Chapter 14

[99]Wiener Akad., 6 November, 1873.

[100]Wiener Gesellschaft der Aerzte, 14 November, 1874.

[101]I have made a contribution to this last question in myAnalysis of the Sensations, (1886), English translation, 1897.

[102]In myGrundlinien der Lehre von den Bewegungsempfindungen, 1875, the matter occupying lines 4 to 13 of page 20 from below, which rests on an error, is, as I have also elsewhere remarked, to be stricken out. For another experiment related to that of Foucault, compare myMechanics, p. 303.

[103]Anzeiger der Wiener Akad., 30 December, 1875.

[104]The experiment was specially interesting for me as I had already attempted in 1874, although with very little confidence and without success, to excite electromagnetically my own labyrinth through which I had caused a current to pass.

[105]Perhaps the discussion concerning the peculiarity of cats always falling on their feet, which occupied the Parisian Academy, and, incidentally, Parisian society a few years ago, will be remembered here. I believe that the questions which arose are disposed of by the considerations advanced in myBewegungsempfindungen(1875). I also partly gave, as early as 1866, the apparatus conceived by the Parisian scientists to illustrate the phenomena in question. One difficulty was left untouched in the Parisian debate. The otolith apparatus of the cat can render it no service infreedescent. The cat, however, while at rest, doubtless knows its position in space and is instinctively conscious of the amount of movement which will put it on its feet.

[106]See the Appendix to the English edition of myAnalysis of the Sensations, Chicago, 1897.

[107]Compare myAnalysis of Sensations, p. 123 ff.

[108]E. H. Weber,De aure et auditu hominis et animalium, Lipsiae, 1820.

[109]Störensen,Journ. Anat. Phys., London, Vol. 29 (1895).

[110]A lecture delivered on Nov. 10, 1897.

[111]Christiansen,Wiedemann's Annalen, XXIII. S. 298, XXIV., p. 439 (1884-1885).

[112]The German phrase isSchlierenmethode, by which term the method is known even by American physicists. It is also called in English the "shadow-method." But a term is necessary which will cover all the derivatives, and so we have employed alternatively the wordsstriateanddifferential. The etymology ofschlieren, it would seem, is uncertain. Its present use is derived from its technological signification in glass-manufacturing, where bydie Schlierenare meant the wavy streaks and imperfections in glass. Hence its application to the method for detecting small opticaldifferencesand faults generally. Professor Crew of Evanston suggests to the translator thatschlierenmay be related to ourslur(L. G.,slüren, to trail, to draggle), a conjecture which is doubtless correct and agrees both with the meaning ofschlierenas given in the large German dictionaries and with the intransitive use of our own verbslur, the faults in question being conceived as "trailings," "streakings," etc.—Trans.

[113]An address delivered before the Congress of Delegates of the German Realschulmännerverein, at Dortmund, April 16, 1886. The full title of the address reads: "On the Relative Educational Value of the Classics and the Mathematico-Physical Sciences in Colleges and High Schools."Although substantially contained in an address which I was to have made at the meeting of Natural Scientists at Salzburg in 1881 (deferred on account of the Paris Exposition), and in the Introduction to a course of lectures on "Physical Instruction in Preparatory Schools," which I delivered in 1883, the invitation of the German Realschulmännerverein afforded me the first opportunity of putting my views upon this subject before a large circle of readers. Owing to the place and circumstances of delivery, my remarks apply of course, primarily, only to German schools, but, with slight modifications, made in this translation, are not without force for the institutions of other countries. In giving here expression to a strong personal conviction formed long ago, it is a matter of deep satisfaction to me to find that they agree in many points with the views recently advanced in independent form by Paulsen (Geschichte des gelehrten Unterrichts, Leipsic, 1885) and Frary (La question du latin, Paris, Cerf, 1885). It is not my desire nor effort here to say much that is new, but merely to contribute my mite towards bringing about the inevitable revolution now preparing in the world of elementary instruction. In the opinion of experienced educationists the first result of that revolution will be to make Greek and mathematics alternately optional subjects in the higher classes of the German Gymnasium and in the corresponding institutions of other countries, as has been done in the splendid system of instruction in Denmark. The gap between the German classical Gymnasium and the German Realgymnasium, or between classical and scientific schools generally, can thus be bridged over, and the remaining inevitable transformations will then be accomplished in relative peace and quiet. (Prague, May, 1886.)

