merveilleux instrument, qui se trouve aujourd'hui dans tous les 

 cabinets de physique d'Europe, remonte a I'annee 1819 ; " and 

 he complains that Helmholtz should have mentioned Seebeck's 

 first, even on the score of simplicity of constniction, as it was 

 invented so long afterwards. 