Although substantially contained in an address which I was to have made at the meeting of Natural Scientists at Salzburg in 1881 (deferred on account of the Paris Exposition), and in the Introduction to a course of lectures on "Physical Instruction in Preparatory Schools," which I delivered in 1883, the invitation of the German Realschulmännerverein afforded me the first opportunity of putting my views upon this subject before a large circle of readers. Owing to the place and circumstances of delivery, my remarks apply of course, primarily, only to German schools, but, with slight modifications, made in this translation, are not without force for the institutions of other countries. In giving here expression to a strong personal conviction formed long ago, it is a matter of deep satisfaction to me to find that they agree in many points with the views recently advanced in independent form by Paulsen (Geschichte des gelehrten Unterrichts, Leipsic, 1885) and Frary (La question du latin, Paris, Cerf, 1885). It is not my desire nor effort here to say much that is new, but merely to contribute my mite towards bringing about the inevitable revolution now preparing in the world of elementary instruction. In the opinion of experienced educationists the first result of that revolution will be to make Greek and mathematics alternately optional subjects in the higher classes of the German Gymnasium and in the corresponding institutions of other countries, as has been done in the splendid system of instruction in Denmark. The gap between the German classical Gymnasium and the German Realgymnasium, or between classical and scientific schools generally, can thus be bridged over, and the remaining inevitable transformations will then be accomplished in relative peace and quiet. (Prague, May, 1886.)

[114]Maupertuis,Œuvres, Dresden, 1752, p. 339.

[115]F. Paulsen,Geschichte des gelehrten Unterrichts, Leipsic, 1885.

[116]There is a peculiar irony of fate in the fact that while Leibnitz was casting about for a new vehicle of universal linguistic intercourse, the Latin language which still subserved this purpose the best of all, was dropping more and more out of use, and that Leibnitz himself contributed not the least to this result.

[117]As a rule, the human brain is too much, and wrongly, burdened with things which might be more conveniently and accurately preserved in books where they could be found at a moment's notice. In a recent letter to me from Düsseldorf, Judge Hartwich writes:"A host of words exist which are out and out Latin or Greek, yet are employed with perfect correctness by people of good education who never had the good luck to be taught the ancient languages. For example, words like 'dynasty.' ... The child learns such words as parts of the common stock of speech, or even as parts of his mother-tongue, just as he does the words 'father,' 'mother,' 'bread,' 'milk.' Does the ordinary mortal know the etymology of these Saxon words? Did it not require the almost incredible industry of the Grimms and other Teutonic philologists to throw the merest glimmerings of light upon the origin and growth of our own mother-tongue? Besides, do not thousands of people of so-called classical education use every moment hosts of words of foreign origin whose derivation they do not know? Very few of them think it worth while to look up such words in the dictionaries, although they love to maintain that people should study the ancient languages for the sake of etymology alone."

"A host of words exist which are out and out Latin or Greek, yet are employed with perfect correctness by people of good education who never had the good luck to be taught the ancient languages. For example, words like 'dynasty.' ... The child learns such words as parts of the common stock of speech, or even as parts of his mother-tongue, just as he does the words 'father,' 'mother,' 'bread,' 'milk.' Does the ordinary mortal know the etymology of these Saxon words? Did it not require the almost incredible industry of the Grimms and other Teutonic philologists to throw the merest glimmerings of light upon the origin and growth of our own mother-tongue? Besides, do not thousands of people of so-called classical education use every moment hosts of words of foreign origin whose derivation they do not know? Very few of them think it worth while to look up such words in the dictionaries, although they love to maintain that people should study the ancient languages for the sake of etymology alone."

[118]Standing remote from the legal profession I should not have ventured to declare that the study of Greek was not necessary for the jurists; yet this view was taken in the debate that followed this lecture by professional jurists of high standing. According to this opinion, the preparatory education obtained in the German Realgymnasium would also be sufficient for the future jurists and insufficient only for theologians and philologists. [In England and America not only is Greek not necessary, but the law-Latin is so peculiar that even persons ofgoodclassical education cannot understand it.—Tr.]

[119]In emphasising here the weak sides of the writings of Plato and Aristotle, forced on my attention while reading them in German translations, I, of course, have no intention of underrating the great merits and the high historical importance of these two men. Their importance must not be measured by the fact that our speculative philosophy still moves to a great extent in their paths of thought. The more probable conclusion is that this branch has made very little progress in the last two thousand years. Natural science also was implicated for centuries in the meshes of the Aristotelian thought, and owes its rise mainly to having thrown off those fetters.

[120]I would not for a moment contend that we derive exactly the same profit from reading a Greek author in a translation as from reading him in the original; but the difference, the excess of gain in the second case, appears to me, and probably will to most men who are not professional philologists, to be too dearly bought with the expenditure of eight years of valuable time.

[121]"The temptation," Judge Hartwich writes, "to regard the 'taste' of the ancients as so lofty and unsurpassable appears to me to have its chief origin in the fact that the ancients were unexcelled in the representation of the nude. First, by their unremitting care of the human body they produced splendid models; and secondly, in their gymnasiums and in their athletic games they had these models constantly before their eyes. No wonder, then, that their statues still excite our admiration! For the form, the ideal of the human body has not changed in the course of the centuries. But with intellectual matters it is totally different; they change from century to century, nay, from decennium to decennium. It is very natural now, that people should unconsciously apply what is thus so easily seen, namely, the works of sculpture, as a universal criterion of the highly developed taste of the ancients—a fallacy against which people cannot, in my judgment, be too strongly warned."

[122]English: "In the beginning God created the heaven and the earth. And the earth was without form and void; and darkness was upon the face of the deep. And the spirit of God moved upon the face of the waters."—Dutch: "In het begin schiep God den hemel en de aarde. De aarde nu was woest en ledig, en duisternis was op den afgrond; en de Geest Gods zwefde op de wateren."—Danish: "I Begyndelsen skabte Gud Himmelen og Jorden. Og Jorden var ode og tom, og der var morkt ovenover Afgrunden, og Guds Aand svoevede ovenover Vandene."—Swedish: "I begynnelsen skapade Gud Himmel och Jord. Och Jorden war öde och tom, och mörker war pä djupet, och Gods Ande swäfde öfwer wattnet."—German: "Am Anfang schuf Gott Himmel und Erde. Und die Erde war wüst und leer, und es war finster auf der Tiefe; und der Geist Gottes schwebte auf dem Wasser."

[123]Compare Herzen's excellent remarks,De l'enseignement secondaire dans la Suisse romande, Lausanne, 1886.

[124]Geschichte der Mathematik, Leipsic, 1874.

[125]Geometrische Analyse, Ulm, 1886.

[126]In his text-books of elementary mathematics

[127]Abhandlungen aus dem Gebiete der Mathematik, Würzburg, 1883.

[128]My idea here is an appropriate selection of readings from Galileo, Huygens, Newton, etc. The choice is so easily made that there can be no question of difficulties. The contents would be discussed with the students, and the original experiments performed with them. Those scholars alone should receive this instruction in the upper classes who did not look forward to systematical instruction in the physical sciences. I do not make this proposition of reform here for the first time. I have no doubt, moreover, that such radical changes will only be slowly introduced.

[129]Die Mathematik als Lehrgegenstand des Gymnasiums, Berlin, 1883.

[130]Wrong as it is to burden future physicians and scientists with Greek for the sake of the theologians and philologists, it would be just as wrong to compel theologians and philologists, on account of the physicians, to study such subjects as analytical geometry. Moreover, I cannot believe that ignorance of analytical geometry would be a serious hindrance to a physician that was otherwise well versed in quantitative thought. No special advantage generally is observable in the graduates of the Austrian gymnasiums, all of whom have studied analytical geometry. [Refers to an assertion of Dubois-Reymond.]

[131]Compare M. Cantor,Geschichte der Mathematik, Leipsic, 1880, Vol. I. p. 193.

[132]Compare Paulsen,l. c., pp. 607, 688.

[133]It is to be hoped that the Americans will jealously guard their schools and universities against the influence of the State.

[134]This article, which appeared in the Proceedings of the German Mathematical Society of Prague for the year 1892, is printed as a supplement to the article on "The Causes of Harmony," at page 32.

[135]The present exposition is taken from the volumes for 1700 (published in 1703) and for 1701 (published in 1704), and partly also from theHistoire de l'Académieand partly from theMémoires. Sauveur's later works enter less into consideration here.

[136]Euler,Tentamen novae theoriae musicae, Petropoli, 1739.

[137]In attempting to perform his experiment of beats before the Academy, Sauveur was not quite successful.Histoire de l'Académie, Année 1700, p. 136.

[138]Histoire de l'Académie, Année 1701, p. 134.

[139]Ibid., p. 298.

[140]Histoire de l'Académie, Année 1702, p. 91.

[141]From theHistoire de l'Académie, Année 1700, p. 139.

[142]Because all octaves in use in music offer too great differences of rates of vibration.

[143]"Les battemens ne plaisent pas à l'Oreille, à cause de l'inégalité du son, et l'on peut croire avec beaucoup d'apparence que ce qui rend les Octaves si agréables, c'est qu'on n'y entend jamais de battemens."En suivant cette idée, on trouve que les accords dont on ne peut entendre les battemens, sont justement ceux que les Musiciens traitent de Consonances, et que ceux dont les battemens se font sentir, sont les Dissonances, et que quand un accord est Dissonance dans une certaine octave et Consonance dans une autre, c'est qu'il bat dans l'une, et qu'il ne bat pas dans l'autre. Aussi est il traité de Consonance imparfaite. Il est fort aisé par les principes de Mr. Sauveur qu'on a établis ici, de voir quels accords battent, et dans quelles Octaves au-dessus on au-dessous du son fixe. Si cette hypothèse est vraye, elle découvrira la véritable source des Règles de la composition, inconnue jusqu'à présent à la Philosophie, qui s'en remettait presque entièrement au jugement de l'Oreille. Ces sortes de jugemens naturels, quelque bisarres qu'ils paroissent quelquefois, ne le sont point, ils ont des causes très réelles, dont la connaissance appartient à la Philosophie, pourvue qu'elle s'en puisse mettre en possession."

"En suivant cette idée, on trouve que les accords dont on ne peut entendre les battemens, sont justement ceux que les Musiciens traitent de Consonances, et que ceux dont les battemens se font sentir, sont les Dissonances, et que quand un accord est Dissonance dans une certaine octave et Consonance dans une autre, c'est qu'il bat dans l'une, et qu'il ne bat pas dans l'autre. Aussi est il traité de Consonance imparfaite. Il est fort aisé par les principes de Mr. Sauveur qu'on a établis ici, de voir quels accords battent, et dans quelles Octaves au-dessus on au-dessous du son fixe. Si cette hypothèse est vraye, elle découvrira la véritable source des Règles de la composition, inconnue jusqu'à présent à la Philosophie, qui s'en remettait presque entièrement au jugement de l'Oreille. Ces sortes de jugemens naturels, quelque bisarres qu'ils paroissent quelquefois, ne le sont point, ils ont des causes très réelles, dont la connaissance appartient à la Philosophie, pourvue qu'elle s'en puisse mettre en possession."

[144]Harmonics or the Philosophy of Musical Sounds, Cambridge, 1749. I saw this book only hastily in 1864 and drew attention to it in a work published in 1866. I did not come into its actual possession until three years ago and then only did I learn its exact contents.

[145]Harmonics, pp. 118 and 243.

[146]"Short cycle" is the period in which the same phases of the two co-operant tones are repeated.

[147]This article, designed to illustrate historically that on Symmetry, at page 89, first appeared in Fichte'sZeitschrift für Philosophie, for 1865.

[148]Comp. Cornelius,Ueber das Sehen; Wundt,Theorie der Sinneswahrnehmung.

[149]Comp. Mach,Ueber das Sehen von Lagen and Winkeln.Sitzungsb. der Wiener Akademie, 1861.

[150]Comp. Mach,Zur Theorie des Gehörorgans.Sitsungsber, der Wiener Akad., 1863.—Ueber einige Erscheinungen der physiolog. Akustik.Ibid., 1864.

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